Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 13:43:18 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318873455sk7t8g4nvv4i5h5.htm/, Retrieved Wed, 15 May 2024 01:46:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130806, Retrieved Wed, 15 May 2024 01:46:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Bestellingen Boeing] [2011-10-17 17:43:18] [e09593412f775de82555261d5bbd0b3f] [Current]
Feedback Forum

Post a new message
Dataseries X:
20
32
11
14
199
162
88
89
24
36
142
193
39
25
95
144
33
131
31
24
160
52
57
210
13
52
96
133
74
131
129
74
127
55
175
185
34
115
95
58
63
56
70
32
32
14
6
23
18
4
6
17
20
20
44
32
20
14
9
59
10
47
43
34
5
49
130
10
117
108
17
55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130806&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130806&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean65.84722222222226.5573687099602310.0417141592487
Geometric Mean43.3752498484842
Harmonic Mean25.8544266363995
Quadratic Mean85.9580808689135
Winsorized Mean ( 1 / 24 )65.70833333333336.509846806045810.0936835060863
Winsorized Mean ( 2 / 24 )65.56944444444446.4590265836887910.1515984792553
Winsorized Mean ( 3 / 24 )65.23611111111116.3685545542875910.243472134064
Winsorized Mean ( 4 / 24 )64.84722222222226.2039748138348610.4525282851911
Winsorized Mean ( 5 / 24 )64.01388888888895.9779031375206210.7084185568519
Winsorized Mean ( 6 / 24 )63.84722222222225.939663360013810.7492998091518
Winsorized Mean ( 7 / 24 )62.38888888888895.5893494864914511.1621019654743
Winsorized Mean ( 8 / 24 )62.38888888888895.5155050886784311.3115458848825
Winsorized Mean ( 9 / 24 )61.38888888888895.2777160032625611.6317150924642
Winsorized Mean ( 10 / 24 )61.11111111111115.2250059174197911.6958931869093
Winsorized Mean ( 11 / 24 )61.11111111111115.2250059174197911.6958931869093
Winsorized Mean ( 12 / 24 )61.44444444444445.131368476809311.9742802962088
Winsorized Mean ( 13 / 24 )61.26388888888895.0974844610662712.0184552511758
Winsorized Mean ( 14 / 24 )61.06944444444445.0013036793725612.210705120011
Winsorized Mean ( 15 / 24 )59.40277777777784.5721335514327512.9923540311203
Winsorized Mean ( 16 / 24 )58.95833333333334.4936678409848813.1203140551687
Winsorized Mean ( 17 / 24 )57.30555555555564.2081335140070413.6178083144963
Winsorized Mean ( 18 / 24 )54.30555555555563.7154584916487314.6161114913862
Winsorized Mean ( 19 / 24 )54.83333333333333.5725216301825315.3486357843358
Winsorized Mean ( 20 / 24 )55.11111111111113.5378876859485515.5774055038537
Winsorized Mean ( 21 / 24 )53.36111111111113.2642072731203616.3473415277644
Winsorized Mean ( 22 / 24 )53.36111111111113.1787086060249416.7870408158741
Winsorized Mean ( 23 / 24 )50.80555555555562.2717940220440422.3636276275802
Winsorized Mean ( 24 / 24 )51.13888888888892.2311903350566522.9200028726327
Trimmed Mean ( 1 / 24 )64.67142857142866.3557320415580410.1752918701675
Trimmed Mean ( 2 / 24 )63.57352941176476.1696571286716610.3042240574967
Trimmed Mean ( 3 / 24 )62.48484848484855.9773949633123910.4535251340029
Trimmed Mean ( 4 / 24 )61.4531255.7865869161916910.619926027214
Trimmed Mean ( 5 / 24 )60.46774193548395.6165464236672810.7660005587565
Trimmed Mean ( 6 / 24 )59.61666666666675.4825399113433410.8739138484556
Trimmed Mean ( 7 / 24 )58.74137931034485.3272553281604711.0265747916814
Trimmed Mean ( 8 / 24 )58.07142857142865.2300863606175411.1033402830029
Trimmed Mean ( 9 / 24 )57.35185185185195.1241169004394611.1925338485024
Trimmed Mean ( 10 / 24 )56.73076923076925.0459513947910611.2428291103502
Trimmed Mean ( 11 / 24 )56.14.9554134488435611.3209524450663
Trimmed Mean ( 12 / 24 )55.41666666666674.8358546859614411.4595392677001
Trimmed Mean ( 13 / 24 )54.63043478260874.6981709562300411.6280219028994
Trimmed Mean ( 14 / 24 )53.79545454545454.5234390209872911.8926008056837
Trimmed Mean ( 15 / 24 )52.90476190476194.3134731424110512.2650032023128
Trimmed Mean ( 16 / 24 )52.1254.1466989497053212.5702397575074
Trimmed Mean ( 17 / 24 )51.31578947368423.9389193597790213.0278852615462
Trimmed Mean ( 18 / 24 )50.61111111111113.7376840673000813.5407675447728
Trimmed Mean ( 19 / 24 )50.17647058823533.6071504023778713.9102795811227
Trimmed Mean ( 20 / 24 )49.6253.4549957985129214.3632591453105
Trimmed Mean ( 21 / 24 )48.96666666666673.2364601541656515.1296986009983
Trimmed Mean ( 22 / 24 )48.42857142857143.0164577545080416.0547819230009
Trimmed Mean ( 23 / 24 )47.80769230769232.7044232888813417.6775923000824
Trimmed Mean ( 24 / 24 )47.41666666666672.6174696450952718.115460003717
Median48
Midrange107
Midmean - Weighted Average at Xnp48.2564102564103
Midmean - Weighted Average at X(n+1)p48.2564102564103
Midmean - Empirical Distribution Function48.2564102564103
Midmean - Empirical Distribution Function - Averaging48.2564102564103
Midmean - Empirical Distribution Function - Interpolation48.2564102564103
Midmean - Closest Observation48.2564102564103
Midmean - True Basic - Statistics Graphics Toolkit48.2564102564103
Midmean - MS Excel (old versions)49.75
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65.8472222222222 & 6.55736870996023 & 10.0417141592487 \tabularnewline
Geometric Mean & 43.3752498484842 &  &  \tabularnewline
Harmonic Mean & 25.8544266363995 &  &  \tabularnewline
Quadratic Mean & 85.9580808689135 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 65.7083333333333 & 6.5098468060458 & 10.0936835060863 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 65.5694444444444 & 6.45902658368879 & 10.1515984792553 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 65.2361111111111 & 6.36855455428759 & 10.243472134064 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 64.8472222222222 & 6.20397481383486 & 10.4525282851911 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 64.0138888888889 & 5.97790313752062 & 10.7084185568519 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 63.8472222222222 & 5.9396633600138 & 10.7492998091518 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 62.3888888888889 & 5.58934948649145 & 11.1621019654743 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 62.3888888888889 & 5.51550508867843 & 11.3115458848825 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 61.3888888888889 & 5.27771600326256 & 11.6317150924642 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 61.1111111111111 & 5.22500591741979 & 11.6958931869093 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 61.1111111111111 & 5.22500591741979 & 11.6958931869093 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 61.4444444444444 & 5.1313684768093 & 11.9742802962088 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 61.2638888888889 & 5.09748446106627 & 12.0184552511758 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 61.0694444444444 & 5.00130367937256 & 12.210705120011 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 59.4027777777778 & 4.57213355143275 & 12.9923540311203 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 58.9583333333333 & 4.49366784098488 & 13.1203140551687 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 57.3055555555556 & 4.20813351400704 & 13.6178083144963 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 54.3055555555556 & 3.71545849164873 & 14.6161114913862 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 54.8333333333333 & 3.57252163018253 & 15.3486357843358 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 55.1111111111111 & 3.53788768594855 & 15.5774055038537 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 53.3611111111111 & 3.26420727312036 & 16.3473415277644 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 53.3611111111111 & 3.17870860602494 & 16.7870408158741 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 50.8055555555556 & 2.27179402204404 & 22.3636276275802 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 51.1388888888889 & 2.23119033505665 & 22.9200028726327 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 64.6714285714286 & 6.35573204155804 & 10.1752918701675 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 63.5735294117647 & 6.16965712867166 & 10.3042240574967 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 62.4848484848485 & 5.97739496331239 & 10.4535251340029 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 61.453125 & 5.78658691619169 & 10.619926027214 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 60.4677419354839 & 5.61654642366728 & 10.7660005587565 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 59.6166666666667 & 5.48253991134334 & 10.8739138484556 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 58.7413793103448 & 5.32725532816047 & 11.0265747916814 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 58.0714285714286 & 5.23008636061754 & 11.1033402830029 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 57.3518518518519 & 5.12411690043946 & 11.1925338485024 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 56.7307692307692 & 5.04595139479106 & 11.2428291103502 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 56.1 & 4.95541344884356 & 11.3209524450663 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 55.4166666666667 & 4.83585468596144 & 11.4595392677001 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 54.6304347826087 & 4.69817095623004 & 11.6280219028994 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 53.7954545454545 & 4.52343902098729 & 11.8926008056837 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 52.9047619047619 & 4.31347314241105 & 12.2650032023128 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 52.125 & 4.14669894970532 & 12.5702397575074 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 51.3157894736842 & 3.93891935977902 & 13.0278852615462 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 50.6111111111111 & 3.73768406730008 & 13.5407675447728 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 50.1764705882353 & 3.60715040237787 & 13.9102795811227 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 49.625 & 3.45499579851292 & 14.3632591453105 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 48.9666666666667 & 3.23646015416565 & 15.1296986009983 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 48.4285714285714 & 3.01645775450804 & 16.0547819230009 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 47.8076923076923 & 2.70442328888134 & 17.6775923000824 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 47.4166666666667 & 2.61746964509527 & 18.115460003717 \tabularnewline
Median & 48 &  &  \tabularnewline
Midrange & 107 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.2564102564103 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.2564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.2564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.2564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.2564102564103 &  &  \tabularnewline
Midmean - Closest Observation & 48.2564102564103 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.2564102564103 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.75 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130806&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]65.8472222222222[/C][C]6.55736870996023[/C][C]10.0417141592487[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]43.3752498484842[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25.8544266363995[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]85.9580808689135[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]65.7083333333333[/C][C]6.5098468060458[/C][C]10.0936835060863[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]65.5694444444444[/C][C]6.45902658368879[/C][C]10.1515984792553[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]65.2361111111111[/C][C]6.36855455428759[/C][C]10.243472134064[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]64.8472222222222[/C][C]6.20397481383486[/C][C]10.4525282851911[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]64.0138888888889[/C][C]5.97790313752062[/C][C]10.7084185568519[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]63.8472222222222[/C][C]5.9396633600138[/C][C]10.7492998091518[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]62.3888888888889[/C][C]5.58934948649145[/C][C]11.1621019654743[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]62.3888888888889[/C][C]5.51550508867843[/C][C]11.3115458848825[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]61.3888888888889[/C][C]5.27771600326256[/C][C]11.6317150924642[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]61.1111111111111[/C][C]5.22500591741979[/C][C]11.6958931869093[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]61.1111111111111[/C][C]5.22500591741979[/C][C]11.6958931869093[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]61.4444444444444[/C][C]5.1313684768093[/C][C]11.9742802962088[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]61.2638888888889[/C][C]5.09748446106627[/C][C]12.0184552511758[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]61.0694444444444[/C][C]5.00130367937256[/C][C]12.210705120011[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]59.4027777777778[/C][C]4.57213355143275[/C][C]12.9923540311203[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]58.9583333333333[/C][C]4.49366784098488[/C][C]13.1203140551687[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]57.3055555555556[/C][C]4.20813351400704[/C][C]13.6178083144963[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]54.3055555555556[/C][C]3.71545849164873[/C][C]14.6161114913862[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]54.8333333333333[/C][C]3.57252163018253[/C][C]15.3486357843358[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]55.1111111111111[/C][C]3.53788768594855[/C][C]15.5774055038537[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]53.3611111111111[/C][C]3.26420727312036[/C][C]16.3473415277644[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]53.3611111111111[/C][C]3.17870860602494[/C][C]16.7870408158741[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]50.8055555555556[/C][C]2.27179402204404[/C][C]22.3636276275802[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]51.1388888888889[/C][C]2.23119033505665[/C][C]22.9200028726327[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]64.6714285714286[/C][C]6.35573204155804[/C][C]10.1752918701675[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]63.5735294117647[/C][C]6.16965712867166[/C][C]10.3042240574967[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]62.4848484848485[/C][C]5.97739496331239[/C][C]10.4535251340029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]61.453125[/C][C]5.78658691619169[/C][C]10.619926027214[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]60.4677419354839[/C][C]5.61654642366728[/C][C]10.7660005587565[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]59.6166666666667[/C][C]5.48253991134334[/C][C]10.8739138484556[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]58.7413793103448[/C][C]5.32725532816047[/C][C]11.0265747916814[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]58.0714285714286[/C][C]5.23008636061754[/C][C]11.1033402830029[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]57.3518518518519[/C][C]5.12411690043946[/C][C]11.1925338485024[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]56.7307692307692[/C][C]5.04595139479106[/C][C]11.2428291103502[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]56.1[/C][C]4.95541344884356[/C][C]11.3209524450663[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]55.4166666666667[/C][C]4.83585468596144[/C][C]11.4595392677001[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]54.6304347826087[/C][C]4.69817095623004[/C][C]11.6280219028994[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]53.7954545454545[/C][C]4.52343902098729[/C][C]11.8926008056837[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]52.9047619047619[/C][C]4.31347314241105[/C][C]12.2650032023128[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]52.125[/C][C]4.14669894970532[/C][C]12.5702397575074[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]51.3157894736842[/C][C]3.93891935977902[/C][C]13.0278852615462[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]50.6111111111111[/C][C]3.73768406730008[/C][C]13.5407675447728[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]50.1764705882353[/C][C]3.60715040237787[/C][C]13.9102795811227[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]49.625[/C][C]3.45499579851292[/C][C]14.3632591453105[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]48.9666666666667[/C][C]3.23646015416565[/C][C]15.1296986009983[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]48.4285714285714[/C][C]3.01645775450804[/C][C]16.0547819230009[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]47.8076923076923[/C][C]2.70442328888134[/C][C]17.6775923000824[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]47.4166666666667[/C][C]2.61746964509527[/C][C]18.115460003717[/C][/ROW]
[ROW][C]Median[/C][C]48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.2564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130806&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 Mean65.84722222222226.5573687099602310.0417141592487
Geometric Mean43.3752498484842
Harmonic Mean25.8544266363995
Quadratic Mean85.9580808689135
Winsorized Mean ( 1 / 24 )65.70833333333336.509846806045810.0936835060863
Winsorized Mean ( 2 / 24 )65.56944444444446.4590265836887910.1515984792553
Winsorized Mean ( 3 / 24 )65.23611111111116.3685545542875910.243472134064
Winsorized Mean ( 4 / 24 )64.84722222222226.2039748138348610.4525282851911
Winsorized Mean ( 5 / 24 )64.01388888888895.9779031375206210.7084185568519
Winsorized Mean ( 6 / 24 )63.84722222222225.939663360013810.7492998091518
Winsorized Mean ( 7 / 24 )62.38888888888895.5893494864914511.1621019654743
Winsorized Mean ( 8 / 24 )62.38888888888895.5155050886784311.3115458848825
Winsorized Mean ( 9 / 24 )61.38888888888895.2777160032625611.6317150924642
Winsorized Mean ( 10 / 24 )61.11111111111115.2250059174197911.6958931869093
Winsorized Mean ( 11 / 24 )61.11111111111115.2250059174197911.6958931869093
Winsorized Mean ( 12 / 24 )61.44444444444445.131368476809311.9742802962088
Winsorized Mean ( 13 / 24 )61.26388888888895.0974844610662712.0184552511758
Winsorized Mean ( 14 / 24 )61.06944444444445.0013036793725612.210705120011
Winsorized Mean ( 15 / 24 )59.40277777777784.5721335514327512.9923540311203
Winsorized Mean ( 16 / 24 )58.95833333333334.4936678409848813.1203140551687
Winsorized Mean ( 17 / 24 )57.30555555555564.2081335140070413.6178083144963
Winsorized Mean ( 18 / 24 )54.30555555555563.7154584916487314.6161114913862
Winsorized Mean ( 19 / 24 )54.83333333333333.5725216301825315.3486357843358
Winsorized Mean ( 20 / 24 )55.11111111111113.5378876859485515.5774055038537
Winsorized Mean ( 21 / 24 )53.36111111111113.2642072731203616.3473415277644
Winsorized Mean ( 22 / 24 )53.36111111111113.1787086060249416.7870408158741
Winsorized Mean ( 23 / 24 )50.80555555555562.2717940220440422.3636276275802
Winsorized Mean ( 24 / 24 )51.13888888888892.2311903350566522.9200028726327
Trimmed Mean ( 1 / 24 )64.67142857142866.3557320415580410.1752918701675
Trimmed Mean ( 2 / 24 )63.57352941176476.1696571286716610.3042240574967
Trimmed Mean ( 3 / 24 )62.48484848484855.9773949633123910.4535251340029
Trimmed Mean ( 4 / 24 )61.4531255.7865869161916910.619926027214
Trimmed Mean ( 5 / 24 )60.46774193548395.6165464236672810.7660005587565
Trimmed Mean ( 6 / 24 )59.61666666666675.4825399113433410.8739138484556
Trimmed Mean ( 7 / 24 )58.74137931034485.3272553281604711.0265747916814
Trimmed Mean ( 8 / 24 )58.07142857142865.2300863606175411.1033402830029
Trimmed Mean ( 9 / 24 )57.35185185185195.1241169004394611.1925338485024
Trimmed Mean ( 10 / 24 )56.73076923076925.0459513947910611.2428291103502
Trimmed Mean ( 11 / 24 )56.14.9554134488435611.3209524450663
Trimmed Mean ( 12 / 24 )55.41666666666674.8358546859614411.4595392677001
Trimmed Mean ( 13 / 24 )54.63043478260874.6981709562300411.6280219028994
Trimmed Mean ( 14 / 24 )53.79545454545454.5234390209872911.8926008056837
Trimmed Mean ( 15 / 24 )52.90476190476194.3134731424110512.2650032023128
Trimmed Mean ( 16 / 24 )52.1254.1466989497053212.5702397575074
Trimmed Mean ( 17 / 24 )51.31578947368423.9389193597790213.0278852615462
Trimmed Mean ( 18 / 24 )50.61111111111113.7376840673000813.5407675447728
Trimmed Mean ( 19 / 24 )50.17647058823533.6071504023778713.9102795811227
Trimmed Mean ( 20 / 24 )49.6253.4549957985129214.3632591453105
Trimmed Mean ( 21 / 24 )48.96666666666673.2364601541656515.1296986009983
Trimmed Mean ( 22 / 24 )48.42857142857143.0164577545080416.0547819230009
Trimmed Mean ( 23 / 24 )47.80769230769232.7044232888813417.6775923000824
Trimmed Mean ( 24 / 24 )47.41666666666672.6174696450952718.115460003717
Median48
Midrange107
Midmean - Weighted Average at Xnp48.2564102564103
Midmean - Weighted Average at X(n+1)p48.2564102564103
Midmean - Empirical Distribution Function48.2564102564103
Midmean - Empirical Distribution Function - Averaging48.2564102564103
Midmean - Empirical Distribution Function - Interpolation48.2564102564103
Midmean - Closest Observation48.2564102564103
Midmean - True Basic - Statistics Graphics Toolkit48.2564102564103
Midmean - MS Excel (old versions)49.75
Number of observations72



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')