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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Nov 2010 14:16:44 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289916891m11pkt57cgeaemd.htm/, Retrieved Sun, 05 May 2024 07:29:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95816, Retrieved Sun, 05 May 2024 07:29:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [Mini tutorial mean Y] [2010-11-15 17:29:21] [49c7a512c56172bc46ae7e93e5b58c1c]
-    D      [Central Tendency] [W6] [2010-11-16 14:16:44] [476d588d86fe88306e0383abd6004235] [Current]
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Dataseries X:
68
70
90
95
75
69
39
80
100
80
81
55
100
75
70
100
61
83
90
60
44
90
100
82
80
88
100
83
75
55
75
80
70
100
60
95
95
90
90
80
76
65
78
70
60
65
100
65
90
90
90
80
91
100
90
80
100
88
61
90
58
90
88
90
80
85
60
95
100
61
80
90
75
85
95
78
90
80
100
30
70
67
35
100
96
74
70
80
100
100
74
59
35
80
91
75
82
100
90
50
90
60
100
80
65
100
72
98
93
45
88
82
90
100
75
100
100
80
71
71
60
100
80
85
100
61
73
80
60
100
83
70
91
45
70
95
80
78
100
100
100
82
90
87
75
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95816&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95816&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean80.4452054794521.3302565563128860.4734516042718
Geometric Mean78.534300089989
Harmonic Mean76.1760297217087
Quadratic Mean82.0245118726421
Winsorized Mean ( 1 / 48 )80.47945205479451.3217135489713560.890237614216
Winsorized Mean ( 2 / 48 )80.47945205479451.3217135489713560.890237614216
Winsorized Mean ( 3 / 48 )80.56164383561641.3029153242832961.8318338376534
Winsorized Mean ( 4 / 48 )80.69863013698631.2742265379460763.3314624470661
Winsorized Mean ( 5 / 48 )80.73287671232881.2674960194303063.6947773205756
Winsorized Mean ( 6 / 48 )80.73287671232881.2674960194303063.6947773205756
Winsorized Mean ( 7 / 48 )80.9726027397261.223218348286366.1963604888421
Winsorized Mean ( 8 / 48 )81.24657534246571.1781975314566068.958364937347
Winsorized Mean ( 9 / 48 )81.24657534246571.1781975314566068.958364937347
Winsorized Mean ( 10 / 48 )81.45205479452051.1479205158879670.9561800378784
Winsorized Mean ( 11 / 48 )81.5273972602741.1374666763552171.6745368941382
Winsorized Mean ( 12 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 13 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 14 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 15 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 16 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 17 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 18 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 19 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 20 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 21 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 22 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 23 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 24 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 25 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 26 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 27 / 48 )82.36986301369860.94701448680933586.9784614290514
Winsorized Mean ( 28 / 48 )82.17808219178080.8830897005013193.0574574079284
Winsorized Mean ( 29 / 48 )82.17808219178080.84016356526081797.8120042211897
Winsorized Mean ( 30 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 31 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 32 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 33 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 34 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 35 / 48 )81.90410958904110.768924600834731106.517738540459
Winsorized Mean ( 36 / 48 )81.41095890410960.721730405852391112.799680107644
Winsorized Mean ( 37 / 48 )81.41095890410960.721730405852391112.799680107644
Winsorized Mean ( 38 / 48 )81.67123287671230.693727180488566117.728172073630
Winsorized Mean ( 39 / 48 )81.40410958904110.669504344126517121.588620452115
Winsorized Mean ( 40 / 48 )81.67808219178080.64053996260542127.514420582835
Winsorized Mean ( 41 / 48 )81.9589041095890.611716550882357133.981831930768
Winsorized Mean ( 42 / 48 )82.24657534246570.583148786918094141.038748922267
Winsorized Mean ( 43 / 48 )82.24657534246570.583148786918094141.038748922267
Winsorized Mean ( 44 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 45 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 46 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 47 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 48 / 48 )82.54794520547950.554287807229553148.926142932985
Trimmed Mean ( 1 / 48 )80.65972222222221.2949067638420762.2899844795773
Trimmed Mean ( 2 / 48 )80.84507042253521.265491194242763.884340555143
Trimmed Mean ( 3 / 48 )81.03571428571431.2331249716524365.715735346048
Trimmed Mean ( 4 / 48 )81.20289855072461.2051829000284167.3780706221526
Trimmed Mean ( 5 / 48 )81.33823529411771.1835943092607968.7213808462102
Trimmed Mean ( 6 / 48 )81.47014925373131.1616458039822270.133382287824
Trimmed Mean ( 7 / 48 )81.60606060606061.1374819079357171.7427328177542
Trimmed Mean ( 8 / 48 )81.70769230769231.1199628451247372.955716935942
Trimmed Mean ( 9 / 48 )81.77343751.1088192696312073.7482110382141
Trimmed Mean ( 10 / 48 )81.84126984126981.0965117967597874.6378379905378
Trimmed Mean ( 11 / 48 )81.88709677419361.0875164659228075.2973397094356
Trimmed Mean ( 12 / 48 )81.92622950819671.0789940490145575.9283423138618
Trimmed Mean ( 13 / 48 )81.95833333333331.0709688167025276.5272826389849
Trimmed Mean ( 14 / 48 )81.99152542372881.0619992245727777.2048825710893
Trimmed Mean ( 15 / 48 )82.02586206896551.0519818668163677.9726957815373
Trimmed Mean ( 16 / 48 )82.0614035087721.0407983249378878.8446729232292
Trimmed Mean ( 17 / 48 )82.09821428571431.0283121941795279.8378301360318
Trimmed Mean ( 18 / 48 )82.13636363636361.0143653153320480.9731586785154
Trimmed Mean ( 19 / 48 )82.1759259259260.99877293213870782.2768852475405
Trimmed Mean ( 20 / 48 )82.20754716981130.98330328561752183.6034500974787
Trimmed Mean ( 21 / 48 )82.24038461538460.9659528058138785.1391332168577
Trimmed Mean ( 22 / 48 )82.27450980392160.94645594257816686.9290435007509
Trimmed Mean ( 23 / 48 )82.310.9244922166172489.0326587076915
Trimmed Mean ( 24 / 48 )82.30612244897960.90866369832620790.5793007914705
Trimmed Mean ( 25 / 48 )82.30208333333330.89075660128562592.3957040728602
Trimmed Mean ( 26 / 48 )82.29787234042550.87044954124366294.5464021071707
Trimmed Mean ( 27 / 48 )82.29347826086960.84734740305919297.1189360630175
Trimmed Mean ( 28 / 48 )82.28888888888890.8309320375622299.0320329088613
Trimmed Mean ( 29 / 48 )82.29545454545450.819236954612518100.453787005224
Trimmed Mean ( 30 / 48 )82.30232558139540.810341801427899101.564951279042
Trimmed Mean ( 31 / 48 )82.2976190476190.802280842456981102.579564028455
Trimmed Mean ( 32 / 48 )82.29268292682930.792825364174422103.796733360721
Trimmed Mean ( 33 / 48 )82.28750.781752686377366105.260271482174
Trimmed Mean ( 34 / 48 )82.28205128205130.768792193765834107.027688300271
Trimmed Mean ( 35 / 48 )82.27631578947370.753610882936868109.176124777867
Trimmed Mean ( 36 / 48 )82.29729729729730.741664709906984110.962940797896
Trimmed Mean ( 37 / 48 )82.34722222222220.732692774609437112.389837972836
Trimmed Mean ( 38 / 48 )82.40.721856360057086114.150133682390
Trimmed Mean ( 39 / 48 )82.44117647058820.712481952374103115.709845275212
Trimmed Mean ( 40 / 48 )82.50.703719720642704117.234173748397
Trimmed Mean ( 41 / 48 )82.5468750.696835850206443118.459569747373
Trimmed Mean ( 42 / 48 )82.58064516129030.69200632866248119.335101054500
Trimmed Mean ( 43 / 48 )82.60.689386856045382119.816615700840
Trimmed Mean ( 44 / 48 )82.62068965517240.685529097045402120.521054483703
Trimmed Mean ( 45 / 48 )82.6250.684030501712261120.791397157252
Trimmed Mean ( 46 / 48 )82.62962962962960.681335626842981121.275956186968
Trimmed Mean ( 47 / 48 )82.63461538461540.67715849293235122.031424322505
Trimmed Mean ( 48 / 48 )82.640.671130632984825123.135490973586
Median80.5
Midrange65
Midmean - Weighted Average at Xnp81.375
Midmean - Weighted Average at X(n+1)p81.375
Midmean - Empirical Distribution Function81.375
Midmean - Empirical Distribution Function - Averaging81.375
Midmean - Empirical Distribution Function - Interpolation81.375
Midmean - Closest Observation81.375
Midmean - True Basic - Statistics Graphics Toolkit81.375
Midmean - MS Excel (old versions)81.375
Number of observations146

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 80.445205479452 & 1.33025655631288 & 60.4734516042718 \tabularnewline
Geometric Mean & 78.534300089989 &  &  \tabularnewline
Harmonic Mean & 76.1760297217087 &  &  \tabularnewline
Quadratic Mean & 82.0245118726421 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 80.4794520547945 & 1.32171354897135 & 60.890237614216 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 80.4794520547945 & 1.32171354897135 & 60.890237614216 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 80.5616438356164 & 1.30291532428329 & 61.8318338376534 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 80.6986301369863 & 1.27422653794607 & 63.3314624470661 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 80.7328767123288 & 1.26749601943030 & 63.6947773205756 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 80.7328767123288 & 1.26749601943030 & 63.6947773205756 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 80.972602739726 & 1.2232183482863 & 66.1963604888421 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 81.2465753424657 & 1.17819753145660 & 68.958364937347 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 81.2465753424657 & 1.17819753145660 & 68.958364937347 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 81.4520547945205 & 1.14792051588796 & 70.9561800378784 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 81.527397260274 & 1.13746667635521 & 71.6745368941382 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 81.6095890410959 & 1.12641548122403 & 72.450699055036 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 81.7397260273973 & 1.10941582650519 & 73.6781683427831 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 81.7397260273973 & 1.10941582650519 & 73.6781683427831 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 81.7397260273973 & 1.10941582650519 & 73.6781683427831 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 81.7397260273973 & 1.10941582650519 & 73.6781683427831 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 82.3698630136986 & 1.03207939565944 & 79.8096186786767 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 82.3698630136986 & 1.03207939565944 & 79.8096186786767 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 82.3698630136986 & 1.03207939565944 & 79.8096186786767 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 82.3698630136986 & 1.03207939565944 & 79.8096186786767 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 82.3698630136986 & 0.947014486809335 & 86.9784614290514 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 82.1780821917808 & 0.88308970050131 & 93.0574574079284 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 82.1780821917808 & 0.840163565260817 & 97.8120042211897 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 82.3835616438356 & 0.818322319972051 & 100.673731649711 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 82.3835616438356 & 0.818322319972051 & 100.673731649711 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 82.3835616438356 & 0.818322319972051 & 100.673731649711 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 82.3835616438356 & 0.818322319972051 & 100.673731649711 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 82.3835616438356 & 0.818322319972051 & 100.673731649711 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 81.9041095890411 & 0.768924600834731 & 106.517738540459 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 81.4109589041096 & 0.721730405852391 & 112.799680107644 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 81.4109589041096 & 0.721730405852391 & 112.799680107644 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 81.6712328767123 & 0.693727180488566 & 117.728172073630 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 81.4041095890411 & 0.669504344126517 & 121.588620452115 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 81.6780821917808 & 0.64053996260542 & 127.514420582835 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 81.958904109589 & 0.611716550882357 & 133.981831930768 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 82.2465753424657 & 0.583148786918094 & 141.038748922267 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 82.2465753424657 & 0.583148786918094 & 141.038748922267 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 82.5479452054795 & 0.554287807229553 & 148.926142932985 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 82.5479452054795 & 0.554287807229553 & 148.926142932985 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 82.5479452054795 & 0.554287807229553 & 148.926142932985 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 82.5479452054795 & 0.554287807229553 & 148.926142932985 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 82.5479452054795 & 0.554287807229553 & 148.926142932985 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 80.6597222222222 & 1.29490676384207 & 62.2899844795773 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 80.8450704225352 & 1.2654911942427 & 63.884340555143 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 81.0357142857143 & 1.23312497165243 & 65.715735346048 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 81.2028985507246 & 1.20518290002841 & 67.3780706221526 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 81.3382352941177 & 1.18359430926079 & 68.7213808462102 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 81.4701492537313 & 1.16164580398222 & 70.133382287824 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 81.6060606060606 & 1.13748190793571 & 71.7427328177542 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 81.7076923076923 & 1.11996284512473 & 72.955716935942 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 81.7734375 & 1.10881926963120 & 73.7482110382141 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 81.8412698412698 & 1.09651179675978 & 74.6378379905378 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 81.8870967741936 & 1.08751646592280 & 75.2973397094356 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 81.9262295081967 & 1.07899404901455 & 75.9283423138618 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 81.9583333333333 & 1.07096881670252 & 76.5272826389849 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 81.9915254237288 & 1.06199922457277 & 77.2048825710893 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 82.0258620689655 & 1.05198186681636 & 77.9726957815373 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 82.061403508772 & 1.04079832493788 & 78.8446729232292 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 82.0982142857143 & 1.02831219417952 & 79.8378301360318 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 82.1363636363636 & 1.01436531533204 & 80.9731586785154 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 82.175925925926 & 0.998772932138707 & 82.2768852475405 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 82.2075471698113 & 0.983303285617521 & 83.6034500974787 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 82.2403846153846 & 0.96595280581387 & 85.1391332168577 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 82.2745098039216 & 0.946455942578166 & 86.9290435007509 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 82.31 & 0.92449221661724 & 89.0326587076915 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 82.3061224489796 & 0.908663698326207 & 90.5793007914705 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 82.3020833333333 & 0.890756601285625 & 92.3957040728602 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 82.2978723404255 & 0.870449541243662 & 94.5464021071707 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 82.2934782608696 & 0.847347403059192 & 97.1189360630175 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 82.2888888888889 & 0.83093203756222 & 99.0320329088613 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 82.2954545454545 & 0.819236954612518 & 100.453787005224 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 82.3023255813954 & 0.810341801427899 & 101.564951279042 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 82.297619047619 & 0.802280842456981 & 102.579564028455 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 82.2926829268293 & 0.792825364174422 & 103.796733360721 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 82.2875 & 0.781752686377366 & 105.260271482174 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 82.2820512820513 & 0.768792193765834 & 107.027688300271 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 82.2763157894737 & 0.753610882936868 & 109.176124777867 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 82.2972972972973 & 0.741664709906984 & 110.962940797896 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 82.3472222222222 & 0.732692774609437 & 112.389837972836 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 82.4 & 0.721856360057086 & 114.150133682390 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 82.4411764705882 & 0.712481952374103 & 115.709845275212 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 82.5 & 0.703719720642704 & 117.234173748397 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 82.546875 & 0.696835850206443 & 118.459569747373 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 82.5806451612903 & 0.69200632866248 & 119.335101054500 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 82.6 & 0.689386856045382 & 119.816615700840 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 82.6206896551724 & 0.685529097045402 & 120.521054483703 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 82.625 & 0.684030501712261 & 120.791397157252 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 82.6296296296296 & 0.681335626842981 & 121.275956186968 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 82.6346153846154 & 0.67715849293235 & 122.031424322505 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 82.64 & 0.671130632984825 & 123.135490973586 \tabularnewline
Median & 80.5 &  &  \tabularnewline
Midrange & 65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 81.375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 81.375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 81.375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 81.375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 81.375 &  &  \tabularnewline
Midmean - Closest Observation & 81.375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 81.375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.375 &  &  \tabularnewline
Number of observations & 146 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95816&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]80.445205479452[/C][C]1.33025655631288[/C][C]60.4734516042718[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.534300089989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]76.1760297217087[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]82.0245118726421[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]80.4794520547945[/C][C]1.32171354897135[/C][C]60.890237614216[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]80.4794520547945[/C][C]1.32171354897135[/C][C]60.890237614216[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]80.5616438356164[/C][C]1.30291532428329[/C][C]61.8318338376534[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]80.6986301369863[/C][C]1.27422653794607[/C][C]63.3314624470661[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]80.7328767123288[/C][C]1.26749601943030[/C][C]63.6947773205756[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]80.7328767123288[/C][C]1.26749601943030[/C][C]63.6947773205756[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]80.972602739726[/C][C]1.2232183482863[/C][C]66.1963604888421[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]81.2465753424657[/C][C]1.17819753145660[/C][C]68.958364937347[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]81.2465753424657[/C][C]1.17819753145660[/C][C]68.958364937347[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]81.4520547945205[/C][C]1.14792051588796[/C][C]70.9561800378784[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]81.527397260274[/C][C]1.13746667635521[/C][C]71.6745368941382[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]81.6095890410959[/C][C]1.12641548122403[/C][C]72.450699055036[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]81.7397260273973[/C][C]1.10941582650519[/C][C]73.6781683427831[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]81.7397260273973[/C][C]1.10941582650519[/C][C]73.6781683427831[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]81.7397260273973[/C][C]1.10941582650519[/C][C]73.6781683427831[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]81.7397260273973[/C][C]1.10941582650519[/C][C]73.6781683427831[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]82.3698630136986[/C][C]1.03207939565944[/C][C]79.8096186786767[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]82.3698630136986[/C][C]1.03207939565944[/C][C]79.8096186786767[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]82.3698630136986[/C][C]1.03207939565944[/C][C]79.8096186786767[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]82.3698630136986[/C][C]1.03207939565944[/C][C]79.8096186786767[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]82.3698630136986[/C][C]0.947014486809335[/C][C]86.9784614290514[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]82.1780821917808[/C][C]0.88308970050131[/C][C]93.0574574079284[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]82.1780821917808[/C][C]0.840163565260817[/C][C]97.8120042211897[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]82.3835616438356[/C][C]0.818322319972051[/C][C]100.673731649711[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]82.3835616438356[/C][C]0.818322319972051[/C][C]100.673731649711[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]82.3835616438356[/C][C]0.818322319972051[/C][C]100.673731649711[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]82.3835616438356[/C][C]0.818322319972051[/C][C]100.673731649711[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]82.3835616438356[/C][C]0.818322319972051[/C][C]100.673731649711[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]81.9041095890411[/C][C]0.768924600834731[/C][C]106.517738540459[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]81.4109589041096[/C][C]0.721730405852391[/C][C]112.799680107644[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]81.4109589041096[/C][C]0.721730405852391[/C][C]112.799680107644[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]81.6712328767123[/C][C]0.693727180488566[/C][C]117.728172073630[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]81.4041095890411[/C][C]0.669504344126517[/C][C]121.588620452115[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]81.6780821917808[/C][C]0.64053996260542[/C][C]127.514420582835[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]81.958904109589[/C][C]0.611716550882357[/C][C]133.981831930768[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]82.2465753424657[/C][C]0.583148786918094[/C][C]141.038748922267[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]82.2465753424657[/C][C]0.583148786918094[/C][C]141.038748922267[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]82.5479452054795[/C][C]0.554287807229553[/C][C]148.926142932985[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]82.5479452054795[/C][C]0.554287807229553[/C][C]148.926142932985[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]82.5479452054795[/C][C]0.554287807229553[/C][C]148.926142932985[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]82.5479452054795[/C][C]0.554287807229553[/C][C]148.926142932985[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]82.5479452054795[/C][C]0.554287807229553[/C][C]148.926142932985[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]80.6597222222222[/C][C]1.29490676384207[/C][C]62.2899844795773[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]80.8450704225352[/C][C]1.2654911942427[/C][C]63.884340555143[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]81.0357142857143[/C][C]1.23312497165243[/C][C]65.715735346048[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]81.2028985507246[/C][C]1.20518290002841[/C][C]67.3780706221526[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]81.3382352941177[/C][C]1.18359430926079[/C][C]68.7213808462102[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]81.4701492537313[/C][C]1.16164580398222[/C][C]70.133382287824[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]81.6060606060606[/C][C]1.13748190793571[/C][C]71.7427328177542[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]81.7076923076923[/C][C]1.11996284512473[/C][C]72.955716935942[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]81.7734375[/C][C]1.10881926963120[/C][C]73.7482110382141[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]81.8412698412698[/C][C]1.09651179675978[/C][C]74.6378379905378[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]81.8870967741936[/C][C]1.08751646592280[/C][C]75.2973397094356[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]81.9262295081967[/C][C]1.07899404901455[/C][C]75.9283423138618[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]81.9583333333333[/C][C]1.07096881670252[/C][C]76.5272826389849[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]81.9915254237288[/C][C]1.06199922457277[/C][C]77.2048825710893[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]82.0258620689655[/C][C]1.05198186681636[/C][C]77.9726957815373[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]82.061403508772[/C][C]1.04079832493788[/C][C]78.8446729232292[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]82.0982142857143[/C][C]1.02831219417952[/C][C]79.8378301360318[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]82.1363636363636[/C][C]1.01436531533204[/C][C]80.9731586785154[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]82.175925925926[/C][C]0.998772932138707[/C][C]82.2768852475405[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]82.2075471698113[/C][C]0.983303285617521[/C][C]83.6034500974787[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]82.2403846153846[/C][C]0.96595280581387[/C][C]85.1391332168577[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]82.2745098039216[/C][C]0.946455942578166[/C][C]86.9290435007509[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]82.31[/C][C]0.92449221661724[/C][C]89.0326587076915[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]82.3061224489796[/C][C]0.908663698326207[/C][C]90.5793007914705[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]82.3020833333333[/C][C]0.890756601285625[/C][C]92.3957040728602[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]82.2978723404255[/C][C]0.870449541243662[/C][C]94.5464021071707[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]82.2934782608696[/C][C]0.847347403059192[/C][C]97.1189360630175[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]82.2888888888889[/C][C]0.83093203756222[/C][C]99.0320329088613[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]82.2954545454545[/C][C]0.819236954612518[/C][C]100.453787005224[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]82.3023255813954[/C][C]0.810341801427899[/C][C]101.564951279042[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]82.297619047619[/C][C]0.802280842456981[/C][C]102.579564028455[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]82.2926829268293[/C][C]0.792825364174422[/C][C]103.796733360721[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]82.2875[/C][C]0.781752686377366[/C][C]105.260271482174[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]82.2820512820513[/C][C]0.768792193765834[/C][C]107.027688300271[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]82.2763157894737[/C][C]0.753610882936868[/C][C]109.176124777867[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]82.2972972972973[/C][C]0.741664709906984[/C][C]110.962940797896[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]82.3472222222222[/C][C]0.732692774609437[/C][C]112.389837972836[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]82.4[/C][C]0.721856360057086[/C][C]114.150133682390[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]82.4411764705882[/C][C]0.712481952374103[/C][C]115.709845275212[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]82.5[/C][C]0.703719720642704[/C][C]117.234173748397[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]82.546875[/C][C]0.696835850206443[/C][C]118.459569747373[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]82.5806451612903[/C][C]0.69200632866248[/C][C]119.335101054500[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]82.6[/C][C]0.689386856045382[/C][C]119.816615700840[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]82.6206896551724[/C][C]0.685529097045402[/C][C]120.521054483703[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]82.625[/C][C]0.684030501712261[/C][C]120.791397157252[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]82.6296296296296[/C][C]0.681335626842981[/C][C]121.275956186968[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]82.6346153846154[/C][C]0.67715849293235[/C][C]122.031424322505[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]82.64[/C][C]0.671130632984825[/C][C]123.135490973586[/C][/ROW]
[ROW][C]Median[/C][C]80.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]146[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95816&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean80.4452054794521.3302565563128860.4734516042718
Geometric Mean78.534300089989
Harmonic Mean76.1760297217087
Quadratic Mean82.0245118726421
Winsorized Mean ( 1 / 48 )80.47945205479451.3217135489713560.890237614216
Winsorized Mean ( 2 / 48 )80.47945205479451.3217135489713560.890237614216
Winsorized Mean ( 3 / 48 )80.56164383561641.3029153242832961.8318338376534
Winsorized Mean ( 4 / 48 )80.69863013698631.2742265379460763.3314624470661
Winsorized Mean ( 5 / 48 )80.73287671232881.2674960194303063.6947773205756
Winsorized Mean ( 6 / 48 )80.73287671232881.2674960194303063.6947773205756
Winsorized Mean ( 7 / 48 )80.9726027397261.223218348286366.1963604888421
Winsorized Mean ( 8 / 48 )81.24657534246571.1781975314566068.958364937347
Winsorized Mean ( 9 / 48 )81.24657534246571.1781975314566068.958364937347
Winsorized Mean ( 10 / 48 )81.45205479452051.1479205158879670.9561800378784
Winsorized Mean ( 11 / 48 )81.5273972602741.1374666763552171.6745368941382
Winsorized Mean ( 12 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 13 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 14 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 15 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 16 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 17 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 18 / 48 )81.60958904109591.1264154812240372.450699055036
Winsorized Mean ( 19 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 20 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 21 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 22 / 48 )81.73972602739731.1094158265051973.6781683427831
Winsorized Mean ( 23 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 24 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 25 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 26 / 48 )82.36986301369861.0320793956594479.8096186786767
Winsorized Mean ( 27 / 48 )82.36986301369860.94701448680933586.9784614290514
Winsorized Mean ( 28 / 48 )82.17808219178080.8830897005013193.0574574079284
Winsorized Mean ( 29 / 48 )82.17808219178080.84016356526081797.8120042211897
Winsorized Mean ( 30 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 31 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 32 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 33 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 34 / 48 )82.38356164383560.818322319972051100.673731649711
Winsorized Mean ( 35 / 48 )81.90410958904110.768924600834731106.517738540459
Winsorized Mean ( 36 / 48 )81.41095890410960.721730405852391112.799680107644
Winsorized Mean ( 37 / 48 )81.41095890410960.721730405852391112.799680107644
Winsorized Mean ( 38 / 48 )81.67123287671230.693727180488566117.728172073630
Winsorized Mean ( 39 / 48 )81.40410958904110.669504344126517121.588620452115
Winsorized Mean ( 40 / 48 )81.67808219178080.64053996260542127.514420582835
Winsorized Mean ( 41 / 48 )81.9589041095890.611716550882357133.981831930768
Winsorized Mean ( 42 / 48 )82.24657534246570.583148786918094141.038748922267
Winsorized Mean ( 43 / 48 )82.24657534246570.583148786918094141.038748922267
Winsorized Mean ( 44 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 45 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 46 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 47 / 48 )82.54794520547950.554287807229553148.926142932985
Winsorized Mean ( 48 / 48 )82.54794520547950.554287807229553148.926142932985
Trimmed Mean ( 1 / 48 )80.65972222222221.2949067638420762.2899844795773
Trimmed Mean ( 2 / 48 )80.84507042253521.265491194242763.884340555143
Trimmed Mean ( 3 / 48 )81.03571428571431.2331249716524365.715735346048
Trimmed Mean ( 4 / 48 )81.20289855072461.2051829000284167.3780706221526
Trimmed Mean ( 5 / 48 )81.33823529411771.1835943092607968.7213808462102
Trimmed Mean ( 6 / 48 )81.47014925373131.1616458039822270.133382287824
Trimmed Mean ( 7 / 48 )81.60606060606061.1374819079357171.7427328177542
Trimmed Mean ( 8 / 48 )81.70769230769231.1199628451247372.955716935942
Trimmed Mean ( 9 / 48 )81.77343751.1088192696312073.7482110382141
Trimmed Mean ( 10 / 48 )81.84126984126981.0965117967597874.6378379905378
Trimmed Mean ( 11 / 48 )81.88709677419361.0875164659228075.2973397094356
Trimmed Mean ( 12 / 48 )81.92622950819671.0789940490145575.9283423138618
Trimmed Mean ( 13 / 48 )81.95833333333331.0709688167025276.5272826389849
Trimmed Mean ( 14 / 48 )81.99152542372881.0619992245727777.2048825710893
Trimmed Mean ( 15 / 48 )82.02586206896551.0519818668163677.9726957815373
Trimmed Mean ( 16 / 48 )82.0614035087721.0407983249378878.8446729232292
Trimmed Mean ( 17 / 48 )82.09821428571431.0283121941795279.8378301360318
Trimmed Mean ( 18 / 48 )82.13636363636361.0143653153320480.9731586785154
Trimmed Mean ( 19 / 48 )82.1759259259260.99877293213870782.2768852475405
Trimmed Mean ( 20 / 48 )82.20754716981130.98330328561752183.6034500974787
Trimmed Mean ( 21 / 48 )82.24038461538460.9659528058138785.1391332168577
Trimmed Mean ( 22 / 48 )82.27450980392160.94645594257816686.9290435007509
Trimmed Mean ( 23 / 48 )82.310.9244922166172489.0326587076915
Trimmed Mean ( 24 / 48 )82.30612244897960.90866369832620790.5793007914705
Trimmed Mean ( 25 / 48 )82.30208333333330.89075660128562592.3957040728602
Trimmed Mean ( 26 / 48 )82.29787234042550.87044954124366294.5464021071707
Trimmed Mean ( 27 / 48 )82.29347826086960.84734740305919297.1189360630175
Trimmed Mean ( 28 / 48 )82.28888888888890.8309320375622299.0320329088613
Trimmed Mean ( 29 / 48 )82.29545454545450.819236954612518100.453787005224
Trimmed Mean ( 30 / 48 )82.30232558139540.810341801427899101.564951279042
Trimmed Mean ( 31 / 48 )82.2976190476190.802280842456981102.579564028455
Trimmed Mean ( 32 / 48 )82.29268292682930.792825364174422103.796733360721
Trimmed Mean ( 33 / 48 )82.28750.781752686377366105.260271482174
Trimmed Mean ( 34 / 48 )82.28205128205130.768792193765834107.027688300271
Trimmed Mean ( 35 / 48 )82.27631578947370.753610882936868109.176124777867
Trimmed Mean ( 36 / 48 )82.29729729729730.741664709906984110.962940797896
Trimmed Mean ( 37 / 48 )82.34722222222220.732692774609437112.389837972836
Trimmed Mean ( 38 / 48 )82.40.721856360057086114.150133682390
Trimmed Mean ( 39 / 48 )82.44117647058820.712481952374103115.709845275212
Trimmed Mean ( 40 / 48 )82.50.703719720642704117.234173748397
Trimmed Mean ( 41 / 48 )82.5468750.696835850206443118.459569747373
Trimmed Mean ( 42 / 48 )82.58064516129030.69200632866248119.335101054500
Trimmed Mean ( 43 / 48 )82.60.689386856045382119.816615700840
Trimmed Mean ( 44 / 48 )82.62068965517240.685529097045402120.521054483703
Trimmed Mean ( 45 / 48 )82.6250.684030501712261120.791397157252
Trimmed Mean ( 46 / 48 )82.62962962962960.681335626842981121.275956186968
Trimmed Mean ( 47 / 48 )82.63461538461540.67715849293235122.031424322505
Trimmed Mean ( 48 / 48 )82.640.671130632984825123.135490973586
Median80.5
Midrange65
Midmean - Weighted Average at Xnp81.375
Midmean - Weighted Average at X(n+1)p81.375
Midmean - Empirical Distribution Function81.375
Midmean - Empirical Distribution Function - Averaging81.375
Midmean - Empirical Distribution Function - Interpolation81.375
Midmean - Closest Observation81.375
Midmean - True Basic - Statistics Graphics Toolkit81.375
Midmean - MS Excel (old versions)81.375
Number of observations146



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')