Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 19 Apr 2008 08:39:17 -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/Apr/19/t12086161453balub1codfyqkx.htm/, Retrieved Tue, 14 May 2024 22:30:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10282, Retrieved Tue, 14 May 2024 22:30:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Eige...] [2008-04-19 14:39:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
2301
2512
3145
2741
2548
1987
2281
2016
2434
2637
1831
1851
1839
2609
2417
2394
2372
2717
2998
2538
3007
2475
2175
2465
2279
2323
2746
2601
2486
2718
2646
2551
2712
2606
2365
3533
3509
2912
3599
2719
2869
4085
2686
2545
3071
3388
2652
3190
2884
3295
3818
3226
3953
3810
2877
3515
3708
3450
3360
4098
4374
3703
4257
3487
3659
3904
2957
3320
3420
3500
2791
2919




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10282&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10282&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2935.6388888888972.081931804214140.7264180552562
Geometric Mean2873.63201821896
Harmonic Mean2812.5904873832
Quadratic Mean2997.81217445879
Winsorized Mean ( 1 / 24 )2934.12571.618189569893340.9689915037093
Winsorized Mean ( 2 / 24 )2930.0416666666770.455741547575741.5869821579855
Winsorized Mean ( 3 / 24 )2935.1666666666769.170317794916742.4339046029708
Winsorized Mean ( 4 / 24 )2929.4444444444467.214643127364843.5834262914028
Winsorized Mean ( 5 / 24 )2937.0833333333364.512323524590845.5274771216972
Winsorized Mean ( 6 / 24 )2938.5833333333361.659842123321447.6579769285832
Winsorized Mean ( 7 / 24 )293861.474745759516447.791982930571
Winsorized Mean ( 8 / 24 )2928.8888888888958.95227823733649.6823698160989
Winsorized Mean ( 9 / 24 )2931.0138888888958.428140572344250.1644218039043
Winsorized Mean ( 10 / 24 )2930.7361111111156.464885126679951.9036938539051
Winsorized Mean ( 11 / 24 )2922.6388888888954.681984662391153.4479300071748
Winsorized Mean ( 12 / 24 )2915.3055555555652.290279525917955.7523421558795
Winsorized Mean ( 13 / 24 )2916.2083333333351.175183710631756.9848141595921
Winsorized Mean ( 14 / 24 )2918.3472222222250.532791843856457.751553312941
Winsorized Mean ( 15 / 24 )2922.9305555555649.366116210712959.2092467448604
Winsorized Mean ( 16 / 24 )2922.2638888888948.602709731189160.1255342562439
Winsorized Mean ( 17 / 24 )2916.12546.850300743678162.2434638350427
Winsorized Mean ( 18 / 24 )2915.12544.821201639322565.0389747124162
Winsorized Mean ( 19 / 24 )2913.5416666666742.628811228472568.3467725865333
Winsorized Mean ( 20 / 24 )2907.7083333333341.176152361270570.616319558509
Winsorized Mean ( 21 / 24 )2896.9166666666739.279314332467673.7517117062333
Winsorized Mean ( 22 / 24 )2890.1944444444438.01194441472576.0338490688955
Winsorized Mean ( 23 / 24 )2884.12532.758302639531988.0425653226462
Winsorized Mean ( 24 / 24 )2873.7916666666730.805011338929193.289745458882
Trimmed Mean ( 1 / 24 )2930.8714285714369.410791224994242.2250110803527
Trimmed Mean ( 2 / 24 )2927.4264705882466.78140179769543.8359541995909
Trimmed Mean ( 3 / 24 )292664.395297284462645.4381006593472
Trimmed Mean ( 4 / 24 )2922.562562.129492567750747.039857871252
Trimmed Mean ( 5 / 24 )2920.5645161290360.142421400481948.5608069665388
Trimmed Mean ( 6 / 24 )2916.658.599373321498249.7718633269068
Trimmed Mean ( 7 / 24 )2912.0517241379357.513781837736650.6322420659746
Trimmed Mean ( 8 / 24 )2907.2857142857156.205482899604551.726016116235
Trimmed Mean ( 9 / 24 )2903.6851851851955.199490979395852.6034775623028
Trimmed Mean ( 10 / 24 )2899.4807692307754.035660048260253.6586536861249
Trimmed Mean ( 11 / 24 )2894.9852.991708939479754.6308103274472
Trimmed Mean ( 12 / 24 )2891.2083333333352.04191367219655.5553808329303
Trimmed Mean ( 13 / 24 )2888.0652173913051.313636369514156.2826067635139
Trimmed Mean ( 14 / 24 )2884.5227272727350.551885394629557.0606359140696
Trimmed Mean ( 15 / 24 )2880.3809523809549.628877645755958.0384060453818
Trimmed Mean ( 16 / 24 )2875.27548.594462429850559.1687788325812
Trimmed Mean ( 17 / 24 )2869.7105263157947.319424042798360.6455083586872
Trimmed Mean ( 18 / 24 )2864.2545.974205587101662.3012396499917
Trimmed Mean ( 19 / 24 )2858.2647058823544.571785293487164.1272205513385
Trimmed Mean ( 20 / 24 )2851.7187543.119938561673566.134573589924
Trimmed Mean ( 21 / 24 )284541.393458309310168.7306670232989
Trimmed Mean ( 22 / 24 )2838.6428571428639.435642242300871.9816565862335
Trimmed Mean ( 23 / 24 )2832.1538461538536.870112653755176.8143529354093
Trimmed Mean ( 24 / 24 )2825.37534.942074867049580.8588216569915
Median2768.5
Midrange3102.5
Midmean - Weighted Average at Xnp2854.02702702703
Midmean - Weighted Average at X(n+1)p2864.25
Midmean - Empirical Distribution Function2854.02702702703
Midmean - Empirical Distribution Function - Averaging2864.25
Midmean - Empirical Distribution Function - Interpolation2864.25
Midmean - Closest Observation2854.02702702703
Midmean - True Basic - Statistics Graphics Toolkit2864.25
Midmean - MS Excel (old versions)2869.71052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2935.63888888889 & 72.0819318042141 & 40.7264180552562 \tabularnewline
Geometric Mean & 2873.63201821896 &  &  \tabularnewline
Harmonic Mean & 2812.5904873832 &  &  \tabularnewline
Quadratic Mean & 2997.81217445879 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2934.125 & 71.6181895698933 & 40.9689915037093 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2930.04166666667 & 70.4557415475757 & 41.5869821579855 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2935.16666666667 & 69.1703177949167 & 42.4339046029708 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2929.44444444444 & 67.2146431273648 & 43.5834262914028 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2937.08333333333 & 64.5123235245908 & 45.5274771216972 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2938.58333333333 & 61.6598421233214 & 47.6579769285832 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2938 & 61.4747457595164 & 47.791982930571 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2928.88888888889 & 58.952278237336 & 49.6823698160989 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2931.01388888889 & 58.4281405723442 & 50.1644218039043 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2930.73611111111 & 56.4648851266799 & 51.9036938539051 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2922.63888888889 & 54.6819846623911 & 53.4479300071748 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2915.30555555556 & 52.2902795259179 & 55.7523421558795 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2916.20833333333 & 51.1751837106317 & 56.9848141595921 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2918.34722222222 & 50.5327918438564 & 57.751553312941 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2922.93055555556 & 49.3661162107129 & 59.2092467448604 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2922.26388888889 & 48.6027097311891 & 60.1255342562439 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2916.125 & 46.8503007436781 & 62.2434638350427 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2915.125 & 44.8212016393225 & 65.0389747124162 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2913.54166666667 & 42.6288112284725 & 68.3467725865333 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2907.70833333333 & 41.1761523612705 & 70.616319558509 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2896.91666666667 & 39.2793143324676 & 73.7517117062333 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2890.19444444444 & 38.011944414725 & 76.0338490688955 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2884.125 & 32.7583026395319 & 88.0425653226462 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2873.79166666667 & 30.8050113389291 & 93.289745458882 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2930.87142857143 & 69.4107912249942 & 42.2250110803527 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2927.42647058824 & 66.781401797695 & 43.8359541995909 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2926 & 64.3952972844626 & 45.4381006593472 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2922.5625 & 62.1294925677507 & 47.039857871252 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2920.56451612903 & 60.1424214004819 & 48.5608069665388 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2916.6 & 58.5993733214982 & 49.7718633269068 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2912.05172413793 & 57.5137818377366 & 50.6322420659746 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2907.28571428571 & 56.2054828996045 & 51.726016116235 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2903.68518518519 & 55.1994909793958 & 52.6034775623028 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2899.48076923077 & 54.0356600482602 & 53.6586536861249 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2894.98 & 52.9917089394797 & 54.6308103274472 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2891.20833333333 & 52.041913672196 & 55.5553808329303 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2888.06521739130 & 51.3136363695141 & 56.2826067635139 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2884.52272727273 & 50.5518853946295 & 57.0606359140696 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2880.38095238095 & 49.6288776457559 & 58.0384060453818 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2875.275 & 48.5944624298505 & 59.1687788325812 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2869.71052631579 & 47.3194240427983 & 60.6455083586872 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2864.25 & 45.9742055871016 & 62.3012396499917 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2858.26470588235 & 44.5717852934871 & 64.1272205513385 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2851.71875 & 43.1199385616735 & 66.134573589924 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2845 & 41.3934583093101 & 68.7306670232989 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2838.64285714286 & 39.4356422423008 & 71.9816565862335 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2832.15384615385 & 36.8701126537551 & 76.8143529354093 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2825.375 & 34.9420748670495 & 80.8588216569915 \tabularnewline
Median & 2768.5 &  &  \tabularnewline
Midrange & 3102.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2854.02702702703 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2864.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2854.02702702703 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2864.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2864.25 &  &  \tabularnewline
Midmean - Closest Observation & 2854.02702702703 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2864.25 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2869.71052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10282&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]2935.63888888889[/C][C]72.0819318042141[/C][C]40.7264180552562[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2873.63201821896[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2812.5904873832[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2997.81217445879[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2934.125[/C][C]71.6181895698933[/C][C]40.9689915037093[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2930.04166666667[/C][C]70.4557415475757[/C][C]41.5869821579855[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2935.16666666667[/C][C]69.1703177949167[/C][C]42.4339046029708[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2929.44444444444[/C][C]67.2146431273648[/C][C]43.5834262914028[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2937.08333333333[/C][C]64.5123235245908[/C][C]45.5274771216972[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2938.58333333333[/C][C]61.6598421233214[/C][C]47.6579769285832[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2938[/C][C]61.4747457595164[/C][C]47.791982930571[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2928.88888888889[/C][C]58.952278237336[/C][C]49.6823698160989[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2931.01388888889[/C][C]58.4281405723442[/C][C]50.1644218039043[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2930.73611111111[/C][C]56.4648851266799[/C][C]51.9036938539051[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2922.63888888889[/C][C]54.6819846623911[/C][C]53.4479300071748[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2915.30555555556[/C][C]52.2902795259179[/C][C]55.7523421558795[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2916.20833333333[/C][C]51.1751837106317[/C][C]56.9848141595921[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2918.34722222222[/C][C]50.5327918438564[/C][C]57.751553312941[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2922.93055555556[/C][C]49.3661162107129[/C][C]59.2092467448604[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2922.26388888889[/C][C]48.6027097311891[/C][C]60.1255342562439[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2916.125[/C][C]46.8503007436781[/C][C]62.2434638350427[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2915.125[/C][C]44.8212016393225[/C][C]65.0389747124162[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2913.54166666667[/C][C]42.6288112284725[/C][C]68.3467725865333[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2907.70833333333[/C][C]41.1761523612705[/C][C]70.616319558509[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2896.91666666667[/C][C]39.2793143324676[/C][C]73.7517117062333[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2890.19444444444[/C][C]38.011944414725[/C][C]76.0338490688955[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2884.125[/C][C]32.7583026395319[/C][C]88.0425653226462[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2873.79166666667[/C][C]30.8050113389291[/C][C]93.289745458882[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2930.87142857143[/C][C]69.4107912249942[/C][C]42.2250110803527[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2927.42647058824[/C][C]66.781401797695[/C][C]43.8359541995909[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2926[/C][C]64.3952972844626[/C][C]45.4381006593472[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2922.5625[/C][C]62.1294925677507[/C][C]47.039857871252[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2920.56451612903[/C][C]60.1424214004819[/C][C]48.5608069665388[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2916.6[/C][C]58.5993733214982[/C][C]49.7718633269068[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2912.05172413793[/C][C]57.5137818377366[/C][C]50.6322420659746[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2907.28571428571[/C][C]56.2054828996045[/C][C]51.726016116235[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2903.68518518519[/C][C]55.1994909793958[/C][C]52.6034775623028[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2899.48076923077[/C][C]54.0356600482602[/C][C]53.6586536861249[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2894.98[/C][C]52.9917089394797[/C][C]54.6308103274472[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2891.20833333333[/C][C]52.041913672196[/C][C]55.5553808329303[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2888.06521739130[/C][C]51.3136363695141[/C][C]56.2826067635139[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2884.52272727273[/C][C]50.5518853946295[/C][C]57.0606359140696[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2880.38095238095[/C][C]49.6288776457559[/C][C]58.0384060453818[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2875.275[/C][C]48.5944624298505[/C][C]59.1687788325812[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2869.71052631579[/C][C]47.3194240427983[/C][C]60.6455083586872[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2864.25[/C][C]45.9742055871016[/C][C]62.3012396499917[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2858.26470588235[/C][C]44.5717852934871[/C][C]64.1272205513385[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2851.71875[/C][C]43.1199385616735[/C][C]66.134573589924[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2845[/C][C]41.3934583093101[/C][C]68.7306670232989[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2838.64285714286[/C][C]39.4356422423008[/C][C]71.9816565862335[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2832.15384615385[/C][C]36.8701126537551[/C][C]76.8143529354093[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2825.375[/C][C]34.9420748670495[/C][C]80.8588216569915[/C][/ROW]
[ROW][C]Median[/C][C]2768.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3102.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2854.02702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2864.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2854.02702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2864.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2864.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2854.02702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2864.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2869.71052631579[/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=10282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10282&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 Mean2935.6388888888972.081931804214140.7264180552562
Geometric Mean2873.63201821896
Harmonic Mean2812.5904873832
Quadratic Mean2997.81217445879
Winsorized Mean ( 1 / 24 )2934.12571.618189569893340.9689915037093
Winsorized Mean ( 2 / 24 )2930.0416666666770.455741547575741.5869821579855
Winsorized Mean ( 3 / 24 )2935.1666666666769.170317794916742.4339046029708
Winsorized Mean ( 4 / 24 )2929.4444444444467.214643127364843.5834262914028
Winsorized Mean ( 5 / 24 )2937.0833333333364.512323524590845.5274771216972
Winsorized Mean ( 6 / 24 )2938.5833333333361.659842123321447.6579769285832
Winsorized Mean ( 7 / 24 )293861.474745759516447.791982930571
Winsorized Mean ( 8 / 24 )2928.8888888888958.95227823733649.6823698160989
Winsorized Mean ( 9 / 24 )2931.0138888888958.428140572344250.1644218039043
Winsorized Mean ( 10 / 24 )2930.7361111111156.464885126679951.9036938539051
Winsorized Mean ( 11 / 24 )2922.6388888888954.681984662391153.4479300071748
Winsorized Mean ( 12 / 24 )2915.3055555555652.290279525917955.7523421558795
Winsorized Mean ( 13 / 24 )2916.2083333333351.175183710631756.9848141595921
Winsorized Mean ( 14 / 24 )2918.3472222222250.532791843856457.751553312941
Winsorized Mean ( 15 / 24 )2922.9305555555649.366116210712959.2092467448604
Winsorized Mean ( 16 / 24 )2922.2638888888948.602709731189160.1255342562439
Winsorized Mean ( 17 / 24 )2916.12546.850300743678162.2434638350427
Winsorized Mean ( 18 / 24 )2915.12544.821201639322565.0389747124162
Winsorized Mean ( 19 / 24 )2913.5416666666742.628811228472568.3467725865333
Winsorized Mean ( 20 / 24 )2907.7083333333341.176152361270570.616319558509
Winsorized Mean ( 21 / 24 )2896.9166666666739.279314332467673.7517117062333
Winsorized Mean ( 22 / 24 )2890.1944444444438.01194441472576.0338490688955
Winsorized Mean ( 23 / 24 )2884.12532.758302639531988.0425653226462
Winsorized Mean ( 24 / 24 )2873.7916666666730.805011338929193.289745458882
Trimmed Mean ( 1 / 24 )2930.8714285714369.410791224994242.2250110803527
Trimmed Mean ( 2 / 24 )2927.4264705882466.78140179769543.8359541995909
Trimmed Mean ( 3 / 24 )292664.395297284462645.4381006593472
Trimmed Mean ( 4 / 24 )2922.562562.129492567750747.039857871252
Trimmed Mean ( 5 / 24 )2920.5645161290360.142421400481948.5608069665388
Trimmed Mean ( 6 / 24 )2916.658.599373321498249.7718633269068
Trimmed Mean ( 7 / 24 )2912.0517241379357.513781837736650.6322420659746
Trimmed Mean ( 8 / 24 )2907.2857142857156.205482899604551.726016116235
Trimmed Mean ( 9 / 24 )2903.6851851851955.199490979395852.6034775623028
Trimmed Mean ( 10 / 24 )2899.4807692307754.035660048260253.6586536861249
Trimmed Mean ( 11 / 24 )2894.9852.991708939479754.6308103274472
Trimmed Mean ( 12 / 24 )2891.2083333333352.04191367219655.5553808329303
Trimmed Mean ( 13 / 24 )2888.0652173913051.313636369514156.2826067635139
Trimmed Mean ( 14 / 24 )2884.5227272727350.551885394629557.0606359140696
Trimmed Mean ( 15 / 24 )2880.3809523809549.628877645755958.0384060453818
Trimmed Mean ( 16 / 24 )2875.27548.594462429850559.1687788325812
Trimmed Mean ( 17 / 24 )2869.7105263157947.319424042798360.6455083586872
Trimmed Mean ( 18 / 24 )2864.2545.974205587101662.3012396499917
Trimmed Mean ( 19 / 24 )2858.2647058823544.571785293487164.1272205513385
Trimmed Mean ( 20 / 24 )2851.7187543.119938561673566.134573589924
Trimmed Mean ( 21 / 24 )284541.393458309310168.7306670232989
Trimmed Mean ( 22 / 24 )2838.6428571428639.435642242300871.9816565862335
Trimmed Mean ( 23 / 24 )2832.1538461538536.870112653755176.8143529354093
Trimmed Mean ( 24 / 24 )2825.37534.942074867049580.8588216569915
Median2768.5
Midrange3102.5
Midmean - Weighted Average at Xnp2854.02702702703
Midmean - Weighted Average at X(n+1)p2864.25
Midmean - Empirical Distribution Function2854.02702702703
Midmean - Empirical Distribution Function - Averaging2864.25
Midmean - Empirical Distribution Function - Interpolation2864.25
Midmean - Closest Observation2854.02702702703
Midmean - True Basic - Statistics Graphics Toolkit2864.25
Midmean - MS Excel (old versions)2869.71052631579
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')