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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 07:56:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t1224424595fl0wydddbjwn4qf.htm/, Retrieved Sat, 18 May 2024 16:20:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16846, Retrieved Sat, 18 May 2024 16:20:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
-    D  [Pearson Correlation] [Verband inflatie ...] [2008-10-19 13:31:27] [e5d91604aae608e98a8ea24759233f66]
-    D    [Pearson Correlation] [Pearson correlati...] [2008-10-19 13:35:43] [e5d91604aae608e98a8ea24759233f66]
- RM D      [Central Tendency] [Central tendency ...] [2008-10-19 13:49:09] [e5d91604aae608e98a8ea24759233f66]
-    D          [Central Tendency] [Central tendency ...] [2008-10-19 13:56:08] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
Feedback Forum

Post a new message
Dataseries X:
1946.81
1765.9
1635.25
1833.42
1910.43
1959.67
1969.6
2061.41
2093.48
2120.88
2174.56
2196.72
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3733.22
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16846&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16846&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3218.81183333333117.32977651031327.433887023985
Geometric Mean3084.91043475535
Harmonic Mean2947.33138006667
Quadratic Mean3342.59778156277
Winsorized Mean ( 1 / 20 )3219.73116.58776712681227.6163621565709
Winsorized Mean ( 2 / 20 )3220.97633333333115.91864111775027.786525983008
Winsorized Mean ( 3 / 20 )3223.40533333333114.87210826284028.0608180878673
Winsorized Mean ( 4 / 20 )3221.81733333333113.62649095983528.354455955805
Winsorized Mean ( 5 / 20 )3217.99483333333112.50344680507428.6035221561603
Winsorized Mean ( 6 / 20 )3218.11983333333112.15566243025428.6933335651652
Winsorized Mean ( 7 / 20 )3219.70183333333108.52487802772129.6678687121943
Winsorized Mean ( 8 / 20 )3215.9125106.34459318001530.2404889974637
Winsorized Mean ( 9 / 20 )3219.1825105.46957446796430.5223806603848
Winsorized Mean ( 10 / 20 )3213.40083333333101.41650870674431.6851849300512
Winsorized Mean ( 11 / 20 )3216.95566666667100.63075996284031.9679158525147
Winsorized Mean ( 12 / 20 )3235.4536666666793.500403875065634.6036330601294
Winsorized Mean ( 13 / 20 )3243.1063333333390.767170835735235.7299484325947
Winsorized Mean ( 14 / 20 )3240.6656666666790.292702455959235.8906708794913
Winsorized Mean ( 15 / 20 )3214.7981666666783.728416214444138.3955449298476
Winsorized Mean ( 16 / 20 )3202.9741666666781.302139052301439.3959396886988
Winsorized Mean ( 17 / 20 )3198.4748333333380.065717044128839.9481195125059
Winsorized Mean ( 18 / 20 )3193.9598333333377.744787777946641.0826233451929
Winsorized Mean ( 19 / 20 )3186.3028333333374.248414300285742.9140859553828
Winsorized Mean ( 20 / 20 )3231.569566.08760769816848.8982672025149
Trimmed Mean ( 1 / 20 )3220.62931034483115.41743720435227.9041831837122
Trimmed Mean ( 2 / 20 )3221.59285714286113.90556167729728.2830162961654
Trimmed Mean ( 3 / 20 )3221.93537037037112.40081179024028.6646984043413
Trimmed Mean ( 4 / 20 )3221.37110.94047298746229.0369232549069
Trimmed Mean ( 5 / 20 )3221.2358109.49624598693729.418687106262
Trimmed Mean ( 6 / 20 )3222.04604166667107.94581469255829.8487352274234
Trimmed Mean ( 7 / 20 )3222.89956521739105.97401109029430.4121692862162
Trimmed Mean ( 8 / 20 )3223.5225104.3754781438230.8839064244408
Trimmed Mean ( 9 / 20 )3224.88142857143102.75974154734531.3827319922328
Trimmed Mean ( 10 / 20 )3225.83125100.72920197762832.0247871189973
Trimmed Mean ( 11 / 20 )3227.7939473684298.96010513498432.6171232636185
Trimmed Mean ( 12 / 20 )3229.4361111111196.61407786133733.426144332155
Trimmed Mean ( 13 / 20 )3228.5511764705995.168948867151833.9244177318527
Trimmed Mean ( 14 / 20 )3226.45187593.644962007373334.4540892092621
Trimmed Mean ( 15 / 20 )3224.4213333333391.338204446074835.302000437692
Trimmed Mean ( 16 / 20 )3225.7960714285789.731422693548535.9494586689585
Trimmed Mean ( 17 / 20 )3229.0876923076987.73075045195936.8067943756611
Trimmed Mean ( 18 / 20 )3233.5895833333384.682267047756438.1849671255230
Trimmed Mean ( 19 / 20 )3239.5940909090980.36203034164640.3124967990043
Trimmed Mean ( 20 / 20 )3248.008574.394812875470843.6590721108047
Median3209.425
Midrange3166.105
Midmean - Weighted Average at Xnp3198.10580645161
Midmean - Weighted Average at X(n+1)p3224.42133333333
Midmean - Empirical Distribution Function3198.10580645161
Midmean - Empirical Distribution Function - Averaging3224.42133333333
Midmean - Empirical Distribution Function - Interpolation3224.42133333333
Midmean - Closest Observation3198.10580645161
Midmean - True Basic - Statistics Graphics Toolkit3224.42133333333
Midmean - MS Excel (old versions)3226.451875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3218.81183333333 & 117.329776510313 & 27.433887023985 \tabularnewline
Geometric Mean & 3084.91043475535 &  &  \tabularnewline
Harmonic Mean & 2947.33138006667 &  &  \tabularnewline
Quadratic Mean & 3342.59778156277 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3219.73 & 116.587767126812 & 27.6163621565709 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3220.97633333333 & 115.918641117750 & 27.786525983008 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3223.40533333333 & 114.872108262840 & 28.0608180878673 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3221.81733333333 & 113.626490959835 & 28.354455955805 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3217.99483333333 & 112.503446805074 & 28.6035221561603 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3218.11983333333 & 112.155662430254 & 28.6933335651652 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3219.70183333333 & 108.524878027721 & 29.6678687121943 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3215.9125 & 106.344593180015 & 30.2404889974637 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3219.1825 & 105.469574467964 & 30.5223806603848 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3213.40083333333 & 101.416508706744 & 31.6851849300512 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3216.95566666667 & 100.630759962840 & 31.9679158525147 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3235.45366666667 & 93.5004038750656 & 34.6036330601294 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3243.10633333333 & 90.7671708357352 & 35.7299484325947 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3240.66566666667 & 90.2927024559592 & 35.8906708794913 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3214.79816666667 & 83.7284162144441 & 38.3955449298476 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3202.97416666667 & 81.3021390523014 & 39.3959396886988 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3198.47483333333 & 80.0657170441288 & 39.9481195125059 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3193.95983333333 & 77.7447877779466 & 41.0826233451929 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3186.30283333333 & 74.2484143002857 & 42.9140859553828 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3231.5695 & 66.087607698168 & 48.8982672025149 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3220.62931034483 & 115.417437204352 & 27.9041831837122 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3221.59285714286 & 113.905561677297 & 28.2830162961654 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3221.93537037037 & 112.400811790240 & 28.6646984043413 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3221.37 & 110.940472987462 & 29.0369232549069 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3221.2358 & 109.496245986937 & 29.418687106262 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3222.04604166667 & 107.945814692558 & 29.8487352274234 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3222.89956521739 & 105.974011090294 & 30.4121692862162 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3223.5225 & 104.37547814382 & 30.8839064244408 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3224.88142857143 & 102.759741547345 & 31.3827319922328 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3225.83125 & 100.729201977628 & 32.0247871189973 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3227.79394736842 & 98.960105134984 & 32.6171232636185 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3229.43611111111 & 96.614077861337 & 33.426144332155 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3228.55117647059 & 95.1689488671518 & 33.9244177318527 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3226.451875 & 93.6449620073733 & 34.4540892092621 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3224.42133333333 & 91.3382044460748 & 35.302000437692 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3225.79607142857 & 89.7314226935485 & 35.9494586689585 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3229.08769230769 & 87.730750451959 & 36.8067943756611 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3233.58958333333 & 84.6822670477564 & 38.1849671255230 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3239.59409090909 & 80.362030341646 & 40.3124967990043 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3248.0085 & 74.3948128754708 & 43.6590721108047 \tabularnewline
Median & 3209.425 &  &  \tabularnewline
Midrange & 3166.105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3198.10580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3224.42133333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3198.10580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3224.42133333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3224.42133333333 &  &  \tabularnewline
Midmean - Closest Observation & 3198.10580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3224.42133333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3226.451875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16846&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]3218.81183333333[/C][C]117.329776510313[/C][C]27.433887023985[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3084.91043475535[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2947.33138006667[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3342.59778156277[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3219.73[/C][C]116.587767126812[/C][C]27.6163621565709[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3220.97633333333[/C][C]115.918641117750[/C][C]27.786525983008[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3223.40533333333[/C][C]114.872108262840[/C][C]28.0608180878673[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3221.81733333333[/C][C]113.626490959835[/C][C]28.354455955805[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3217.99483333333[/C][C]112.503446805074[/C][C]28.6035221561603[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3218.11983333333[/C][C]112.155662430254[/C][C]28.6933335651652[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3219.70183333333[/C][C]108.524878027721[/C][C]29.6678687121943[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3215.9125[/C][C]106.344593180015[/C][C]30.2404889974637[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3219.1825[/C][C]105.469574467964[/C][C]30.5223806603848[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3213.40083333333[/C][C]101.416508706744[/C][C]31.6851849300512[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3216.95566666667[/C][C]100.630759962840[/C][C]31.9679158525147[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3235.45366666667[/C][C]93.5004038750656[/C][C]34.6036330601294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3243.10633333333[/C][C]90.7671708357352[/C][C]35.7299484325947[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3240.66566666667[/C][C]90.2927024559592[/C][C]35.8906708794913[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3214.79816666667[/C][C]83.7284162144441[/C][C]38.3955449298476[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3202.97416666667[/C][C]81.3021390523014[/C][C]39.3959396886988[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3198.47483333333[/C][C]80.0657170441288[/C][C]39.9481195125059[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3193.95983333333[/C][C]77.7447877779466[/C][C]41.0826233451929[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3186.30283333333[/C][C]74.2484143002857[/C][C]42.9140859553828[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3231.5695[/C][C]66.087607698168[/C][C]48.8982672025149[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3220.62931034483[/C][C]115.417437204352[/C][C]27.9041831837122[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3221.59285714286[/C][C]113.905561677297[/C][C]28.2830162961654[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3221.93537037037[/C][C]112.400811790240[/C][C]28.6646984043413[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3221.37[/C][C]110.940472987462[/C][C]29.0369232549069[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3221.2358[/C][C]109.496245986937[/C][C]29.418687106262[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3222.04604166667[/C][C]107.945814692558[/C][C]29.8487352274234[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3222.89956521739[/C][C]105.974011090294[/C][C]30.4121692862162[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3223.5225[/C][C]104.37547814382[/C][C]30.8839064244408[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3224.88142857143[/C][C]102.759741547345[/C][C]31.3827319922328[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3225.83125[/C][C]100.729201977628[/C][C]32.0247871189973[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3227.79394736842[/C][C]98.960105134984[/C][C]32.6171232636185[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3229.43611111111[/C][C]96.614077861337[/C][C]33.426144332155[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3228.55117647059[/C][C]95.1689488671518[/C][C]33.9244177318527[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3226.451875[/C][C]93.6449620073733[/C][C]34.4540892092621[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3224.42133333333[/C][C]91.3382044460748[/C][C]35.302000437692[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3225.79607142857[/C][C]89.7314226935485[/C][C]35.9494586689585[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3229.08769230769[/C][C]87.730750451959[/C][C]36.8067943756611[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3233.58958333333[/C][C]84.6822670477564[/C][C]38.1849671255230[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3239.59409090909[/C][C]80.362030341646[/C][C]40.3124967990043[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3248.0085[/C][C]74.3948128754708[/C][C]43.6590721108047[/C][/ROW]
[ROW][C]Median[/C][C]3209.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3166.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3198.10580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3224.42133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3198.10580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3224.42133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3224.42133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3198.10580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3224.42133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3226.451875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16846&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 Mean3218.81183333333117.32977651031327.433887023985
Geometric Mean3084.91043475535
Harmonic Mean2947.33138006667
Quadratic Mean3342.59778156277
Winsorized Mean ( 1 / 20 )3219.73116.58776712681227.6163621565709
Winsorized Mean ( 2 / 20 )3220.97633333333115.91864111775027.786525983008
Winsorized Mean ( 3 / 20 )3223.40533333333114.87210826284028.0608180878673
Winsorized Mean ( 4 / 20 )3221.81733333333113.62649095983528.354455955805
Winsorized Mean ( 5 / 20 )3217.99483333333112.50344680507428.6035221561603
Winsorized Mean ( 6 / 20 )3218.11983333333112.15566243025428.6933335651652
Winsorized Mean ( 7 / 20 )3219.70183333333108.52487802772129.6678687121943
Winsorized Mean ( 8 / 20 )3215.9125106.34459318001530.2404889974637
Winsorized Mean ( 9 / 20 )3219.1825105.46957446796430.5223806603848
Winsorized Mean ( 10 / 20 )3213.40083333333101.41650870674431.6851849300512
Winsorized Mean ( 11 / 20 )3216.95566666667100.63075996284031.9679158525147
Winsorized Mean ( 12 / 20 )3235.4536666666793.500403875065634.6036330601294
Winsorized Mean ( 13 / 20 )3243.1063333333390.767170835735235.7299484325947
Winsorized Mean ( 14 / 20 )3240.6656666666790.292702455959235.8906708794913
Winsorized Mean ( 15 / 20 )3214.7981666666783.728416214444138.3955449298476
Winsorized Mean ( 16 / 20 )3202.9741666666781.302139052301439.3959396886988
Winsorized Mean ( 17 / 20 )3198.4748333333380.065717044128839.9481195125059
Winsorized Mean ( 18 / 20 )3193.9598333333377.744787777946641.0826233451929
Winsorized Mean ( 19 / 20 )3186.3028333333374.248414300285742.9140859553828
Winsorized Mean ( 20 / 20 )3231.569566.08760769816848.8982672025149
Trimmed Mean ( 1 / 20 )3220.62931034483115.41743720435227.9041831837122
Trimmed Mean ( 2 / 20 )3221.59285714286113.90556167729728.2830162961654
Trimmed Mean ( 3 / 20 )3221.93537037037112.40081179024028.6646984043413
Trimmed Mean ( 4 / 20 )3221.37110.94047298746229.0369232549069
Trimmed Mean ( 5 / 20 )3221.2358109.49624598693729.418687106262
Trimmed Mean ( 6 / 20 )3222.04604166667107.94581469255829.8487352274234
Trimmed Mean ( 7 / 20 )3222.89956521739105.97401109029430.4121692862162
Trimmed Mean ( 8 / 20 )3223.5225104.3754781438230.8839064244408
Trimmed Mean ( 9 / 20 )3224.88142857143102.75974154734531.3827319922328
Trimmed Mean ( 10 / 20 )3225.83125100.72920197762832.0247871189973
Trimmed Mean ( 11 / 20 )3227.7939473684298.96010513498432.6171232636185
Trimmed Mean ( 12 / 20 )3229.4361111111196.61407786133733.426144332155
Trimmed Mean ( 13 / 20 )3228.5511764705995.168948867151833.9244177318527
Trimmed Mean ( 14 / 20 )3226.45187593.644962007373334.4540892092621
Trimmed Mean ( 15 / 20 )3224.4213333333391.338204446074835.302000437692
Trimmed Mean ( 16 / 20 )3225.7960714285789.731422693548535.9494586689585
Trimmed Mean ( 17 / 20 )3229.0876923076987.73075045195936.8067943756611
Trimmed Mean ( 18 / 20 )3233.5895833333384.682267047756438.1849671255230
Trimmed Mean ( 19 / 20 )3239.5940909090980.36203034164640.3124967990043
Trimmed Mean ( 20 / 20 )3248.008574.394812875470843.6590721108047
Median3209.425
Midrange3166.105
Midmean - Weighted Average at Xnp3198.10580645161
Midmean - Weighted Average at X(n+1)p3224.42133333333
Midmean - Empirical Distribution Function3198.10580645161
Midmean - Empirical Distribution Function - Averaging3224.42133333333
Midmean - Empirical Distribution Function - Interpolation3224.42133333333
Midmean - Closest Observation3198.10580645161
Midmean - True Basic - Statistics Graphics Toolkit3224.42133333333
Midmean - MS Excel (old versions)3226.451875
Number of observations60



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')