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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, 15 Nov 2011 17:10:15 -0500
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/Nov/15/t1321395044qrdu0j3pcb41eso.htm/, Retrieved Tue, 23 Apr 2024 22:08:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143608, Retrieved Tue, 23 Apr 2024 22:08:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
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]
- RM D    [Central Tendency] [claims] [2011-11-15 22:10:15] [13dfa60174f50d862e8699db2153bfc5] [Current]
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Dataseries X:
108
19
13
124
40
57
23
14
45
10
5
48
11
23
7
2
24
6
3
23
6
9
9
3
29
7
4
20
7
4
0
25
6
5
22
11
61
12
4
16
13
60
41
37
55
41
11
27
8
3
17
13
13
15
8
29
30
24
9
31
14
53
26




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=143608&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=143608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143608&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 Mean22.90476190476192.942068606171087.78525757581534
Geometric Mean0
Harmonic Mean0
Quadratic Mean32.5773804085859
Winsorized Mean ( 1 / 21 )22.68253968253972.805326054819328.08552704366501
Winsorized Mean ( 2 / 21 )21.22222222222222.199874832873349.64701350508342
Winsorized Mean ( 3 / 21 )21.17460317460322.186110285064269.68597207527467
Winsorized Mean ( 4 / 21 )20.9841269841272.132873902080769.83842831198582
Winsorized Mean ( 5 / 21 )20.90476190476192.0796621153289810.0519991928857
Winsorized Mean ( 6 / 21 )20.71428571428572.0300392056210910.2038845638689
Winsorized Mean ( 7 / 21 )20.15873015873021.8926930329972610.6508185993621
Winsorized Mean ( 8 / 21 )19.90476190476191.7870092590749511.1385891279968
Winsorized Mean ( 9 / 21 )19.33333333333331.6620519831445911.6322073734149
Winsorized Mean ( 10 / 21 )19.49206349206351.6404813987354611.881916800208
Winsorized Mean ( 11 / 21 )19.31746031746031.603858857387912.0443642708819
Winsorized Mean ( 12 / 21 )18.74603174603171.4877840603131912.5999681311854
Winsorized Mean ( 13 / 21 )17.71428571428571.2270272151430814.4367504613336
Winsorized Mean ( 14 / 21 )17.49206349206351.188757933910114.714571396826
Winsorized Mean ( 15 / 21 )17.25396825396831.148914368568115.0176277066428
Winsorized Mean ( 16 / 21 )17.50793650793651.1131281523711215.7285901633538
Winsorized Mean ( 17 / 21 )16.9682539682541.0255237953218116.5459388125941
Winsorized Mean ( 18 / 21 )16.9682539682540.94116971756412318.0288992002103
Winsorized Mean ( 19 / 21 )16.66666666666670.89517109269806818.6184147395029
Winsorized Mean ( 20 / 21 )16.34920634920630.84822598228865919.2745880114323
Winsorized Mean ( 21 / 21 )16.68253968253970.80252590128619920.7875405090387
Trimmed Mean ( 1 / 21 )21.62295081967212.504876548164488.63234191541974
Trimmed Mean ( 2 / 21 )20.49152542372882.096638494271489.77351387934381
Trimmed Mean ( 3 / 21 )20.08771929824562.024796270848659.9208594896445
Trimmed Mean ( 4 / 21 )19.67272727272731.9412333448856710.1341383427998
Trimmed Mean ( 5 / 21 )19.28301886792451.8578623885874410.3791427106642
Trimmed Mean ( 6 / 21 )18.88235294117651.7707087445146910.663726036069
Trimmed Mean ( 7 / 21 )18.48979591836731.6754333506283111.0358289760875
Trimmed Mean ( 8 / 21 )18.17021276595741.5973842948739311.3749789729788
Trimmed Mean ( 9 / 21 )17.86666666666671.5273929726593911.6974917303426
Trimmed Mean ( 10 / 21 )17.62790697674421.4725330387402411.9711453074255
Trimmed Mean ( 11 / 21 )17.34146341463411.4036580068232412.3544790328817
Trimmed Mean ( 12 / 21 )17.05128205128211.3209352992134512.9084914767856
Trimmed Mean ( 13 / 21 )16.81081081081081.2447112367210213.5057917972172
Trimmed Mean ( 14 / 21 )16.68571428571431.2180515012855213.6986935840597
Trimmed Mean ( 15 / 21 )16.57575757575761.1894663170412113.935457724427
Trimmed Mean ( 16 / 21 )16.48387096774191.1582996137200214.2310942458161
Trimmed Mean ( 17 / 21 )16.34482758620691.1199884126654414.593747043604
Trimmed Mean ( 18 / 21 )16.25925925925931.0907440057221414.9065767714163
Trimmed Mean ( 19 / 21 )16.161.0703270528207715.0981888735891
Trimmed Mean ( 20 / 21 )16.08695652173911.049963378767115.3214453447214
Trimmed Mean ( 21 / 21 )16.0476190476191.0292766541795315.5911619897871
Median14
Midrange62
Midmean - Weighted Average at Xnp16.0285714285714
Midmean - Weighted Average at X(n+1)p16.0285714285714
Midmean - Empirical Distribution Function16.0285714285714
Midmean - Empirical Distribution Function - Averaging16.0285714285714
Midmean - Empirical Distribution Function - Interpolation16.875
Midmean - Closest Observation16.0285714285714
Midmean - True Basic - Statistics Graphics Toolkit16.0285714285714
Midmean - MS Excel (old versions)16.0285714285714
Number of observations63

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22.9047619047619 & 2.94206860617108 & 7.78525757581534 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 32.5773804085859 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 22.6825396825397 & 2.80532605481932 & 8.08552704366501 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 21.2222222222222 & 2.19987483287334 & 9.64701350508342 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 21.1746031746032 & 2.18611028506426 & 9.68597207527467 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 20.984126984127 & 2.13287390208076 & 9.83842831198582 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 20.9047619047619 & 2.07966211532898 & 10.0519991928857 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 20.7142857142857 & 2.03003920562109 & 10.2038845638689 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 20.1587301587302 & 1.89269303299726 & 10.6508185993621 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 19.9047619047619 & 1.78700925907495 & 11.1385891279968 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 19.3333333333333 & 1.66205198314459 & 11.6322073734149 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 19.4920634920635 & 1.64048139873546 & 11.881916800208 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 19.3174603174603 & 1.6038588573879 & 12.0443642708819 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 18.7460317460317 & 1.48778406031319 & 12.5999681311854 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 17.7142857142857 & 1.22702721514308 & 14.4367504613336 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 17.4920634920635 & 1.1887579339101 & 14.714571396826 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 17.2539682539683 & 1.1489143685681 & 15.0176277066428 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 17.5079365079365 & 1.11312815237112 & 15.7285901633538 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 16.968253968254 & 1.02552379532181 & 16.5459388125941 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 16.968253968254 & 0.941169717564123 & 18.0288992002103 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 16.6666666666667 & 0.895171092698068 & 18.6184147395029 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 16.3492063492063 & 0.848225982288659 & 19.2745880114323 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 16.6825396825397 & 0.802525901286199 & 20.7875405090387 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 21.6229508196721 & 2.50487654816448 & 8.63234191541974 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 20.4915254237288 & 2.09663849427148 & 9.77351387934381 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 20.0877192982456 & 2.02479627084865 & 9.9208594896445 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 19.6727272727273 & 1.94123334488567 & 10.1341383427998 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 19.2830188679245 & 1.85786238858744 & 10.3791427106642 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 18.8823529411765 & 1.77070874451469 & 10.663726036069 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 18.4897959183673 & 1.67543335062831 & 11.0358289760875 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 18.1702127659574 & 1.59738429487393 & 11.3749789729788 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 17.8666666666667 & 1.52739297265939 & 11.6974917303426 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 17.6279069767442 & 1.47253303874024 & 11.9711453074255 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 17.3414634146341 & 1.40365800682324 & 12.3544790328817 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 17.0512820512821 & 1.32093529921345 & 12.9084914767856 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 16.8108108108108 & 1.24471123672102 & 13.5057917972172 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 16.6857142857143 & 1.21805150128552 & 13.6986935840597 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 16.5757575757576 & 1.18946631704121 & 13.935457724427 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 16.4838709677419 & 1.15829961372002 & 14.2310942458161 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 16.3448275862069 & 1.11998841266544 & 14.593747043604 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 16.2592592592593 & 1.09074400572214 & 14.9065767714163 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 16.16 & 1.07032705282077 & 15.0981888735891 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 16.0869565217391 & 1.0499633787671 & 15.3214453447214 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 16.047619047619 & 1.02927665417953 & 15.5911619897871 \tabularnewline
Median & 14 &  &  \tabularnewline
Midrange & 62 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.0285714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.0285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.0285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.0285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.875 &  &  \tabularnewline
Midmean - Closest Observation & 16.0285714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.0285714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.0285714285714 &  &  \tabularnewline
Number of observations & 63 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143608&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]22.9047619047619[/C][C]2.94206860617108[/C][C]7.78525757581534[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32.5773804085859[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]22.6825396825397[/C][C]2.80532605481932[/C][C]8.08552704366501[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]21.2222222222222[/C][C]2.19987483287334[/C][C]9.64701350508342[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]21.1746031746032[/C][C]2.18611028506426[/C][C]9.68597207527467[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]20.984126984127[/C][C]2.13287390208076[/C][C]9.83842831198582[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]20.9047619047619[/C][C]2.07966211532898[/C][C]10.0519991928857[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]20.7142857142857[/C][C]2.03003920562109[/C][C]10.2038845638689[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]20.1587301587302[/C][C]1.89269303299726[/C][C]10.6508185993621[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]19.9047619047619[/C][C]1.78700925907495[/C][C]11.1385891279968[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]19.3333333333333[/C][C]1.66205198314459[/C][C]11.6322073734149[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]19.4920634920635[/C][C]1.64048139873546[/C][C]11.881916800208[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]19.3174603174603[/C][C]1.6038588573879[/C][C]12.0443642708819[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]18.7460317460317[/C][C]1.48778406031319[/C][C]12.5999681311854[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]17.7142857142857[/C][C]1.22702721514308[/C][C]14.4367504613336[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]17.4920634920635[/C][C]1.1887579339101[/C][C]14.714571396826[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]17.2539682539683[/C][C]1.1489143685681[/C][C]15.0176277066428[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]17.5079365079365[/C][C]1.11312815237112[/C][C]15.7285901633538[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]16.968253968254[/C][C]1.02552379532181[/C][C]16.5459388125941[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]16.968253968254[/C][C]0.941169717564123[/C][C]18.0288992002103[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]16.6666666666667[/C][C]0.895171092698068[/C][C]18.6184147395029[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]16.3492063492063[/C][C]0.848225982288659[/C][C]19.2745880114323[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]16.6825396825397[/C][C]0.802525901286199[/C][C]20.7875405090387[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]21.6229508196721[/C][C]2.50487654816448[/C][C]8.63234191541974[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]20.4915254237288[/C][C]2.09663849427148[/C][C]9.77351387934381[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]20.0877192982456[/C][C]2.02479627084865[/C][C]9.9208594896445[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]19.6727272727273[/C][C]1.94123334488567[/C][C]10.1341383427998[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]19.2830188679245[/C][C]1.85786238858744[/C][C]10.3791427106642[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]18.8823529411765[/C][C]1.77070874451469[/C][C]10.663726036069[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]18.4897959183673[/C][C]1.67543335062831[/C][C]11.0358289760875[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]18.1702127659574[/C][C]1.59738429487393[/C][C]11.3749789729788[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]17.8666666666667[/C][C]1.52739297265939[/C][C]11.6974917303426[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]17.6279069767442[/C][C]1.47253303874024[/C][C]11.9711453074255[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]17.3414634146341[/C][C]1.40365800682324[/C][C]12.3544790328817[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]17.0512820512821[/C][C]1.32093529921345[/C][C]12.9084914767856[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]16.8108108108108[/C][C]1.24471123672102[/C][C]13.5057917972172[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]16.6857142857143[/C][C]1.21805150128552[/C][C]13.6986935840597[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]16.5757575757576[/C][C]1.18946631704121[/C][C]13.935457724427[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]16.4838709677419[/C][C]1.15829961372002[/C][C]14.2310942458161[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]16.3448275862069[/C][C]1.11998841266544[/C][C]14.593747043604[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]16.2592592592593[/C][C]1.09074400572214[/C][C]14.9065767714163[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]16.16[/C][C]1.07032705282077[/C][C]15.0981888735891[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]16.0869565217391[/C][C]1.0499633787671[/C][C]15.3214453447214[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]16.047619047619[/C][C]1.02927665417953[/C][C]15.5911619897871[/C][/ROW]
[ROW][C]Median[/C][C]14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.0285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]63[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143608&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 Mean22.90476190476192.942068606171087.78525757581534
Geometric Mean0
Harmonic Mean0
Quadratic Mean32.5773804085859
Winsorized Mean ( 1 / 21 )22.68253968253972.805326054819328.08552704366501
Winsorized Mean ( 2 / 21 )21.22222222222222.199874832873349.64701350508342
Winsorized Mean ( 3 / 21 )21.17460317460322.186110285064269.68597207527467
Winsorized Mean ( 4 / 21 )20.9841269841272.132873902080769.83842831198582
Winsorized Mean ( 5 / 21 )20.90476190476192.0796621153289810.0519991928857
Winsorized Mean ( 6 / 21 )20.71428571428572.0300392056210910.2038845638689
Winsorized Mean ( 7 / 21 )20.15873015873021.8926930329972610.6508185993621
Winsorized Mean ( 8 / 21 )19.90476190476191.7870092590749511.1385891279968
Winsorized Mean ( 9 / 21 )19.33333333333331.6620519831445911.6322073734149
Winsorized Mean ( 10 / 21 )19.49206349206351.6404813987354611.881916800208
Winsorized Mean ( 11 / 21 )19.31746031746031.603858857387912.0443642708819
Winsorized Mean ( 12 / 21 )18.74603174603171.4877840603131912.5999681311854
Winsorized Mean ( 13 / 21 )17.71428571428571.2270272151430814.4367504613336
Winsorized Mean ( 14 / 21 )17.49206349206351.188757933910114.714571396826
Winsorized Mean ( 15 / 21 )17.25396825396831.148914368568115.0176277066428
Winsorized Mean ( 16 / 21 )17.50793650793651.1131281523711215.7285901633538
Winsorized Mean ( 17 / 21 )16.9682539682541.0255237953218116.5459388125941
Winsorized Mean ( 18 / 21 )16.9682539682540.94116971756412318.0288992002103
Winsorized Mean ( 19 / 21 )16.66666666666670.89517109269806818.6184147395029
Winsorized Mean ( 20 / 21 )16.34920634920630.84822598228865919.2745880114323
Winsorized Mean ( 21 / 21 )16.68253968253970.80252590128619920.7875405090387
Trimmed Mean ( 1 / 21 )21.62295081967212.504876548164488.63234191541974
Trimmed Mean ( 2 / 21 )20.49152542372882.096638494271489.77351387934381
Trimmed Mean ( 3 / 21 )20.08771929824562.024796270848659.9208594896445
Trimmed Mean ( 4 / 21 )19.67272727272731.9412333448856710.1341383427998
Trimmed Mean ( 5 / 21 )19.28301886792451.8578623885874410.3791427106642
Trimmed Mean ( 6 / 21 )18.88235294117651.7707087445146910.663726036069
Trimmed Mean ( 7 / 21 )18.48979591836731.6754333506283111.0358289760875
Trimmed Mean ( 8 / 21 )18.17021276595741.5973842948739311.3749789729788
Trimmed Mean ( 9 / 21 )17.86666666666671.5273929726593911.6974917303426
Trimmed Mean ( 10 / 21 )17.62790697674421.4725330387402411.9711453074255
Trimmed Mean ( 11 / 21 )17.34146341463411.4036580068232412.3544790328817
Trimmed Mean ( 12 / 21 )17.05128205128211.3209352992134512.9084914767856
Trimmed Mean ( 13 / 21 )16.81081081081081.2447112367210213.5057917972172
Trimmed Mean ( 14 / 21 )16.68571428571431.2180515012855213.6986935840597
Trimmed Mean ( 15 / 21 )16.57575757575761.1894663170412113.935457724427
Trimmed Mean ( 16 / 21 )16.48387096774191.1582996137200214.2310942458161
Trimmed Mean ( 17 / 21 )16.34482758620691.1199884126654414.593747043604
Trimmed Mean ( 18 / 21 )16.25925925925931.0907440057221414.9065767714163
Trimmed Mean ( 19 / 21 )16.161.0703270528207715.0981888735891
Trimmed Mean ( 20 / 21 )16.08695652173911.049963378767115.3214453447214
Trimmed Mean ( 21 / 21 )16.0476190476191.0292766541795315.5911619897871
Median14
Midrange62
Midmean - Weighted Average at Xnp16.0285714285714
Midmean - Weighted Average at X(n+1)p16.0285714285714
Midmean - Empirical Distribution Function16.0285714285714
Midmean - Empirical Distribution Function - Averaging16.0285714285714
Midmean - Empirical Distribution Function - Interpolation16.875
Midmean - Closest Observation16.0285714285714
Midmean - True Basic - Statistics Graphics Toolkit16.0285714285714
Midmean - MS Excel (old versions)16.0285714285714
Number of observations63



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')