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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, 04 Jun 2010 11:25:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/04/t1275650891uc2ycu4db7kga1p.htm/, Retrieved Sun, 28 Apr 2024 22:34:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77422, Retrieved Sun, 28 Apr 2024 22:34:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5] [2010-06-04 11:25:20] [4fe0863fefe2b0d2b48fece67084e8c1] [Current]
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Dataseries X:
103,6
104,7
105,5
106,6
107,2
107,5
108,3
108,7
108,8
109,8
109,5
109,2
110,6
110,1
109,9
109,7
109,4
109,4
109,4
109,5
109,5
109,9
110
110,8
112,4
112,8
113,7
114,5
114,8
115,6
115,8
115,8
116,3
116,3
116,8
116,7
116,8
117
117,2
117,1
117,3
117,4
117,7
117,9
118,8
119,9
122,4
123,5
125,6
127,4
128,9
129,5
130,8
132,7
134
132,9
133,1
131,7
128,8
125,1
123,9
121,8
119,2
118,9
119,6
120,2
119,6
121
120,4
120,4
121,4
121,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77422&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77422&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.9541666666670.909412047374145128.604153644503
Geometric Mean116.70747967954
Harmonic Mean116.46520065578
Quadratic Mean117.204932703364
Winsorized Mean ( 1 / 24 )116.9569444444440.903147916778278129.499212998968
Winsorized Mean ( 2 / 24 )116.9736111111110.897629884445995130.313855563427
Winsorized Mean ( 3 / 24 )117.0111111111110.8876380087445131.823006629262
Winsorized Mean ( 4 / 24 )116.9888888888890.868694709920375134.672040191901
Winsorized Mean ( 5 / 24 )116.9472222222220.85078894671671137.457383142476
Winsorized Mean ( 6 / 24 )116.9055555555560.81641724870218143.193392522506
Winsorized Mean ( 7 / 24 )116.8861111111110.798199032965302146.437299825935
Winsorized Mean ( 8 / 24 )116.8861111111110.794248460127269147.165675451711
Winsorized Mean ( 9 / 24 )116.7611111111110.751148196619446155.443508533464
Winsorized Mean ( 10 / 24 )116.5388888888890.699361310334384166.63616812484
Winsorized Mean ( 11 / 24 )116.46250.685612360935768169.866394825561
Winsorized Mean ( 12 / 24 )116.26250.65132114893145178.502571566637
Winsorized Mean ( 13 / 24 )116.2083333333330.636853173036187182.472724096375
Winsorized Mean ( 14 / 24 )115.9944444444440.603588281959884192.174778588816
Winsorized Mean ( 15 / 24 )115.8694444444440.585320688718565197.958908129689
Winsorized Mean ( 16 / 24 )115.8916666666670.575380903978866201.41729742029
Winsorized Mean ( 17 / 24 )115.8444444444440.561833464906015206.19000412128
Winsorized Mean ( 18 / 24 )115.7694444444440.544306995361162212.691450653925
Winsorized Mean ( 19 / 24 )115.6111111111110.523379664957984220.893395085176
Winsorized Mean ( 20 / 24 )115.6388888888890.519120161051519222.759387064939
Winsorized Mean ( 21 / 24 )115.6097222222220.507171417879149227.949995103569
Winsorized Mean ( 22 / 24 )115.6708333333330.472301814842585244.908720860803
Winsorized Mean ( 23 / 24 )115.6388888888890.450662681749073256.597436557386
Winsorized Mean ( 24 / 24 )116.1722222222220.372038237293821312.258823359799
Trimmed Mean ( 1 / 24 )116.9014285714290.882154554368764132.518080865182
Trimmed Mean ( 2 / 24 )116.8426470588240.857132744445082136.318029868838
Trimmed Mean ( 3 / 24 )116.7712121212120.830698207049874140.569958054817
Trimmed Mean ( 4 / 24 )116.681250.803430377832336145.228825321252
Trimmed Mean ( 5 / 24 )116.5919354838710.77757878013635149.942280399455
Trimmed Mean ( 6 / 24 )116.5066666666670.751972422061135154.93475990426
Trimmed Mean ( 7 / 24 )116.4241379310340.730703819793978159.331503103214
Trimmed Mean ( 8 / 24 )116.3392857142860.709273812693598164.025914438411
Trimmed Mean ( 9 / 24 )116.2481481481480.683461105509684170.087437618644
Trimmed Mean ( 10 / 24 )116.1692307692310.662087621515188175.4589981661
Trimmed Mean ( 11 / 24 )116.1160.647641624256338179.290514462117
Trimmed Mean ( 12 / 24 )116.068750.632211279167884183.591710278832
Trimmed Mean ( 13 / 24 )116.043478260870.620064295979795187.147492628169
Trimmed Mean ( 14 / 24 )116.0227272727270.607144423787099191.095763589541
Trimmed Mean ( 15 / 24 )116.026190476190.597235788281167194.271999020875
Trimmed Mean ( 16 / 24 )116.0450.587410113145527197.553629743604
Trimmed Mean ( 17 / 24 )116.0631578947370.575722948976059201.595503707397
Trimmed Mean ( 18 / 24 )116.0888888888890.562234456231785206.477720463704
Trimmed Mean ( 19 / 24 )116.1264705882350.547092604327615212.261086458949
Trimmed Mean ( 20 / 24 )116.18750.530021111874101219.212966044263
Trimmed Mean ( 21 / 24 )116.2533333333330.505731138723264229.871812178342
Trimmed Mean ( 22 / 24 )116.3321428571430.472667024073246246.118592861929
Trimmed Mean ( 23 / 24 )116.4153846153850.435243249678306267.472004910883
Trimmed Mean ( 24 / 24 )116.5166666666670.383569555445599303.76932948004
Median116.8
Midrange118.8
Midmean - Weighted Average at Xnp115.918918918919
Midmean - Weighted Average at X(n+1)p116.088888888889
Midmean - Empirical Distribution Function115.918918918919
Midmean - Empirical Distribution Function - Averaging116.088888888889
Midmean - Empirical Distribution Function - Interpolation116.088888888889
Midmean - Closest Observation115.918918918919
Midmean - True Basic - Statistics Graphics Toolkit116.088888888889
Midmean - MS Excel (old versions)116.063157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.954166666667 & 0.909412047374145 & 128.604153644503 \tabularnewline
Geometric Mean & 116.70747967954 &  &  \tabularnewline
Harmonic Mean & 116.46520065578 &  &  \tabularnewline
Quadratic Mean & 117.204932703364 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 116.956944444444 & 0.903147916778278 & 129.499212998968 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 116.973611111111 & 0.897629884445995 & 130.313855563427 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 117.011111111111 & 0.8876380087445 & 131.823006629262 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 116.988888888889 & 0.868694709920375 & 134.672040191901 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 116.947222222222 & 0.85078894671671 & 137.457383142476 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 116.905555555556 & 0.81641724870218 & 143.193392522506 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 116.886111111111 & 0.798199032965302 & 146.437299825935 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 116.886111111111 & 0.794248460127269 & 147.165675451711 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 116.761111111111 & 0.751148196619446 & 155.443508533464 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 116.538888888889 & 0.699361310334384 & 166.63616812484 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 116.4625 & 0.685612360935768 & 169.866394825561 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 116.2625 & 0.65132114893145 & 178.502571566637 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 116.208333333333 & 0.636853173036187 & 182.472724096375 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 115.994444444444 & 0.603588281959884 & 192.174778588816 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 115.869444444444 & 0.585320688718565 & 197.958908129689 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 115.891666666667 & 0.575380903978866 & 201.41729742029 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 115.844444444444 & 0.561833464906015 & 206.19000412128 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 115.769444444444 & 0.544306995361162 & 212.691450653925 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 115.611111111111 & 0.523379664957984 & 220.893395085176 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 115.638888888889 & 0.519120161051519 & 222.759387064939 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 115.609722222222 & 0.507171417879149 & 227.949995103569 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 115.670833333333 & 0.472301814842585 & 244.908720860803 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 115.638888888889 & 0.450662681749073 & 256.597436557386 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 116.172222222222 & 0.372038237293821 & 312.258823359799 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 116.901428571429 & 0.882154554368764 & 132.518080865182 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 116.842647058824 & 0.857132744445082 & 136.318029868838 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 116.771212121212 & 0.830698207049874 & 140.569958054817 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 116.68125 & 0.803430377832336 & 145.228825321252 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 116.591935483871 & 0.77757878013635 & 149.942280399455 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 116.506666666667 & 0.751972422061135 & 154.93475990426 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 116.424137931034 & 0.730703819793978 & 159.331503103214 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 116.339285714286 & 0.709273812693598 & 164.025914438411 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 116.248148148148 & 0.683461105509684 & 170.087437618644 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 116.169230769231 & 0.662087621515188 & 175.4589981661 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 116.116 & 0.647641624256338 & 179.290514462117 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 116.06875 & 0.632211279167884 & 183.591710278832 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 116.04347826087 & 0.620064295979795 & 187.147492628169 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 116.022727272727 & 0.607144423787099 & 191.095763589541 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 116.02619047619 & 0.597235788281167 & 194.271999020875 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 116.045 & 0.587410113145527 & 197.553629743604 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 116.063157894737 & 0.575722948976059 & 201.595503707397 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 116.088888888889 & 0.562234456231785 & 206.477720463704 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 116.126470588235 & 0.547092604327615 & 212.261086458949 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 116.1875 & 0.530021111874101 & 219.212966044263 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 116.253333333333 & 0.505731138723264 & 229.871812178342 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 116.332142857143 & 0.472667024073246 & 246.118592861929 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 116.415384615385 & 0.435243249678306 & 267.472004910883 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 116.516666666667 & 0.383569555445599 & 303.76932948004 \tabularnewline
Median & 116.8 &  &  \tabularnewline
Midrange & 118.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.918918918919 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.088888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.918918918919 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.088888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.088888888889 &  &  \tabularnewline
Midmean - Closest Observation & 115.918918918919 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.088888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.063157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77422&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]116.954166666667[/C][C]0.909412047374145[/C][C]128.604153644503[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.70747967954[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]116.46520065578[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.204932703364[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]116.956944444444[/C][C]0.903147916778278[/C][C]129.499212998968[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]116.973611111111[/C][C]0.897629884445995[/C][C]130.313855563427[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]117.011111111111[/C][C]0.8876380087445[/C][C]131.823006629262[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]116.988888888889[/C][C]0.868694709920375[/C][C]134.672040191901[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]116.947222222222[/C][C]0.85078894671671[/C][C]137.457383142476[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]116.905555555556[/C][C]0.81641724870218[/C][C]143.193392522506[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]116.886111111111[/C][C]0.798199032965302[/C][C]146.437299825935[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]116.886111111111[/C][C]0.794248460127269[/C][C]147.165675451711[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]116.761111111111[/C][C]0.751148196619446[/C][C]155.443508533464[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]116.538888888889[/C][C]0.699361310334384[/C][C]166.63616812484[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]116.4625[/C][C]0.685612360935768[/C][C]169.866394825561[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]116.2625[/C][C]0.65132114893145[/C][C]178.502571566637[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]116.208333333333[/C][C]0.636853173036187[/C][C]182.472724096375[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]115.994444444444[/C][C]0.603588281959884[/C][C]192.174778588816[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]115.869444444444[/C][C]0.585320688718565[/C][C]197.958908129689[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]115.891666666667[/C][C]0.575380903978866[/C][C]201.41729742029[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]115.844444444444[/C][C]0.561833464906015[/C][C]206.19000412128[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]115.769444444444[/C][C]0.544306995361162[/C][C]212.691450653925[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]115.611111111111[/C][C]0.523379664957984[/C][C]220.893395085176[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]115.638888888889[/C][C]0.519120161051519[/C][C]222.759387064939[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]115.609722222222[/C][C]0.507171417879149[/C][C]227.949995103569[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]115.670833333333[/C][C]0.472301814842585[/C][C]244.908720860803[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]115.638888888889[/C][C]0.450662681749073[/C][C]256.597436557386[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]116.172222222222[/C][C]0.372038237293821[/C][C]312.258823359799[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]116.901428571429[/C][C]0.882154554368764[/C][C]132.518080865182[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]116.842647058824[/C][C]0.857132744445082[/C][C]136.318029868838[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]116.771212121212[/C][C]0.830698207049874[/C][C]140.569958054817[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]116.68125[/C][C]0.803430377832336[/C][C]145.228825321252[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]116.591935483871[/C][C]0.77757878013635[/C][C]149.942280399455[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]116.506666666667[/C][C]0.751972422061135[/C][C]154.93475990426[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]116.424137931034[/C][C]0.730703819793978[/C][C]159.331503103214[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]116.339285714286[/C][C]0.709273812693598[/C][C]164.025914438411[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]116.248148148148[/C][C]0.683461105509684[/C][C]170.087437618644[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]116.169230769231[/C][C]0.662087621515188[/C][C]175.4589981661[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]116.116[/C][C]0.647641624256338[/C][C]179.290514462117[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]116.06875[/C][C]0.632211279167884[/C][C]183.591710278832[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]116.04347826087[/C][C]0.620064295979795[/C][C]187.147492628169[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]116.022727272727[/C][C]0.607144423787099[/C][C]191.095763589541[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]116.02619047619[/C][C]0.597235788281167[/C][C]194.271999020875[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]116.045[/C][C]0.587410113145527[/C][C]197.553629743604[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]116.063157894737[/C][C]0.575722948976059[/C][C]201.595503707397[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]116.088888888889[/C][C]0.562234456231785[/C][C]206.477720463704[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]116.126470588235[/C][C]0.547092604327615[/C][C]212.261086458949[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]116.1875[/C][C]0.530021111874101[/C][C]219.212966044263[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]116.253333333333[/C][C]0.505731138723264[/C][C]229.871812178342[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]116.332142857143[/C][C]0.472667024073246[/C][C]246.118592861929[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]116.415384615385[/C][C]0.435243249678306[/C][C]267.472004910883[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]116.516666666667[/C][C]0.383569555445599[/C][C]303.76932948004[/C][/ROW]
[ROW][C]Median[/C][C]116.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]118.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.063157894737[/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=77422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77422&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 Mean116.9541666666670.909412047374145128.604153644503
Geometric Mean116.70747967954
Harmonic Mean116.46520065578
Quadratic Mean117.204932703364
Winsorized Mean ( 1 / 24 )116.9569444444440.903147916778278129.499212998968
Winsorized Mean ( 2 / 24 )116.9736111111110.897629884445995130.313855563427
Winsorized Mean ( 3 / 24 )117.0111111111110.8876380087445131.823006629262
Winsorized Mean ( 4 / 24 )116.9888888888890.868694709920375134.672040191901
Winsorized Mean ( 5 / 24 )116.9472222222220.85078894671671137.457383142476
Winsorized Mean ( 6 / 24 )116.9055555555560.81641724870218143.193392522506
Winsorized Mean ( 7 / 24 )116.8861111111110.798199032965302146.437299825935
Winsorized Mean ( 8 / 24 )116.8861111111110.794248460127269147.165675451711
Winsorized Mean ( 9 / 24 )116.7611111111110.751148196619446155.443508533464
Winsorized Mean ( 10 / 24 )116.5388888888890.699361310334384166.63616812484
Winsorized Mean ( 11 / 24 )116.46250.685612360935768169.866394825561
Winsorized Mean ( 12 / 24 )116.26250.65132114893145178.502571566637
Winsorized Mean ( 13 / 24 )116.2083333333330.636853173036187182.472724096375
Winsorized Mean ( 14 / 24 )115.9944444444440.603588281959884192.174778588816
Winsorized Mean ( 15 / 24 )115.8694444444440.585320688718565197.958908129689
Winsorized Mean ( 16 / 24 )115.8916666666670.575380903978866201.41729742029
Winsorized Mean ( 17 / 24 )115.8444444444440.561833464906015206.19000412128
Winsorized Mean ( 18 / 24 )115.7694444444440.544306995361162212.691450653925
Winsorized Mean ( 19 / 24 )115.6111111111110.523379664957984220.893395085176
Winsorized Mean ( 20 / 24 )115.6388888888890.519120161051519222.759387064939
Winsorized Mean ( 21 / 24 )115.6097222222220.507171417879149227.949995103569
Winsorized Mean ( 22 / 24 )115.6708333333330.472301814842585244.908720860803
Winsorized Mean ( 23 / 24 )115.6388888888890.450662681749073256.597436557386
Winsorized Mean ( 24 / 24 )116.1722222222220.372038237293821312.258823359799
Trimmed Mean ( 1 / 24 )116.9014285714290.882154554368764132.518080865182
Trimmed Mean ( 2 / 24 )116.8426470588240.857132744445082136.318029868838
Trimmed Mean ( 3 / 24 )116.7712121212120.830698207049874140.569958054817
Trimmed Mean ( 4 / 24 )116.681250.803430377832336145.228825321252
Trimmed Mean ( 5 / 24 )116.5919354838710.77757878013635149.942280399455
Trimmed Mean ( 6 / 24 )116.5066666666670.751972422061135154.93475990426
Trimmed Mean ( 7 / 24 )116.4241379310340.730703819793978159.331503103214
Trimmed Mean ( 8 / 24 )116.3392857142860.709273812693598164.025914438411
Trimmed Mean ( 9 / 24 )116.2481481481480.683461105509684170.087437618644
Trimmed Mean ( 10 / 24 )116.1692307692310.662087621515188175.4589981661
Trimmed Mean ( 11 / 24 )116.1160.647641624256338179.290514462117
Trimmed Mean ( 12 / 24 )116.068750.632211279167884183.591710278832
Trimmed Mean ( 13 / 24 )116.043478260870.620064295979795187.147492628169
Trimmed Mean ( 14 / 24 )116.0227272727270.607144423787099191.095763589541
Trimmed Mean ( 15 / 24 )116.026190476190.597235788281167194.271999020875
Trimmed Mean ( 16 / 24 )116.0450.587410113145527197.553629743604
Trimmed Mean ( 17 / 24 )116.0631578947370.575722948976059201.595503707397
Trimmed Mean ( 18 / 24 )116.0888888888890.562234456231785206.477720463704
Trimmed Mean ( 19 / 24 )116.1264705882350.547092604327615212.261086458949
Trimmed Mean ( 20 / 24 )116.18750.530021111874101219.212966044263
Trimmed Mean ( 21 / 24 )116.2533333333330.505731138723264229.871812178342
Trimmed Mean ( 22 / 24 )116.3321428571430.472667024073246246.118592861929
Trimmed Mean ( 23 / 24 )116.4153846153850.435243249678306267.472004910883
Trimmed Mean ( 24 / 24 )116.5166666666670.383569555445599303.76932948004
Median116.8
Midrange118.8
Midmean - Weighted Average at Xnp115.918918918919
Midmean - Weighted Average at X(n+1)p116.088888888889
Midmean - Empirical Distribution Function115.918918918919
Midmean - Empirical Distribution Function - Averaging116.088888888889
Midmean - Empirical Distribution Function - Interpolation116.088888888889
Midmean - Closest Observation115.918918918919
Midmean - True Basic - Statistics Graphics Toolkit116.088888888889
Midmean - MS Excel (old versions)116.063157894737
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')