Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 24 Dec 2007 02:34:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/24/t1198487737phuswcwnrq8iiff.htm/, Retrieved Sun, 05 May 2024 12:58:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4851, Retrieved Sun, 05 May 2024 12:58:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt
Estimated Impact270
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 4] [2007-12-24 09:34:14] [6abd901c2e17b7d5559c695bbff3d863] [Current]
Feedback Forum

Post a new message
Dataseries X:
92,1
91,4
90,7
92,5
94,4
94,3
87,3
85,9
89
83,3
78,6
75,7
79,6
78,5
82,6
88,7
88,5
84,6
83,4
84,4
94,1
100,4
93,1
93,1
82,1
88,1
87,7
80,2
73,8
75,3
77,3
80,1
81,3
81,5
83,2
80,8
81,3
78,8
82,8
84,9
93,2
94,7
94,8
103,9
107
118,6
112,2
112,2
93,8
96,7
108,7
112,1
107,2
113,1
120
124,4
139,5
145,8
135,6
135,5
141,6
141,2
141,6
147,1
146,5
144,1
148,5
146,9
135,7
128,5
128,7
127,6
122,5
123,4
129,4
135,3
138,5
140,6
144,2
144,3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4851&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4851&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4851&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.38252.7108576664913038.8742283678795
Geometric Mean102.759056647837
Harmonic Mean100.320703777068
Quadratic Mean108.101907938759
Winsorized Mean ( 1 / 26 )105.383752.7046850139203538.9634095865566
Winsorized Mean ( 2 / 26 )105.388752.7023114776046238.9994828032994
Winsorized Mean ( 3 / 26 )105.433752.6912621996113639.1763203210841
Winsorized Mean ( 4 / 26 )105.458752.6767486262384939.3980775655413
Winsorized Mean ( 5 / 26 )105.371252.6583193949444839.6382956090198
Winsorized Mean ( 6 / 26 )105.378752.6550237154474939.6903234373705
Winsorized Mean ( 7 / 26 )105.442.6446402689021339.8693165342186
Winsorized Mean ( 8 / 26 )105.242.5931546937702740.5837724424331
Winsorized Mean ( 9 / 26 )105.251252.5917761820207140.6096987579921
Winsorized Mean ( 10 / 26 )105.276252.5738185465570940.9027474531273
Winsorized Mean ( 11 / 26 )105.26252.5510722336184941.2620617373478
Winsorized Mean ( 12 / 26 )105.09752.5223619977054041.6663032885873
Winsorized Mean ( 13 / 26 )104.96752.4906075303534242.145339528908
Winsorized Mean ( 14 / 26 )104.58252.3960507954876443.6478643094524
Winsorized Mean ( 15 / 26 )104.65752.3819055337101443.9385603328197
Winsorized Mean ( 16 / 26 )104.67752.3739401199352144.0944146488653
Winsorized Mean ( 17 / 26 )104.722.3570882863977444.427695222244
Winsorized Mean ( 18 / 26 )103.4152.1432452767837148.2515935624461
Winsorized Mean ( 19 / 26 )103.27252.1150141207596448.8282791998137
Winsorized Mean ( 20 / 26 )103.47252.0780056582749749.794137753165
Winsorized Mean ( 21 / 26 )103.288752.0360415442949450.730178020885
Winsorized Mean ( 22 / 26 )102.491251.8954477392215954.0723164660241
Winsorized Mean ( 23 / 26 )102.491251.8200276407606956.3130183875468
Winsorized Mean ( 24 / 26 )102.641251.7330322932907559.2263920282181
Winsorized Mean ( 25 / 26 )101.9851.6068544828682963.4687217089834
Winsorized Mean ( 26 / 26 )101.661.5280174546686866.5306536187723
Trimmed Mean ( 1 / 26 )105.2346153846152.6938904414804239.0641778760624
Trimmed Mean ( 2 / 26 )105.0776315789472.6798517887036739.2102399176996
Trimmed Mean ( 3 / 26 )104.9094594594592.6634256591525839.3889197165872
Trimmed Mean ( 4 / 26 )104.7152777777782.6473084477809939.5553747677388
Trimmed Mean ( 5 / 26 )104.5028571428572.6315406310509339.7116639240804
Trimmed Mean ( 6 / 26 )104.2985294117652.6164775467450539.862191648277
Trimmed Mean ( 7 / 26 )104.0803030303032.59750303238540.0693672856803
Trimmed Mean ( 8 / 26 )103.83752.5752605238835640.3211632520233
Trimmed Mean ( 9 / 26 )103.6112903225812.5580227119419340.5044450304837
Trimmed Mean ( 10 / 26 )103.3683333333332.5352135733550240.7730277321523
Trimmed Mean ( 11 / 26 )103.1051724137932.5087920685374941.0975360241387
Trimmed Mean ( 12 / 26 )102.8252.4786336962124941.4845485870393
Trimmed Mean ( 13 / 26 )102.5444444444442.4450447137951341.9397010884427
Trimmed Mean ( 14 / 26 )102.2576923076922.4073939430298942.4765097560199
Trimmed Mean ( 15 / 26 )101.9922.3768901651407642.9098498095557
Trimmed Mean ( 16 / 26 )101.6958333333332.3379936205263243.4970533882125
Trimmed Mean ( 17 / 26 )101.3717391304352.2870326809015844.3245695511761
Trimmed Mean ( 18 / 26 )101.0136363636362.2218632803732945.4634797991105
Trimmed Mean ( 19 / 26 )100.7595238095242.1845621889301446.1234403488735
Trimmed Mean ( 20 / 26 )100.4952.1383403281457246.9967285736714
Trimmed Mean ( 21 / 26 )100.1815789473682.0805331384770048.1518785231672
Trimmed Mean ( 22 / 26 )99.85277777777782.0094202200663049.6923325348459
Trimmed Mean ( 23 / 26 )99.57058823529411.9482453800319351.107827204837
Trimmed Mean ( 24 / 26 )99.2531251.8785664166470252.834504077398
Trimmed Mean ( 25 / 26 )98.87666666666671.7982218761067354.9857990164935
Trimmed Mean ( 26 / 26 )98.52142857142861.7207829916373557.2538368000046
Median94.35
Midrange111.15
Midmean - Weighted Average at Xnp100.078048780488
Midmean - Weighted Average at X(n+1)p100.495
Midmean - Empirical Distribution Function100.078048780488
Midmean - Empirical Distribution Function - Averaging100.495
Midmean - Empirical Distribution Function - Interpolation100.495
Midmean - Closest Observation100.078048780488
Midmean - True Basic - Statistics Graphics Toolkit100.495
Midmean - MS Excel (old versions)100.759523809524
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.3825 & 2.71085766649130 & 38.8742283678795 \tabularnewline
Geometric Mean & 102.759056647837 &  &  \tabularnewline
Harmonic Mean & 100.320703777068 &  &  \tabularnewline
Quadratic Mean & 108.101907938759 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 105.38375 & 2.70468501392035 & 38.9634095865566 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 105.38875 & 2.70231147760462 & 38.9994828032994 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 105.43375 & 2.69126219961136 & 39.1763203210841 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 105.45875 & 2.67674862623849 & 39.3980775655413 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 105.37125 & 2.65831939494448 & 39.6382956090198 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 105.37875 & 2.65502371544749 & 39.6903234373705 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 105.44 & 2.64464026890213 & 39.8693165342186 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 105.24 & 2.59315469377027 & 40.5837724424331 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 105.25125 & 2.59177618202071 & 40.6096987579921 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 105.27625 & 2.57381854655709 & 40.9027474531273 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 105.2625 & 2.55107223361849 & 41.2620617373478 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 105.0975 & 2.52236199770540 & 41.6663032885873 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 104.9675 & 2.49060753035342 & 42.145339528908 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 104.5825 & 2.39605079548764 & 43.6478643094524 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 104.6575 & 2.38190553371014 & 43.9385603328197 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 104.6775 & 2.37394011993521 & 44.0944146488653 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 104.72 & 2.35708828639774 & 44.427695222244 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 103.415 & 2.14324527678371 & 48.2515935624461 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 103.2725 & 2.11501412075964 & 48.8282791998137 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 103.4725 & 2.07800565827497 & 49.794137753165 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 103.28875 & 2.03604154429494 & 50.730178020885 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 102.49125 & 1.89544773922159 & 54.0723164660241 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 102.49125 & 1.82002764076069 & 56.3130183875468 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 102.64125 & 1.73303229329075 & 59.2263920282181 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 101.985 & 1.60685448286829 & 63.4687217089834 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 101.66 & 1.52801745466868 & 66.5306536187723 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 105.234615384615 & 2.69389044148042 & 39.0641778760624 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 105.077631578947 & 2.67985178870367 & 39.2102399176996 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 104.909459459459 & 2.66342565915258 & 39.3889197165872 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 104.715277777778 & 2.64730844778099 & 39.5553747677388 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 104.502857142857 & 2.63154063105093 & 39.7116639240804 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 104.298529411765 & 2.61647754674505 & 39.862191648277 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 104.080303030303 & 2.597503032385 & 40.0693672856803 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 103.8375 & 2.57526052388356 & 40.3211632520233 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 103.611290322581 & 2.55802271194193 & 40.5044450304837 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 103.368333333333 & 2.53521357335502 & 40.7730277321523 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 103.105172413793 & 2.50879206853749 & 41.0975360241387 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 102.825 & 2.47863369621249 & 41.4845485870393 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 102.544444444444 & 2.44504471379513 & 41.9397010884427 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 102.257692307692 & 2.40739394302989 & 42.4765097560199 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 101.992 & 2.37689016514076 & 42.9098498095557 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 101.695833333333 & 2.33799362052632 & 43.4970533882125 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 101.371739130435 & 2.28703268090158 & 44.3245695511761 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 101.013636363636 & 2.22186328037329 & 45.4634797991105 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 100.759523809524 & 2.18456218893014 & 46.1234403488735 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 100.495 & 2.13834032814572 & 46.9967285736714 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 100.181578947368 & 2.08053313847700 & 48.1518785231672 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 99.8527777777778 & 2.00942022006630 & 49.6923325348459 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 99.5705882352941 & 1.94824538003193 & 51.107827204837 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 99.253125 & 1.87856641664702 & 52.834504077398 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 98.8766666666667 & 1.79822187610673 & 54.9857990164935 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 98.5214285714286 & 1.72078299163735 & 57.2538368000046 \tabularnewline
Median & 94.35 &  &  \tabularnewline
Midrange & 111.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.078048780488 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.495 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.078048780488 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.495 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.495 &  &  \tabularnewline
Midmean - Closest Observation & 100.078048780488 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.495 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.759523809524 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4851&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]105.3825[/C][C]2.71085766649130[/C][C]38.8742283678795[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.759056647837[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.320703777068[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.101907938759[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]105.38375[/C][C]2.70468501392035[/C][C]38.9634095865566[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]105.38875[/C][C]2.70231147760462[/C][C]38.9994828032994[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]105.43375[/C][C]2.69126219961136[/C][C]39.1763203210841[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]105.45875[/C][C]2.67674862623849[/C][C]39.3980775655413[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]105.37125[/C][C]2.65831939494448[/C][C]39.6382956090198[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]105.37875[/C][C]2.65502371544749[/C][C]39.6903234373705[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]105.44[/C][C]2.64464026890213[/C][C]39.8693165342186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]105.24[/C][C]2.59315469377027[/C][C]40.5837724424331[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]105.25125[/C][C]2.59177618202071[/C][C]40.6096987579921[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]105.27625[/C][C]2.57381854655709[/C][C]40.9027474531273[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]105.2625[/C][C]2.55107223361849[/C][C]41.2620617373478[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]105.0975[/C][C]2.52236199770540[/C][C]41.6663032885873[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]104.9675[/C][C]2.49060753035342[/C][C]42.145339528908[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]104.5825[/C][C]2.39605079548764[/C][C]43.6478643094524[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]104.6575[/C][C]2.38190553371014[/C][C]43.9385603328197[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]104.6775[/C][C]2.37394011993521[/C][C]44.0944146488653[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]104.72[/C][C]2.35708828639774[/C][C]44.427695222244[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]103.415[/C][C]2.14324527678371[/C][C]48.2515935624461[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]103.2725[/C][C]2.11501412075964[/C][C]48.8282791998137[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]103.4725[/C][C]2.07800565827497[/C][C]49.794137753165[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]103.28875[/C][C]2.03604154429494[/C][C]50.730178020885[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]102.49125[/C][C]1.89544773922159[/C][C]54.0723164660241[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]102.49125[/C][C]1.82002764076069[/C][C]56.3130183875468[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]102.64125[/C][C]1.73303229329075[/C][C]59.2263920282181[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]101.985[/C][C]1.60685448286829[/C][C]63.4687217089834[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]101.66[/C][C]1.52801745466868[/C][C]66.5306536187723[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]105.234615384615[/C][C]2.69389044148042[/C][C]39.0641778760624[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]105.077631578947[/C][C]2.67985178870367[/C][C]39.2102399176996[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]104.909459459459[/C][C]2.66342565915258[/C][C]39.3889197165872[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]104.715277777778[/C][C]2.64730844778099[/C][C]39.5553747677388[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]104.502857142857[/C][C]2.63154063105093[/C][C]39.7116639240804[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]104.298529411765[/C][C]2.61647754674505[/C][C]39.862191648277[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]104.080303030303[/C][C]2.597503032385[/C][C]40.0693672856803[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]103.8375[/C][C]2.57526052388356[/C][C]40.3211632520233[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]103.611290322581[/C][C]2.55802271194193[/C][C]40.5044450304837[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]103.368333333333[/C][C]2.53521357335502[/C][C]40.7730277321523[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]103.105172413793[/C][C]2.50879206853749[/C][C]41.0975360241387[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]102.825[/C][C]2.47863369621249[/C][C]41.4845485870393[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]102.544444444444[/C][C]2.44504471379513[/C][C]41.9397010884427[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]102.257692307692[/C][C]2.40739394302989[/C][C]42.4765097560199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]101.992[/C][C]2.37689016514076[/C][C]42.9098498095557[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]101.695833333333[/C][C]2.33799362052632[/C][C]43.4970533882125[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]101.371739130435[/C][C]2.28703268090158[/C][C]44.3245695511761[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]101.013636363636[/C][C]2.22186328037329[/C][C]45.4634797991105[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]100.759523809524[/C][C]2.18456218893014[/C][C]46.1234403488735[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]100.495[/C][C]2.13834032814572[/C][C]46.9967285736714[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]100.181578947368[/C][C]2.08053313847700[/C][C]48.1518785231672[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]99.8527777777778[/C][C]2.00942022006630[/C][C]49.6923325348459[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]99.5705882352941[/C][C]1.94824538003193[/C][C]51.107827204837[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]99.253125[/C][C]1.87856641664702[/C][C]52.834504077398[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]98.8766666666667[/C][C]1.79822187610673[/C][C]54.9857990164935[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]98.5214285714286[/C][C]1.72078299163735[/C][C]57.2538368000046[/C][/ROW]
[ROW][C]Median[/C][C]94.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.078048780488[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.078048780488[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.078048780488[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.759523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4851&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4851&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 Mean105.38252.7108576664913038.8742283678795
Geometric Mean102.759056647837
Harmonic Mean100.320703777068
Quadratic Mean108.101907938759
Winsorized Mean ( 1 / 26 )105.383752.7046850139203538.9634095865566
Winsorized Mean ( 2 / 26 )105.388752.7023114776046238.9994828032994
Winsorized Mean ( 3 / 26 )105.433752.6912621996113639.1763203210841
Winsorized Mean ( 4 / 26 )105.458752.6767486262384939.3980775655413
Winsorized Mean ( 5 / 26 )105.371252.6583193949444839.6382956090198
Winsorized Mean ( 6 / 26 )105.378752.6550237154474939.6903234373705
Winsorized Mean ( 7 / 26 )105.442.6446402689021339.8693165342186
Winsorized Mean ( 8 / 26 )105.242.5931546937702740.5837724424331
Winsorized Mean ( 9 / 26 )105.251252.5917761820207140.6096987579921
Winsorized Mean ( 10 / 26 )105.276252.5738185465570940.9027474531273
Winsorized Mean ( 11 / 26 )105.26252.5510722336184941.2620617373478
Winsorized Mean ( 12 / 26 )105.09752.5223619977054041.6663032885873
Winsorized Mean ( 13 / 26 )104.96752.4906075303534242.145339528908
Winsorized Mean ( 14 / 26 )104.58252.3960507954876443.6478643094524
Winsorized Mean ( 15 / 26 )104.65752.3819055337101443.9385603328197
Winsorized Mean ( 16 / 26 )104.67752.3739401199352144.0944146488653
Winsorized Mean ( 17 / 26 )104.722.3570882863977444.427695222244
Winsorized Mean ( 18 / 26 )103.4152.1432452767837148.2515935624461
Winsorized Mean ( 19 / 26 )103.27252.1150141207596448.8282791998137
Winsorized Mean ( 20 / 26 )103.47252.0780056582749749.794137753165
Winsorized Mean ( 21 / 26 )103.288752.0360415442949450.730178020885
Winsorized Mean ( 22 / 26 )102.491251.8954477392215954.0723164660241
Winsorized Mean ( 23 / 26 )102.491251.8200276407606956.3130183875468
Winsorized Mean ( 24 / 26 )102.641251.7330322932907559.2263920282181
Winsorized Mean ( 25 / 26 )101.9851.6068544828682963.4687217089834
Winsorized Mean ( 26 / 26 )101.661.5280174546686866.5306536187723
Trimmed Mean ( 1 / 26 )105.2346153846152.6938904414804239.0641778760624
Trimmed Mean ( 2 / 26 )105.0776315789472.6798517887036739.2102399176996
Trimmed Mean ( 3 / 26 )104.9094594594592.6634256591525839.3889197165872
Trimmed Mean ( 4 / 26 )104.7152777777782.6473084477809939.5553747677388
Trimmed Mean ( 5 / 26 )104.5028571428572.6315406310509339.7116639240804
Trimmed Mean ( 6 / 26 )104.2985294117652.6164775467450539.862191648277
Trimmed Mean ( 7 / 26 )104.0803030303032.59750303238540.0693672856803
Trimmed Mean ( 8 / 26 )103.83752.5752605238835640.3211632520233
Trimmed Mean ( 9 / 26 )103.6112903225812.5580227119419340.5044450304837
Trimmed Mean ( 10 / 26 )103.3683333333332.5352135733550240.7730277321523
Trimmed Mean ( 11 / 26 )103.1051724137932.5087920685374941.0975360241387
Trimmed Mean ( 12 / 26 )102.8252.4786336962124941.4845485870393
Trimmed Mean ( 13 / 26 )102.5444444444442.4450447137951341.9397010884427
Trimmed Mean ( 14 / 26 )102.2576923076922.4073939430298942.4765097560199
Trimmed Mean ( 15 / 26 )101.9922.3768901651407642.9098498095557
Trimmed Mean ( 16 / 26 )101.6958333333332.3379936205263243.4970533882125
Trimmed Mean ( 17 / 26 )101.3717391304352.2870326809015844.3245695511761
Trimmed Mean ( 18 / 26 )101.0136363636362.2218632803732945.4634797991105
Trimmed Mean ( 19 / 26 )100.7595238095242.1845621889301446.1234403488735
Trimmed Mean ( 20 / 26 )100.4952.1383403281457246.9967285736714
Trimmed Mean ( 21 / 26 )100.1815789473682.0805331384770048.1518785231672
Trimmed Mean ( 22 / 26 )99.85277777777782.0094202200663049.6923325348459
Trimmed Mean ( 23 / 26 )99.57058823529411.9482453800319351.107827204837
Trimmed Mean ( 24 / 26 )99.2531251.8785664166470252.834504077398
Trimmed Mean ( 25 / 26 )98.87666666666671.7982218761067354.9857990164935
Trimmed Mean ( 26 / 26 )98.52142857142861.7207829916373557.2538368000046
Median94.35
Midrange111.15
Midmean - Weighted Average at Xnp100.078048780488
Midmean - Weighted Average at X(n+1)p100.495
Midmean - Empirical Distribution Function100.078048780488
Midmean - Empirical Distribution Function - Averaging100.495
Midmean - Empirical Distribution Function - Interpolation100.495
Midmean - Closest Observation100.078048780488
Midmean - True Basic - Statistics Graphics Toolkit100.495
Midmean - MS Excel (old versions)100.759523809524
Number of observations80



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')