Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 18:46:10 +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/2014/Oct/13/t1413222528dok65xcfje31fhe.htm/, Retrieved Fri, 10 May 2024 17:12:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240810, Retrieved Fri, 10 May 2024 17:12:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 17:46:10] [1a08c6aa6bf9a3504070a6066c5cb670] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,64
1,65
1,65
1,66
1,67
1,67
1,68
1,68
1,69
1,7
1,71
1,72
1,72
1,73
1,73
1,73
1,73
1,74
1,75
1,75
1,75
1,76
1,76
1,76
1,77
1,78
1,78
1,79
1,79
1,79
1,79
1,79
1,83
1,83
1,83
1,83
1,84
1,84
1,84
1,85
1,85
1,85
1,86
1,86
1,86
1,87
1,87
1,88
1,88
1,88
1,89
1,89
1,9
1,91
1,91
1,91
1,91
1,91
1,92
1,92
1,92
1,93
1,94
1,94
1,94
1,95
1,95
1,95
1,95
1,96
1,96
1,97




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=240810&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=240810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240810&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 Mean1.820694444444440.0111370857387165163.480329339215
Geometric Mean1.81825354231217
Harmonic Mean1.8157921589661
Quadratic Mean1.82311127532639
Winsorized Mean ( 1 / 24 )1.820694444444440.0110807365535865164.311680513254
Winsorized Mean ( 2 / 24 )1.820694444444440.0110807365535865164.311680513254
Winsorized Mean ( 3 / 24 )1.820694444444440.0109206957566551166.719638108672
Winsorized Mean ( 4 / 24 )1.821250.0108083632416033168.503774280058
Winsorized Mean ( 5 / 24 )1.821250.0108083632416033168.503774280058
Winsorized Mean ( 6 / 24 )1.822083333333330.0106479029138711171.121332347959
Winsorized Mean ( 7 / 24 )1.821111111111110.0104880055860001173.637503925628
Winsorized Mean ( 8 / 24 )1.822222222222220.0102820593374283177.223468803477
Winsorized Mean ( 9 / 24 )1.823472222222220.0100607694270415181.245801868897
Winsorized Mean ( 10 / 24 )1.823472222222220.0096031581476783189.882556777748
Winsorized Mean ( 11 / 24 )1.823472222222220.00912047628821401199.931688280207
Winsorized Mean ( 12 / 24 )1.823472222222220.00912047628821401199.931688280207
Winsorized Mean ( 13 / 24 )1.825277777777780.00883904993120388206.50158014541
Winsorized Mean ( 14 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 15 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 16 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 17 / 24 )1.825694444444440.00819802446929111222.69931631496
Winsorized Mean ( 18 / 24 )1.828194444444440.00783816749469154233.242584530453
Winsorized Mean ( 19 / 24 )1.825555555555560.00745851565305233244.761242112358
Winsorized Mean ( 20 / 24 )1.822777777777780.00707721282720079257.555880017068
Winsorized Mean ( 21 / 24 )1.825694444444440.00666322208220465273.995736885357
Winsorized Mean ( 22 / 24 )1.822638888888890.0062579934972577291.249725600959
Winsorized Mean ( 23 / 24 )1.822638888888890.0062579934972577291.249725600959
Winsorized Mean ( 24 / 24 )1.825972222222220.0057960232785885315.038800649348
Trimmed Mean ( 1 / 24 )1.821142857142860.0109498061605745166.317360365702
Trimmed Mean ( 2 / 24 )1.821617647058820.0107909546025508168.809684977103
Trimmed Mean ( 3 / 24 )1.822121212121210.0105986654204831171.919872911523
Trimmed Mean ( 4 / 24 )1.822656250.0104374606441136174.626406953488
Trimmed Mean ( 5 / 24 )1.823064516129030.0102805405498296177.331581670504
Trimmed Mean ( 6 / 24 )1.82350.0100867004230189180.782607148577
Trimmed Mean ( 7 / 24 )1.823793103448280.00989303832359122184.351161270568
Trimmed Mean ( 8 / 24 )1.824285714285710.00969287173768389188.209001795956
Trimmed Mean ( 9 / 24 )1.824629629629630.00949350788860233192.197620841526
Trimmed Mean ( 10 / 24 )1.824807692307690.00929445570400652196.332926899752
Trimmed Mean ( 11 / 24 )1.8250.00914397314617443199.585013081926
Trimmed Mean ( 12 / 24 )1.825208333333330.00905063368796154201.666357987849
Trimmed Mean ( 13 / 24 )1.82543478260870.00892105213427904204.621019486534
Trimmed Mean ( 14 / 24 )1.825454545454550.00880523667856786207.314648327142
Trimmed Mean ( 15 / 24 )1.825714285714290.00870301626557131209.779486789737
Trimmed Mean ( 16 / 24 )1.8260.00855450098950764213.454882083671
Trimmed Mean ( 17 / 24 )1.826315789473680.00834379568335838218.883090955385
Trimmed Mean ( 18 / 24 )1.826388888888890.00813724318374431224.448114385649
Trimmed Mean ( 19 / 24 )1.826176470588240.00793258927009641230.211902874185
Trimmed Mean ( 20 / 24 )1.826250.00773489683397639236.105282229233
Trimmed Mean ( 21 / 24 )1.826666666666670.00754044014284927242.249342486848
Trimmed Mean ( 22 / 24 )1.826785714285710.00736525468455811248.02750108774
Trimmed Mean ( 23 / 24 )1.827307692307690.00720165990070649253.734238703557
Trimmed Mean ( 24 / 24 )1.827916666666670.00691509498469421264.337174068116
Median1.835
Midrange1.805
Midmean - Weighted Average at Xnp1.83243902439024
Midmean - Weighted Average at X(n+1)p1.83475
Midmean - Empirical Distribution Function1.83243902439024
Midmean - Empirical Distribution Function - Averaging1.83475
Midmean - Empirical Distribution Function - Interpolation1.83475
Midmean - Closest Observation1.83243902439024
Midmean - True Basic - Statistics Graphics Toolkit1.83475
Midmean - MS Excel (old versions)1.83243902439024
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.82069444444444 & 0.0111370857387165 & 163.480329339215 \tabularnewline
Geometric Mean & 1.81825354231217 &  &  \tabularnewline
Harmonic Mean & 1.8157921589661 &  &  \tabularnewline
Quadratic Mean & 1.82311127532639 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.82069444444444 & 0.0110807365535865 & 164.311680513254 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.82069444444444 & 0.0110807365535865 & 164.311680513254 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.82069444444444 & 0.0109206957566551 & 166.719638108672 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.82125 & 0.0108083632416033 & 168.503774280058 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.82125 & 0.0108083632416033 & 168.503774280058 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.82208333333333 & 0.0106479029138711 & 171.121332347959 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.82111111111111 & 0.0104880055860001 & 173.637503925628 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.82222222222222 & 0.0102820593374283 & 177.223468803477 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.82347222222222 & 0.0100607694270415 & 181.245801868897 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.82347222222222 & 0.0096031581476783 & 189.882556777748 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.82347222222222 & 0.00912047628821401 & 199.931688280207 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.82347222222222 & 0.00912047628821401 & 199.931688280207 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.82527777777778 & 0.00883904993120388 & 206.50158014541 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.82333333333333 & 0.00855343143763791 & 213.169807535964 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.82333333333333 & 0.00855343143763791 & 213.169807535964 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.82333333333333 & 0.00855343143763791 & 213.169807535964 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.82569444444444 & 0.00819802446929111 & 222.69931631496 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.82819444444444 & 0.00783816749469154 & 233.242584530453 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.82555555555556 & 0.00745851565305233 & 244.761242112358 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.82277777777778 & 0.00707721282720079 & 257.555880017068 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.82569444444444 & 0.00666322208220465 & 273.995736885357 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.82263888888889 & 0.0062579934972577 & 291.249725600959 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.82263888888889 & 0.0062579934972577 & 291.249725600959 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.82597222222222 & 0.0057960232785885 & 315.038800649348 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.82114285714286 & 0.0109498061605745 & 166.317360365702 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.82161764705882 & 0.0107909546025508 & 168.809684977103 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.82212121212121 & 0.0105986654204831 & 171.919872911523 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.82265625 & 0.0104374606441136 & 174.626406953488 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.82306451612903 & 0.0102805405498296 & 177.331581670504 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.8235 & 0.0100867004230189 & 180.782607148577 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.82379310344828 & 0.00989303832359122 & 184.351161270568 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.82428571428571 & 0.00969287173768389 & 188.209001795956 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.82462962962963 & 0.00949350788860233 & 192.197620841526 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.82480769230769 & 0.00929445570400652 & 196.332926899752 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.825 & 0.00914397314617443 & 199.585013081926 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.82520833333333 & 0.00905063368796154 & 201.666357987849 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.8254347826087 & 0.00892105213427904 & 204.621019486534 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.82545454545455 & 0.00880523667856786 & 207.314648327142 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.82571428571429 & 0.00870301626557131 & 209.779486789737 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.826 & 0.00855450098950764 & 213.454882083671 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.82631578947368 & 0.00834379568335838 & 218.883090955385 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.82638888888889 & 0.00813724318374431 & 224.448114385649 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.82617647058824 & 0.00793258927009641 & 230.211902874185 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.82625 & 0.00773489683397639 & 236.105282229233 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.82666666666667 & 0.00754044014284927 & 242.249342486848 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.82678571428571 & 0.00736525468455811 & 248.02750108774 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.82730769230769 & 0.00720165990070649 & 253.734238703557 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.82791666666667 & 0.00691509498469421 & 264.337174068116 \tabularnewline
Median & 1.835 &  &  \tabularnewline
Midrange & 1.805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.83243902439024 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.83475 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.83243902439024 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.83475 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.83475 &  &  \tabularnewline
Midmean - Closest Observation & 1.83243902439024 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.83475 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.83243902439024 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240810&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]1.82069444444444[/C][C]0.0111370857387165[/C][C]163.480329339215[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.81825354231217[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.8157921589661[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.82311127532639[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.82069444444444[/C][C]0.0110807365535865[/C][C]164.311680513254[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.82069444444444[/C][C]0.0110807365535865[/C][C]164.311680513254[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.82069444444444[/C][C]0.0109206957566551[/C][C]166.719638108672[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.82125[/C][C]0.0108083632416033[/C][C]168.503774280058[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.82125[/C][C]0.0108083632416033[/C][C]168.503774280058[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.82208333333333[/C][C]0.0106479029138711[/C][C]171.121332347959[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.82111111111111[/C][C]0.0104880055860001[/C][C]173.637503925628[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.82222222222222[/C][C]0.0102820593374283[/C][C]177.223468803477[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.82347222222222[/C][C]0.0100607694270415[/C][C]181.245801868897[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.82347222222222[/C][C]0.0096031581476783[/C][C]189.882556777748[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.82347222222222[/C][C]0.00912047628821401[/C][C]199.931688280207[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.82347222222222[/C][C]0.00912047628821401[/C][C]199.931688280207[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.82527777777778[/C][C]0.00883904993120388[/C][C]206.50158014541[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.82333333333333[/C][C]0.00855343143763791[/C][C]213.169807535964[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.82333333333333[/C][C]0.00855343143763791[/C][C]213.169807535964[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.82333333333333[/C][C]0.00855343143763791[/C][C]213.169807535964[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.82569444444444[/C][C]0.00819802446929111[/C][C]222.69931631496[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.82819444444444[/C][C]0.00783816749469154[/C][C]233.242584530453[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.82555555555556[/C][C]0.00745851565305233[/C][C]244.761242112358[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.82277777777778[/C][C]0.00707721282720079[/C][C]257.555880017068[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.82569444444444[/C][C]0.00666322208220465[/C][C]273.995736885357[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.82263888888889[/C][C]0.0062579934972577[/C][C]291.249725600959[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.82263888888889[/C][C]0.0062579934972577[/C][C]291.249725600959[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.82597222222222[/C][C]0.0057960232785885[/C][C]315.038800649348[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.82114285714286[/C][C]0.0109498061605745[/C][C]166.317360365702[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.82161764705882[/C][C]0.0107909546025508[/C][C]168.809684977103[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.82212121212121[/C][C]0.0105986654204831[/C][C]171.919872911523[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.82265625[/C][C]0.0104374606441136[/C][C]174.626406953488[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.82306451612903[/C][C]0.0102805405498296[/C][C]177.331581670504[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.8235[/C][C]0.0100867004230189[/C][C]180.782607148577[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.82379310344828[/C][C]0.00989303832359122[/C][C]184.351161270568[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.82428571428571[/C][C]0.00969287173768389[/C][C]188.209001795956[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.82462962962963[/C][C]0.00949350788860233[/C][C]192.197620841526[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.82480769230769[/C][C]0.00929445570400652[/C][C]196.332926899752[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.825[/C][C]0.00914397314617443[/C][C]199.585013081926[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.82520833333333[/C][C]0.00905063368796154[/C][C]201.666357987849[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.8254347826087[/C][C]0.00892105213427904[/C][C]204.621019486534[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.82545454545455[/C][C]0.00880523667856786[/C][C]207.314648327142[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.82571428571429[/C][C]0.00870301626557131[/C][C]209.779486789737[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.826[/C][C]0.00855450098950764[/C][C]213.454882083671[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.82631578947368[/C][C]0.00834379568335838[/C][C]218.883090955385[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.82638888888889[/C][C]0.00813724318374431[/C][C]224.448114385649[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.82617647058824[/C][C]0.00793258927009641[/C][C]230.211902874185[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.82625[/C][C]0.00773489683397639[/C][C]236.105282229233[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.82666666666667[/C][C]0.00754044014284927[/C][C]242.249342486848[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.82678571428571[/C][C]0.00736525468455811[/C][C]248.02750108774[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.82730769230769[/C][C]0.00720165990070649[/C][C]253.734238703557[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.82791666666667[/C][C]0.00691509498469421[/C][C]264.337174068116[/C][/ROW]
[ROW][C]Median[/C][C]1.835[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.83243902439024[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.83475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.83243902439024[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.83475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.83475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.83243902439024[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.83475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.83243902439024[/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=240810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240810&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 Mean1.820694444444440.0111370857387165163.480329339215
Geometric Mean1.81825354231217
Harmonic Mean1.8157921589661
Quadratic Mean1.82311127532639
Winsorized Mean ( 1 / 24 )1.820694444444440.0110807365535865164.311680513254
Winsorized Mean ( 2 / 24 )1.820694444444440.0110807365535865164.311680513254
Winsorized Mean ( 3 / 24 )1.820694444444440.0109206957566551166.719638108672
Winsorized Mean ( 4 / 24 )1.821250.0108083632416033168.503774280058
Winsorized Mean ( 5 / 24 )1.821250.0108083632416033168.503774280058
Winsorized Mean ( 6 / 24 )1.822083333333330.0106479029138711171.121332347959
Winsorized Mean ( 7 / 24 )1.821111111111110.0104880055860001173.637503925628
Winsorized Mean ( 8 / 24 )1.822222222222220.0102820593374283177.223468803477
Winsorized Mean ( 9 / 24 )1.823472222222220.0100607694270415181.245801868897
Winsorized Mean ( 10 / 24 )1.823472222222220.0096031581476783189.882556777748
Winsorized Mean ( 11 / 24 )1.823472222222220.00912047628821401199.931688280207
Winsorized Mean ( 12 / 24 )1.823472222222220.00912047628821401199.931688280207
Winsorized Mean ( 13 / 24 )1.825277777777780.00883904993120388206.50158014541
Winsorized Mean ( 14 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 15 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 16 / 24 )1.823333333333330.00855343143763791213.169807535964
Winsorized Mean ( 17 / 24 )1.825694444444440.00819802446929111222.69931631496
Winsorized Mean ( 18 / 24 )1.828194444444440.00783816749469154233.242584530453
Winsorized Mean ( 19 / 24 )1.825555555555560.00745851565305233244.761242112358
Winsorized Mean ( 20 / 24 )1.822777777777780.00707721282720079257.555880017068
Winsorized Mean ( 21 / 24 )1.825694444444440.00666322208220465273.995736885357
Winsorized Mean ( 22 / 24 )1.822638888888890.0062579934972577291.249725600959
Winsorized Mean ( 23 / 24 )1.822638888888890.0062579934972577291.249725600959
Winsorized Mean ( 24 / 24 )1.825972222222220.0057960232785885315.038800649348
Trimmed Mean ( 1 / 24 )1.821142857142860.0109498061605745166.317360365702
Trimmed Mean ( 2 / 24 )1.821617647058820.0107909546025508168.809684977103
Trimmed Mean ( 3 / 24 )1.822121212121210.0105986654204831171.919872911523
Trimmed Mean ( 4 / 24 )1.822656250.0104374606441136174.626406953488
Trimmed Mean ( 5 / 24 )1.823064516129030.0102805405498296177.331581670504
Trimmed Mean ( 6 / 24 )1.82350.0100867004230189180.782607148577
Trimmed Mean ( 7 / 24 )1.823793103448280.00989303832359122184.351161270568
Trimmed Mean ( 8 / 24 )1.824285714285710.00969287173768389188.209001795956
Trimmed Mean ( 9 / 24 )1.824629629629630.00949350788860233192.197620841526
Trimmed Mean ( 10 / 24 )1.824807692307690.00929445570400652196.332926899752
Trimmed Mean ( 11 / 24 )1.8250.00914397314617443199.585013081926
Trimmed Mean ( 12 / 24 )1.825208333333330.00905063368796154201.666357987849
Trimmed Mean ( 13 / 24 )1.82543478260870.00892105213427904204.621019486534
Trimmed Mean ( 14 / 24 )1.825454545454550.00880523667856786207.314648327142
Trimmed Mean ( 15 / 24 )1.825714285714290.00870301626557131209.779486789737
Trimmed Mean ( 16 / 24 )1.8260.00855450098950764213.454882083671
Trimmed Mean ( 17 / 24 )1.826315789473680.00834379568335838218.883090955385
Trimmed Mean ( 18 / 24 )1.826388888888890.00813724318374431224.448114385649
Trimmed Mean ( 19 / 24 )1.826176470588240.00793258927009641230.211902874185
Trimmed Mean ( 20 / 24 )1.826250.00773489683397639236.105282229233
Trimmed Mean ( 21 / 24 )1.826666666666670.00754044014284927242.249342486848
Trimmed Mean ( 22 / 24 )1.826785714285710.00736525468455811248.02750108774
Trimmed Mean ( 23 / 24 )1.827307692307690.00720165990070649253.734238703557
Trimmed Mean ( 24 / 24 )1.827916666666670.00691509498469421264.337174068116
Median1.835
Midrange1.805
Midmean - Weighted Average at Xnp1.83243902439024
Midmean - Weighted Average at X(n+1)p1.83475
Midmean - Empirical Distribution Function1.83243902439024
Midmean - Empirical Distribution Function - Averaging1.83475
Midmean - Empirical Distribution Function - Interpolation1.83475
Midmean - Closest Observation1.83243902439024
Midmean - True Basic - Statistics Graphics Toolkit1.83475
Midmean - MS Excel (old versions)1.83243902439024
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')