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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 14:22:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444397257dzrim1auiuw6dh1.htm/, Retrieved Mon, 13 May 2024 21:46:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281897, Retrieved Mon, 13 May 2024 21:46:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [Kwartielen maximu...] [2015-10-09 11:30:25] [9a9e8da277f220390e943650176db0bb]
- RM D    [Central Tendency] [Centrummaten cons...] [2015-10-09 13:22:09] [25948359fd1b125334369436fee15348] [Current]
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Dataseries X:
98,91
98,15
98,59
98,6
98,7
98,33
98,33
98,6
98,52
99,17
99,49
98,83
98,83
97,39
99,28
98,78
98,75
98,47
98,47
97,82
97,79
97,96
98,21
98,34
98,34
98,49
98,14
98,05
97,77
97,59
97,59
97,67
97,67
97,36
97,31
97,24
97,24
96,89
96,48
96,47
97,13
97,21
97,43
97,98
97,97
98,2
98,67
98,75
98,77
98,72
99,23
99,67
99,76
99,57
99,57
100,21
100,62
101,05
101,42
101,42
101,52
101,87
101,53
101,77
101,76
102,04
102,05
101,9
102,17
102,14
102,09
102,27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281897&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281897&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281897&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.04263888888890.19208109849255515.629281934424
Geometric Mean99.0295152296734
Harmonic Mean99.0164925426247
Quadratic Mean99.0558623889122
Winsorized Mean ( 1 / 24 )99.04138888888890.191730985896588516.564333228368
Winsorized Mean ( 2 / 24 )99.05194444444440.189552499828599522.556782601185
Winsorized Mean ( 3 / 24 )99.05986111111110.187548167319149528.183572930052
Winsorized Mean ( 4 / 24 )99.06208333333330.186411413497564531.416405651728
Winsorized Mean ( 5 / 24 )99.06347222222220.185965121980444532.699202771151
Winsorized Mean ( 6 / 24 )99.05180555555550.183373696622563540.163651493775
Winsorized Mean ( 7 / 24 )99.05569444444440.181802919398762544.852056127758
Winsorized Mean ( 8 / 24 )99.05013888888890.178654387525586554.423209307991
Winsorized Mean ( 9 / 24 )99.05263888888890.177889733154553556.820436639987
Winsorized Mean ( 10 / 24 )99.026250.170426423380839581.049863252212
Winsorized Mean ( 11 / 24 )99.04916666666670.166991555407645593.138775340324
Winsorized Mean ( 12 / 24 )99.03250.163541205032093605.550753894508
Winsorized Mean ( 13 / 24 )99.04694444444440.161778026465225612.239786876958
Winsorized Mean ( 14 / 24 )98.9750.147190033980859672.43003702867
Winsorized Mean ( 15 / 24 )98.906250.127154120976163777.845415002644
Winsorized Mean ( 16 / 24 )98.81958333333330.109768649425569900.253249452066
Winsorized Mean ( 17 / 24 )98.72041666666670.09066512993640421088.84658011203
Winsorized Mean ( 18 / 24 )98.73291666666670.08227317124417181200.06212442748
Winsorized Mean ( 19 / 24 )98.70916666666670.07774596236163481269.63720903629
Winsorized Mean ( 20 / 24 )98.71194444444440.07737492782385491275.76137672352
Winsorized Mean ( 21 / 24 )98.70902777777780.07105100763207331389.26992125048
Winsorized Mean ( 22 / 24 )98.67236111111110.05772197849918651709.44177030421
Winsorized Mean ( 23 / 24 )98.65958333333330.05495389926657561795.31543075308
Winsorized Mean ( 24 / 24 )98.656250.04987795649200621977.95292627538
Trimmed Mean ( 1 / 24 )99.03328571428570.188470768823646525.457004990266
Trimmed Mean ( 2 / 24 )99.02470588235290.184569531045967536.517080154961
Trimmed Mean ( 3 / 24 )99.00984848484850.181246460288464546.271901405793
Trimmed Mean ( 4 / 24 )98.991093750.178093424127995555.838006005519
Trimmed Mean ( 5 / 24 )98.97048387096770.174625447540085566.758655540448
Trimmed Mean ( 6 / 24 )98.94816666666670.170477974067574580.416134153761
Trimmed Mean ( 7 / 24 )98.9267241379310.166113065076328595.53849116248
Trimmed Mean ( 8 / 24 )98.90303571428570.161080144536258613.99892580816
Trimmed Mean ( 9 / 24 )98.87851851851850.155589186408125635.510222793702
Trimmed Mean ( 10 / 24 )98.85173076923080.148810446900158664.279510131123
Trimmed Mean ( 11 / 24 )98.82660.142142960516832695.262006930671
Trimmed Mean ( 12 / 24 )98.796250.134272278484814735.790373968916
Trimmed Mean ( 13 / 24 )98.76543478260870.124897525733969790.771748296905
Trimmed Mean ( 14 / 24 )98.730.112601375513099876.809892864186
Trimmed Mean ( 15 / 24 )98.70.100651189863339980.614338827109
Trimmed Mean ( 16 / 24 )98.675250.09082667877294131086.41261943178
Trimmed Mean ( 17 / 24 )98.65815789473680.08314142885759991186.63053125672
Trimmed Mean ( 18 / 24 )98.65083333333330.07868197490278931253.79203375634
Trimmed Mean ( 19 / 24 )98.64117647058820.07482214765705841318.34195568273
Trimmed Mean ( 20 / 24 )98.6331250.07075405707619821394.02783495196
Trimmed Mean ( 21 / 24 )98.62366666666670.06485258851848471520.73600945869
Trimmed Mean ( 22 / 24 )98.61321428571430.05837765565926841689.22874980263
Trimmed Mean ( 23 / 24 )98.60576923076920.05415696013774181820.74047324623
Trimmed Mean ( 24 / 24 )98.598750.04867562144635042025.6289918902
Median98.6
Midrange99.37
Midmean - Weighted Average at Xnp98.6283783783784
Midmean - Weighted Average at X(n+1)p98.6508333333333
Midmean - Empirical Distribution Function98.6283783783784
Midmean - Empirical Distribution Function - Averaging98.6508333333333
Midmean - Empirical Distribution Function - Interpolation98.6508333333333
Midmean - Closest Observation98.6283783783784
Midmean - True Basic - Statistics Graphics Toolkit98.6508333333333
Midmean - MS Excel (old versions)98.6581578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.0426388888889 & 0.19208109849255 & 515.629281934424 \tabularnewline
Geometric Mean & 99.0295152296734 &  &  \tabularnewline
Harmonic Mean & 99.0164925426247 &  &  \tabularnewline
Quadratic Mean & 99.0558623889122 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.0413888888889 & 0.191730985896588 & 516.564333228368 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.0519444444444 & 0.189552499828599 & 522.556782601185 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.0598611111111 & 0.187548167319149 & 528.183572930052 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.0620833333333 & 0.186411413497564 & 531.416405651728 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.0634722222222 & 0.185965121980444 & 532.699202771151 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.0518055555555 & 0.183373696622563 & 540.163651493775 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.0556944444444 & 0.181802919398762 & 544.852056127758 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.0501388888889 & 0.178654387525586 & 554.423209307991 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.0526388888889 & 0.177889733154553 & 556.820436639987 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.02625 & 0.170426423380839 & 581.049863252212 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.0491666666667 & 0.166991555407645 & 593.138775340324 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.0325 & 0.163541205032093 & 605.550753894508 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.0469444444444 & 0.161778026465225 & 612.239786876958 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.975 & 0.147190033980859 & 672.43003702867 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.90625 & 0.127154120976163 & 777.845415002644 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.8195833333333 & 0.109768649425569 & 900.253249452066 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.7204166666667 & 0.0906651299364042 & 1088.84658011203 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.7329166666667 & 0.0822731712441718 & 1200.06212442748 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.7091666666667 & 0.0777459623616348 & 1269.63720903629 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.7119444444444 & 0.0773749278238549 & 1275.76137672352 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.7090277777778 & 0.0710510076320733 & 1389.26992125048 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.6723611111111 & 0.0577219784991865 & 1709.44177030421 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.6595833333333 & 0.0549538992665756 & 1795.31543075308 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.65625 & 0.0498779564920062 & 1977.95292627538 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.0332857142857 & 0.188470768823646 & 525.457004990266 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.0247058823529 & 0.184569531045967 & 536.517080154961 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.0098484848485 & 0.181246460288464 & 546.271901405793 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.99109375 & 0.178093424127995 & 555.838006005519 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.9704838709677 & 0.174625447540085 & 566.758655540448 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.9481666666667 & 0.170477974067574 & 580.416134153761 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.926724137931 & 0.166113065076328 & 595.53849116248 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.9030357142857 & 0.161080144536258 & 613.99892580816 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.8785185185185 & 0.155589186408125 & 635.510222793702 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.8517307692308 & 0.148810446900158 & 664.279510131123 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.8266 & 0.142142960516832 & 695.262006930671 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.79625 & 0.134272278484814 & 735.790373968916 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.7654347826087 & 0.124897525733969 & 790.771748296905 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.73 & 0.112601375513099 & 876.809892864186 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.7 & 0.100651189863339 & 980.614338827109 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.67525 & 0.0908266787729413 & 1086.41261943178 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.6581578947368 & 0.0831414288575999 & 1186.63053125672 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.6508333333333 & 0.0786819749027893 & 1253.79203375634 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.6411764705882 & 0.0748221476570584 & 1318.34195568273 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.633125 & 0.0707540570761982 & 1394.02783495196 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.6236666666667 & 0.0648525885184847 & 1520.73600945869 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.6132142857143 & 0.0583776556592684 & 1689.22874980263 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.6057692307692 & 0.0541569601377418 & 1820.74047324623 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.59875 & 0.0486756214463504 & 2025.6289918902 \tabularnewline
Median & 98.6 &  &  \tabularnewline
Midrange & 99.37 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.6283783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.6508333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.6283783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.6508333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.6508333333333 &  &  \tabularnewline
Midmean - Closest Observation & 98.6283783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.6508333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.6581578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281897&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]99.0426388888889[/C][C]0.19208109849255[/C][C]515.629281934424[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.0295152296734[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.0164925426247[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.0558623889122[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.0413888888889[/C][C]0.191730985896588[/C][C]516.564333228368[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.0519444444444[/C][C]0.189552499828599[/C][C]522.556782601185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.0598611111111[/C][C]0.187548167319149[/C][C]528.183572930052[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.0620833333333[/C][C]0.186411413497564[/C][C]531.416405651728[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.0634722222222[/C][C]0.185965121980444[/C][C]532.699202771151[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.0518055555555[/C][C]0.183373696622563[/C][C]540.163651493775[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.0556944444444[/C][C]0.181802919398762[/C][C]544.852056127758[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.0501388888889[/C][C]0.178654387525586[/C][C]554.423209307991[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.0526388888889[/C][C]0.177889733154553[/C][C]556.820436639987[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.02625[/C][C]0.170426423380839[/C][C]581.049863252212[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.0491666666667[/C][C]0.166991555407645[/C][C]593.138775340324[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.0325[/C][C]0.163541205032093[/C][C]605.550753894508[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.0469444444444[/C][C]0.161778026465225[/C][C]612.239786876958[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.975[/C][C]0.147190033980859[/C][C]672.43003702867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.90625[/C][C]0.127154120976163[/C][C]777.845415002644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.8195833333333[/C][C]0.109768649425569[/C][C]900.253249452066[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.7204166666667[/C][C]0.0906651299364042[/C][C]1088.84658011203[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.7329166666667[/C][C]0.0822731712441718[/C][C]1200.06212442748[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.7091666666667[/C][C]0.0777459623616348[/C][C]1269.63720903629[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.7119444444444[/C][C]0.0773749278238549[/C][C]1275.76137672352[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.7090277777778[/C][C]0.0710510076320733[/C][C]1389.26992125048[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.6723611111111[/C][C]0.0577219784991865[/C][C]1709.44177030421[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.6595833333333[/C][C]0.0549538992665756[/C][C]1795.31543075308[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.65625[/C][C]0.0498779564920062[/C][C]1977.95292627538[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.0332857142857[/C][C]0.188470768823646[/C][C]525.457004990266[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.0247058823529[/C][C]0.184569531045967[/C][C]536.517080154961[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.0098484848485[/C][C]0.181246460288464[/C][C]546.271901405793[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.99109375[/C][C]0.178093424127995[/C][C]555.838006005519[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.9704838709677[/C][C]0.174625447540085[/C][C]566.758655540448[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.9481666666667[/C][C]0.170477974067574[/C][C]580.416134153761[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.926724137931[/C][C]0.166113065076328[/C][C]595.53849116248[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.9030357142857[/C][C]0.161080144536258[/C][C]613.99892580816[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.8785185185185[/C][C]0.155589186408125[/C][C]635.510222793702[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.8517307692308[/C][C]0.148810446900158[/C][C]664.279510131123[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.8266[/C][C]0.142142960516832[/C][C]695.262006930671[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.79625[/C][C]0.134272278484814[/C][C]735.790373968916[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.7654347826087[/C][C]0.124897525733969[/C][C]790.771748296905[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.73[/C][C]0.112601375513099[/C][C]876.809892864186[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.7[/C][C]0.100651189863339[/C][C]980.614338827109[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.67525[/C][C]0.0908266787729413[/C][C]1086.41261943178[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.6581578947368[/C][C]0.0831414288575999[/C][C]1186.63053125672[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.6508333333333[/C][C]0.0786819749027893[/C][C]1253.79203375634[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.6411764705882[/C][C]0.0748221476570584[/C][C]1318.34195568273[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.633125[/C][C]0.0707540570761982[/C][C]1394.02783495196[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.6236666666667[/C][C]0.0648525885184847[/C][C]1520.73600945869[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.6132142857143[/C][C]0.0583776556592684[/C][C]1689.22874980263[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.6057692307692[/C][C]0.0541569601377418[/C][C]1820.74047324623[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.59875[/C][C]0.0486756214463504[/C][C]2025.6289918902[/C][/ROW]
[ROW][C]Median[/C][C]98.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.6283783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.6508333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.6283783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.6508333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.6508333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.6283783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.6508333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.6581578947368[/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=281897&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281897&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 Mean99.04263888888890.19208109849255515.629281934424
Geometric Mean99.0295152296734
Harmonic Mean99.0164925426247
Quadratic Mean99.0558623889122
Winsorized Mean ( 1 / 24 )99.04138888888890.191730985896588516.564333228368
Winsorized Mean ( 2 / 24 )99.05194444444440.189552499828599522.556782601185
Winsorized Mean ( 3 / 24 )99.05986111111110.187548167319149528.183572930052
Winsorized Mean ( 4 / 24 )99.06208333333330.186411413497564531.416405651728
Winsorized Mean ( 5 / 24 )99.06347222222220.185965121980444532.699202771151
Winsorized Mean ( 6 / 24 )99.05180555555550.183373696622563540.163651493775
Winsorized Mean ( 7 / 24 )99.05569444444440.181802919398762544.852056127758
Winsorized Mean ( 8 / 24 )99.05013888888890.178654387525586554.423209307991
Winsorized Mean ( 9 / 24 )99.05263888888890.177889733154553556.820436639987
Winsorized Mean ( 10 / 24 )99.026250.170426423380839581.049863252212
Winsorized Mean ( 11 / 24 )99.04916666666670.166991555407645593.138775340324
Winsorized Mean ( 12 / 24 )99.03250.163541205032093605.550753894508
Winsorized Mean ( 13 / 24 )99.04694444444440.161778026465225612.239786876958
Winsorized Mean ( 14 / 24 )98.9750.147190033980859672.43003702867
Winsorized Mean ( 15 / 24 )98.906250.127154120976163777.845415002644
Winsorized Mean ( 16 / 24 )98.81958333333330.109768649425569900.253249452066
Winsorized Mean ( 17 / 24 )98.72041666666670.09066512993640421088.84658011203
Winsorized Mean ( 18 / 24 )98.73291666666670.08227317124417181200.06212442748
Winsorized Mean ( 19 / 24 )98.70916666666670.07774596236163481269.63720903629
Winsorized Mean ( 20 / 24 )98.71194444444440.07737492782385491275.76137672352
Winsorized Mean ( 21 / 24 )98.70902777777780.07105100763207331389.26992125048
Winsorized Mean ( 22 / 24 )98.67236111111110.05772197849918651709.44177030421
Winsorized Mean ( 23 / 24 )98.65958333333330.05495389926657561795.31543075308
Winsorized Mean ( 24 / 24 )98.656250.04987795649200621977.95292627538
Trimmed Mean ( 1 / 24 )99.03328571428570.188470768823646525.457004990266
Trimmed Mean ( 2 / 24 )99.02470588235290.184569531045967536.517080154961
Trimmed Mean ( 3 / 24 )99.00984848484850.181246460288464546.271901405793
Trimmed Mean ( 4 / 24 )98.991093750.178093424127995555.838006005519
Trimmed Mean ( 5 / 24 )98.97048387096770.174625447540085566.758655540448
Trimmed Mean ( 6 / 24 )98.94816666666670.170477974067574580.416134153761
Trimmed Mean ( 7 / 24 )98.9267241379310.166113065076328595.53849116248
Trimmed Mean ( 8 / 24 )98.90303571428570.161080144536258613.99892580816
Trimmed Mean ( 9 / 24 )98.87851851851850.155589186408125635.510222793702
Trimmed Mean ( 10 / 24 )98.85173076923080.148810446900158664.279510131123
Trimmed Mean ( 11 / 24 )98.82660.142142960516832695.262006930671
Trimmed Mean ( 12 / 24 )98.796250.134272278484814735.790373968916
Trimmed Mean ( 13 / 24 )98.76543478260870.124897525733969790.771748296905
Trimmed Mean ( 14 / 24 )98.730.112601375513099876.809892864186
Trimmed Mean ( 15 / 24 )98.70.100651189863339980.614338827109
Trimmed Mean ( 16 / 24 )98.675250.09082667877294131086.41261943178
Trimmed Mean ( 17 / 24 )98.65815789473680.08314142885759991186.63053125672
Trimmed Mean ( 18 / 24 )98.65083333333330.07868197490278931253.79203375634
Trimmed Mean ( 19 / 24 )98.64117647058820.07482214765705841318.34195568273
Trimmed Mean ( 20 / 24 )98.6331250.07075405707619821394.02783495196
Trimmed Mean ( 21 / 24 )98.62366666666670.06485258851848471520.73600945869
Trimmed Mean ( 22 / 24 )98.61321428571430.05837765565926841689.22874980263
Trimmed Mean ( 23 / 24 )98.60576923076920.05415696013774181820.74047324623
Trimmed Mean ( 24 / 24 )98.598750.04867562144635042025.6289918902
Median98.6
Midrange99.37
Midmean - Weighted Average at Xnp98.6283783783784
Midmean - Weighted Average at X(n+1)p98.6508333333333
Midmean - Empirical Distribution Function98.6283783783784
Midmean - Empirical Distribution Function - Averaging98.6508333333333
Midmean - Empirical Distribution Function - Interpolation98.6508333333333
Midmean - Closest Observation98.6283783783784
Midmean - True Basic - Statistics Graphics Toolkit98.6508333333333
Midmean - MS Excel (old versions)98.6581578947368
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')