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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Mar 2010 15:05:15 -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/2010/Mar/15/t1268687157qhb95vtszwnkaxq.htm/, Retrieved Mon, 08 Aug 2022 12:54:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74455, Retrieved Mon, 08 Aug 2022 12:54:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-03-15 21:05:15] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
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Dataseries X:
7089
77102
35123
23109
11115
48105
7896
79102
2494
76101
9484
8183
9092
49109
27127
31116
77120
80115
67117
18110
3099
3105
5786
7387
5089
288
65108
44100
68102
8798
8183
288
3680
9374
2271
4671
3466
8068
2780
9883
6479
3373
6468
460
5553
6157
2345
3744
6144
9948
2049
9549
6049
745
9643
9938
5535
6932
1827
9726
7624
9529
7631
6132
7534
2137
8738
8836
3230
633
9126
123




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=74455&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=74455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74455&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 Mean16545.44444444442688.41595425096.15434691878053
Geometric Mean7368.56467028937
Harmonic Mean2357.01121146322
Quadratic Mean28051.9150188044
Winsorized Mean ( 1 / 24 )16533.66666666672683.566708788226.16107906411335
Winsorized Mean ( 2 / 24 )16478.61111111112665.706233114576.1817055857118
Winsorized Mean ( 3 / 24 )16485.02777777782664.855907881336.1860859827442
Winsorized Mean ( 4 / 24 )16439.02777777782646.306674599496.21206451072635
Winsorized Mean ( 5 / 24 )15891.31944444442474.72924917856.42143759755523
Winsorized Mean ( 6 / 24 )15899.40277777782442.868125676126.5084981913943
Winsorized Mean ( 7 / 24 )15725.66666666672383.782921743696.59693738185005
Winsorized Mean ( 8 / 24 )13957.77777777781887.430998668527.39511949714944
Winsorized Mean ( 9 / 24 )13849.02777777781853.157059199557.47320779370946
Winsorized Mean ( 10 / 24 )13303.05555555561709.172690728697.78333027886371
Winsorized Mean ( 11 / 24 )11954.33333333331368.315368606808.73653370239132
Winsorized Mean ( 12 / 24 )11334.16666666671206.729409179899.39246742512846
Winsorized Mean ( 13 / 24 )10671.52777777781037.0708867988610.2900659093012
Winsorized Mean ( 14 / 24 )9891.41666666667865.30941071475611.4310748781713
Winsorized Mean ( 15 / 24 )8876644.10476474372613.7803669307299
Winsorized Mean ( 16 / 24 )7353.33333333333355.02215705942920.7123222793737
Winsorized Mean ( 17 / 24 )7099.75313.10332042404722.6754222548153
Winsorized Mean ( 18 / 24 )7150.75304.10831181817723.5138262326594
Winsorized Mean ( 19 / 24 )7153.125299.52883314429223.8812568556768
Winsorized Mean ( 20 / 24 )7367.01388888889253.86976539731129.0188706692165
Winsorized Mean ( 21 / 24 )7464.72222222222232.79596171240132.0655142267641
Winsorized Mean ( 22 / 24 )7572.27777777778209.863687429136.0818866309875
Winsorized Mean ( 23 / 24 )7571.63888888889208.23133588193536.3616688949349
Winsorized Mean ( 24 / 24 )7634.30555555556195.77013028531338.9962735603711
Trimmed Mean ( 1 / 24 )15871.91428571432598.169870202426.10888243595778
Trimmed Mean ( 2 / 24 )15171.23529411762493.651458177686.08394378627579
Trimmed Mean ( 3 / 24 )14458.12121212122376.940532661956.08266004700147
Trimmed Mean ( 4 / 24 )13698.031252231.663738814446.13803549869793
Trimmed Mean ( 5 / 24 )12902.25806451612055.327727040066.27746996003264
Trimmed Mean ( 6 / 24 )12184.88333333331897.87921544976.42026280394569
Trimmed Mean ( 7 / 24 )11416.36206896551703.330044528026.70237814781745
Trimmed Mean ( 8 / 24 )10624.85714285711462.317294043987.26576727645374
Trimmed Mean ( 9 / 24 )10069.37037037041323.925120041727.605694776796
Trimmed Mean ( 10 / 24 )9487.884615384621147.385973807988.26913073017263
Trimmed Mean ( 11 / 24 )8938.5953.4541078176169.37486128247908
Trimmed Mean ( 12 / 24 )8527.25813.22060434410310.4857771119530
Trimmed Mean ( 13 / 24 )8161.1304347826674.77206572644212.0946477326333
Trimmed Mean ( 14 / 24 )7845.13636363636540.526729630414.5138731048522
Trimmed Mean ( 15 / 24 )7594.57142857143413.6834344106118.3584132136973
Trimmed Mean ( 16 / 24 )7440.8324.35653499640122.9401883334416
Trimmed Mean ( 17 / 24 )7451.15789473684308.79976093913724.1294160075643
Trimmed Mean ( 18 / 24 )7492.5298.00276844351625.1423838749342
Trimmed Mean ( 19 / 24 )7532.70588235294285.29706046224726.4030266212636
Trimmed Mean ( 20 / 24 )7577.65625268.24868701154428.2486238214985
Trimmed Mean ( 21 / 24 )7602.93333333333258.86245375041529.3705526745249
Trimmed Mean ( 22 / 24 )7619.85714285714251.47382348909930.3007964691301
Trimmed Mean ( 23 / 24 )7625.84615384615247.26066402954530.8413236038829
Trimmed Mean ( 24 / 24 )7632.91666666667240.09247853440231.7915692872194
Median7627.5
Midrange40119
Midmean - Weighted Average at Xnp7383.67567567568
Midmean - Weighted Average at X(n+1)p7492.5
Midmean - Empirical Distribution Function7383.67567567568
Midmean - Empirical Distribution Function - Averaging7492.5
Midmean - Empirical Distribution Function - Interpolation7492.5
Midmean - Closest Observation7383.67567567568
Midmean - True Basic - Statistics Graphics Toolkit7492.5
Midmean - MS Excel (old versions)7451.15789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16545.4444444444 & 2688.4159542509 & 6.15434691878053 \tabularnewline
Geometric Mean & 7368.56467028937 &  &  \tabularnewline
Harmonic Mean & 2357.01121146322 &  &  \tabularnewline
Quadratic Mean & 28051.9150188044 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16533.6666666667 & 2683.56670878822 & 6.16107906411335 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16478.6111111111 & 2665.70623311457 & 6.1817055857118 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16485.0277777778 & 2664.85590788133 & 6.1860859827442 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16439.0277777778 & 2646.30667459949 & 6.21206451072635 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15891.3194444444 & 2474.7292491785 & 6.42143759755523 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15899.4027777778 & 2442.86812567612 & 6.5084981913943 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15725.6666666667 & 2383.78292174369 & 6.59693738185005 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13957.7777777778 & 1887.43099866852 & 7.39511949714944 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13849.0277777778 & 1853.15705919955 & 7.47320779370946 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13303.0555555556 & 1709.17269072869 & 7.78333027886371 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11954.3333333333 & 1368.31536860680 & 8.73653370239132 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 11334.1666666667 & 1206.72940917989 & 9.39246742512846 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 10671.5277777778 & 1037.07088679886 & 10.2900659093012 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9891.41666666667 & 865.309410714756 & 11.4310748781713 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8876 & 644.104764743726 & 13.7803669307299 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7353.33333333333 & 355.022157059429 & 20.7123222793737 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7099.75 & 313.103320424047 & 22.6754222548153 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7150.75 & 304.108311818177 & 23.5138262326594 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7153.125 & 299.528833144292 & 23.8812568556768 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7367.01388888889 & 253.869765397311 & 29.0188706692165 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7464.72222222222 & 232.795961712401 & 32.0655142267641 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7572.27777777778 & 209.8636874291 & 36.0818866309875 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7571.63888888889 & 208.231335881935 & 36.3616688949349 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7634.30555555556 & 195.770130285313 & 38.9962735603711 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15871.9142857143 & 2598.16987020242 & 6.10888243595778 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15171.2352941176 & 2493.65145817768 & 6.08394378627579 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 14458.1212121212 & 2376.94053266195 & 6.08266004700147 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13698.03125 & 2231.66373881444 & 6.13803549869793 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 12902.2580645161 & 2055.32772704006 & 6.27746996003264 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 12184.8833333333 & 1897.8792154497 & 6.42026280394569 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 11416.3620689655 & 1703.33004452802 & 6.70237814781745 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 10624.8571428571 & 1462.31729404398 & 7.26576727645374 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 10069.3703703704 & 1323.92512004172 & 7.605694776796 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9487.88461538462 & 1147.38597380798 & 8.26913073017263 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8938.5 & 953.454107817616 & 9.37486128247908 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8527.25 & 813.220604344103 & 10.4857771119530 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8161.1304347826 & 674.772065726442 & 12.0946477326333 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7845.13636363636 & 540.5267296304 & 14.5138731048522 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7594.57142857143 & 413.68343441061 & 18.3584132136973 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7440.8 & 324.356534996401 & 22.9401883334416 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7451.15789473684 & 308.799760939137 & 24.1294160075643 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7492.5 & 298.002768443516 & 25.1423838749342 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7532.70588235294 & 285.297060462247 & 26.4030266212636 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7577.65625 & 268.248687011544 & 28.2486238214985 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7602.93333333333 & 258.862453750415 & 29.3705526745249 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7619.85714285714 & 251.473823489099 & 30.3007964691301 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7625.84615384615 & 247.260664029545 & 30.8413236038829 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7632.91666666667 & 240.092478534402 & 31.7915692872194 \tabularnewline
Median & 7627.5 &  &  \tabularnewline
Midrange & 40119 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7383.67567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7492.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7383.67567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7492.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7492.5 &  &  \tabularnewline
Midmean - Closest Observation & 7383.67567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7492.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7451.15789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74455&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]16545.4444444444[/C][C]2688.4159542509[/C][C]6.15434691878053[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7368.56467028937[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2357.01121146322[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]28051.9150188044[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16533.6666666667[/C][C]2683.56670878822[/C][C]6.16107906411335[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16478.6111111111[/C][C]2665.70623311457[/C][C]6.1817055857118[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16485.0277777778[/C][C]2664.85590788133[/C][C]6.1860859827442[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16439.0277777778[/C][C]2646.30667459949[/C][C]6.21206451072635[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15891.3194444444[/C][C]2474.7292491785[/C][C]6.42143759755523[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15899.4027777778[/C][C]2442.86812567612[/C][C]6.5084981913943[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15725.6666666667[/C][C]2383.78292174369[/C][C]6.59693738185005[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13957.7777777778[/C][C]1887.43099866852[/C][C]7.39511949714944[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13849.0277777778[/C][C]1853.15705919955[/C][C]7.47320779370946[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13303.0555555556[/C][C]1709.17269072869[/C][C]7.78333027886371[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11954.3333333333[/C][C]1368.31536860680[/C][C]8.73653370239132[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]11334.1666666667[/C][C]1206.72940917989[/C][C]9.39246742512846[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]10671.5277777778[/C][C]1037.07088679886[/C][C]10.2900659093012[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9891.41666666667[/C][C]865.309410714756[/C][C]11.4310748781713[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8876[/C][C]644.104764743726[/C][C]13.7803669307299[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7353.33333333333[/C][C]355.022157059429[/C][C]20.7123222793737[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7099.75[/C][C]313.103320424047[/C][C]22.6754222548153[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7150.75[/C][C]304.108311818177[/C][C]23.5138262326594[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7153.125[/C][C]299.528833144292[/C][C]23.8812568556768[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7367.01388888889[/C][C]253.869765397311[/C][C]29.0188706692165[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7464.72222222222[/C][C]232.795961712401[/C][C]32.0655142267641[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7572.27777777778[/C][C]209.8636874291[/C][C]36.0818866309875[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7571.63888888889[/C][C]208.231335881935[/C][C]36.3616688949349[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7634.30555555556[/C][C]195.770130285313[/C][C]38.9962735603711[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15871.9142857143[/C][C]2598.16987020242[/C][C]6.10888243595778[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15171.2352941176[/C][C]2493.65145817768[/C][C]6.08394378627579[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]14458.1212121212[/C][C]2376.94053266195[/C][C]6.08266004700147[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13698.03125[/C][C]2231.66373881444[/C][C]6.13803549869793[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]12902.2580645161[/C][C]2055.32772704006[/C][C]6.27746996003264[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]12184.8833333333[/C][C]1897.8792154497[/C][C]6.42026280394569[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]11416.3620689655[/C][C]1703.33004452802[/C][C]6.70237814781745[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]10624.8571428571[/C][C]1462.31729404398[/C][C]7.26576727645374[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]10069.3703703704[/C][C]1323.92512004172[/C][C]7.605694776796[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9487.88461538462[/C][C]1147.38597380798[/C][C]8.26913073017263[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8938.5[/C][C]953.454107817616[/C][C]9.37486128247908[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8527.25[/C][C]813.220604344103[/C][C]10.4857771119530[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8161.1304347826[/C][C]674.772065726442[/C][C]12.0946477326333[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7845.13636363636[/C][C]540.5267296304[/C][C]14.5138731048522[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7594.57142857143[/C][C]413.68343441061[/C][C]18.3584132136973[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7440.8[/C][C]324.356534996401[/C][C]22.9401883334416[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7451.15789473684[/C][C]308.799760939137[/C][C]24.1294160075643[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7492.5[/C][C]298.002768443516[/C][C]25.1423838749342[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7532.70588235294[/C][C]285.297060462247[/C][C]26.4030266212636[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7577.65625[/C][C]268.248687011544[/C][C]28.2486238214985[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7602.93333333333[/C][C]258.862453750415[/C][C]29.3705526745249[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7619.85714285714[/C][C]251.473823489099[/C][C]30.3007964691301[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7625.84615384615[/C][C]247.260664029545[/C][C]30.8413236038829[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7632.91666666667[/C][C]240.092478534402[/C][C]31.7915692872194[/C][/ROW]
[ROW][C]Median[/C][C]7627.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]40119[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7383.67567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7492.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7383.67567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7492.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7492.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7383.67567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7492.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7451.15789473684[/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=74455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74455&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 Mean16545.44444444442688.41595425096.15434691878053
Geometric Mean7368.56467028937
Harmonic Mean2357.01121146322
Quadratic Mean28051.9150188044
Winsorized Mean ( 1 / 24 )16533.66666666672683.566708788226.16107906411335
Winsorized Mean ( 2 / 24 )16478.61111111112665.706233114576.1817055857118
Winsorized Mean ( 3 / 24 )16485.02777777782664.855907881336.1860859827442
Winsorized Mean ( 4 / 24 )16439.02777777782646.306674599496.21206451072635
Winsorized Mean ( 5 / 24 )15891.31944444442474.72924917856.42143759755523
Winsorized Mean ( 6 / 24 )15899.40277777782442.868125676126.5084981913943
Winsorized Mean ( 7 / 24 )15725.66666666672383.782921743696.59693738185005
Winsorized Mean ( 8 / 24 )13957.77777777781887.430998668527.39511949714944
Winsorized Mean ( 9 / 24 )13849.02777777781853.157059199557.47320779370946
Winsorized Mean ( 10 / 24 )13303.05555555561709.172690728697.78333027886371
Winsorized Mean ( 11 / 24 )11954.33333333331368.315368606808.73653370239132
Winsorized Mean ( 12 / 24 )11334.16666666671206.729409179899.39246742512846
Winsorized Mean ( 13 / 24 )10671.52777777781037.0708867988610.2900659093012
Winsorized Mean ( 14 / 24 )9891.41666666667865.30941071475611.4310748781713
Winsorized Mean ( 15 / 24 )8876644.10476474372613.7803669307299
Winsorized Mean ( 16 / 24 )7353.33333333333355.02215705942920.7123222793737
Winsorized Mean ( 17 / 24 )7099.75313.10332042404722.6754222548153
Winsorized Mean ( 18 / 24 )7150.75304.10831181817723.5138262326594
Winsorized Mean ( 19 / 24 )7153.125299.52883314429223.8812568556768
Winsorized Mean ( 20 / 24 )7367.01388888889253.86976539731129.0188706692165
Winsorized Mean ( 21 / 24 )7464.72222222222232.79596171240132.0655142267641
Winsorized Mean ( 22 / 24 )7572.27777777778209.863687429136.0818866309875
Winsorized Mean ( 23 / 24 )7571.63888888889208.23133588193536.3616688949349
Winsorized Mean ( 24 / 24 )7634.30555555556195.77013028531338.9962735603711
Trimmed Mean ( 1 / 24 )15871.91428571432598.169870202426.10888243595778
Trimmed Mean ( 2 / 24 )15171.23529411762493.651458177686.08394378627579
Trimmed Mean ( 3 / 24 )14458.12121212122376.940532661956.08266004700147
Trimmed Mean ( 4 / 24 )13698.031252231.663738814446.13803549869793
Trimmed Mean ( 5 / 24 )12902.25806451612055.327727040066.27746996003264
Trimmed Mean ( 6 / 24 )12184.88333333331897.87921544976.42026280394569
Trimmed Mean ( 7 / 24 )11416.36206896551703.330044528026.70237814781745
Trimmed Mean ( 8 / 24 )10624.85714285711462.317294043987.26576727645374
Trimmed Mean ( 9 / 24 )10069.37037037041323.925120041727.605694776796
Trimmed Mean ( 10 / 24 )9487.884615384621147.385973807988.26913073017263
Trimmed Mean ( 11 / 24 )8938.5953.4541078176169.37486128247908
Trimmed Mean ( 12 / 24 )8527.25813.22060434410310.4857771119530
Trimmed Mean ( 13 / 24 )8161.1304347826674.77206572644212.0946477326333
Trimmed Mean ( 14 / 24 )7845.13636363636540.526729630414.5138731048522
Trimmed Mean ( 15 / 24 )7594.57142857143413.6834344106118.3584132136973
Trimmed Mean ( 16 / 24 )7440.8324.35653499640122.9401883334416
Trimmed Mean ( 17 / 24 )7451.15789473684308.79976093913724.1294160075643
Trimmed Mean ( 18 / 24 )7492.5298.00276844351625.1423838749342
Trimmed Mean ( 19 / 24 )7532.70588235294285.29706046224726.4030266212636
Trimmed Mean ( 20 / 24 )7577.65625268.24868701154428.2486238214985
Trimmed Mean ( 21 / 24 )7602.93333333333258.86245375041529.3705526745249
Trimmed Mean ( 22 / 24 )7619.85714285714251.47382348909930.3007964691301
Trimmed Mean ( 23 / 24 )7625.84615384615247.26066402954530.8413236038829
Trimmed Mean ( 24 / 24 )7632.91666666667240.09247853440231.7915692872194
Median7627.5
Midrange40119
Midmean - Weighted Average at Xnp7383.67567567568
Midmean - Weighted Average at X(n+1)p7492.5
Midmean - Empirical Distribution Function7383.67567567568
Midmean - Empirical Distribution Function - Averaging7492.5
Midmean - Empirical Distribution Function - Interpolation7492.5
Midmean - Closest Observation7383.67567567568
Midmean - True Basic - Statistics Graphics Toolkit7492.5
Midmean - MS Excel (old versions)7451.15789473684
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')