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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, 07 Oct 2013 06:26:48 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/07/t1381141628luejoh2q2d29w0x.htm/, Retrieved Sat, 04 May 2024 05:44:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=213623, Retrieved Sat, 04 May 2024 05:44:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-07 10:26:48] [0f9b748f6fe1dd88ddc67537cf760c5a] [Current]
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Dataseries X:
9244
7074
7044
6492
6362
8287
18177
10379
11130
9606
7294
7415
9230
7423
6927
7572
5877
8878
16706
9611
12714
10549
8421
9993
12384
9798
11738
9011
7673
10736
18316
10973
14027
10242
8547
8187
11101
8685
9790
8003
7412
9397
17774
11230
13321
9432
7653
7651
10762
8614
8748
7235
7735
8360
16202
11053
13593
9738
8226
7866
11606
9456
8471
7553
8259
9009
13968
12844
14388
12048
9167
7733




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213623&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=213623&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213623&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9973.88888888889336.48354416110629.6415354092724
Geometric Mean9626.74897555659
Harmonic Mean9327.40621658677
Quadratic Mean10369.0483183259
Winsorized Mean ( 1 / 24 )9978.69444444445334.72317156145629.811782667733
Winsorized Mean ( 2 / 24 )9971.11111111111330.38738439864730.1800600808653
Winsorized Mean ( 3 / 24 )9944.73611111111313.63842403338731.707645967678
Winsorized Mean ( 4 / 24 )9923.23611111111304.44482457436532.5945304702896
Winsorized Mean ( 5 / 24 )9799.34722222222270.63002637105936.2093864957408
Winsorized Mean ( 6 / 24 )9782.68055555555261.72805178900237.3772718999265
Winsorized Mean ( 7 / 24 )9782.68055555555259.64138912987637.6776622107123
Winsorized Mean ( 8 / 24 )9754.125248.62128430917139.2328638599998
Winsorized Mean ( 9 / 24 )9720.5241.29956090048540.2839522945044
Winsorized Mean ( 10 / 24 )9655.36111111111227.6390281011842.4152272641911
Winsorized Mean ( 11 / 24 )9655.36111111111221.04158513143243.6811973881295
Winsorized Mean ( 12 / 24 )9603.52777777778210.12318278884445.7042752271106
Winsorized Mean ( 13 / 24 )9557.125197.12057801258948.4836494310078
Winsorized Mean ( 14 / 24 )9497.23611111111186.59823264876650.8967098792825
Winsorized Mean ( 15 / 24 )9473.90277777778181.414635615652.2223730496148
Winsorized Mean ( 16 / 24 )9403.68055555555166.13521938901356.6025710270164
Winsorized Mean ( 17 / 24 )9380.54166666667162.44915171402357.7444792274463
Winsorized Mean ( 18 / 24 )9406.04166666667156.74374594415460.0090396590235
Winsorized Mean ( 19 / 24 )9429.52777777778149.8866968692262.9110386361057
Winsorized Mean ( 20 / 24 )9458.41666666667139.79149708224267.6608868499497
Winsorized Mean ( 21 / 24 )9408.25129.08265592950672.8854696415447
Winsorized Mean ( 22 / 24 )9410.38888888889126.61401264699874.3234393425727
Winsorized Mean ( 23 / 24 )9359.59722222222116.76865371202780.1550495332827
Winsorized Mean ( 24 / 24 )9327.26388888889105.5798691085488.3432037531715
Trimmed Mean ( 1 / 24 )9913.24285714286319.21029526439231.0555235974831
Trimmed Mean ( 2 / 24 )9843.94117647059300.32404351973932.7777325488213
Trimmed Mean ( 3 / 24 )9774.57575757576280.06300411753934.9013458181484
Trimmed Mean ( 4 / 24 )9710.765625263.5577034855236.8449318558185
Trimmed Mean ( 5 / 24 )9649.08064516129246.92170531459339.0774907085135
Trimmed Mean ( 6 / 24 )9613.01666666667238.53563910920240.3001274885629
Trimmed Mean ( 7 / 24 )9577.91379310345230.87046187429741.4860944762971
Trimmed Mean ( 8 / 24 )9540.30357142857221.89073583437142.9955019778287
Trimmed Mean ( 9 / 24 )9504.66666666667213.63606337676844.4899916073827
Trimmed Mean ( 10 / 24 )9471.46153846154205.16914528291746.1641614064383
Trimmed Mean ( 11 / 24 )9444.98197.97857746406347.7070808416858
Trimmed Mean ( 12 / 24 )9416.29166666667190.32846737936149.4739005484566
Trimmed Mean ( 13 / 24 )9391.86956521739183.21773854773651.2607001901752
Trimmed Mean ( 14 / 24 )9371.06818181818177.16136860540152.8956637419682
Trimmed Mean ( 15 / 24 )9355.61904761905171.78851471812854.4600962582967
Trimmed Mean ( 16 / 24 )9341.425165.86016618695456.321087906487
Trimmed Mean ( 17 / 24 )9334.05263157895161.69258517792357.7271531734617
Trimmed Mean ( 18 / 24 )9328.58333333333156.79245899727759.4963775234583
Trimmed Mean ( 19 / 24 )9319.47058823529151.32289045353461.5866546052857
Trimmed Mean ( 20 / 24 )9306.4375145.31873295685464.0415541110115
Trimmed Mean ( 21 / 24 )9288.2139.40779839332466.6261149451222
Trimmed Mean ( 22 / 24 )9273.5134.13271777920569.1367486884521
Trimmed Mean ( 23 / 24 )9256.26923076923126.64792576505873.0866232103977
Trimmed Mean ( 24 / 24 )9242.79166666667118.95383313399677.7006627121893
Median9237
Midrange12096.5
Midmean - Weighted Average at Xnp9285.51351351351
Midmean - Weighted Average at X(n+1)p9328.58333333333
Midmean - Empirical Distribution Function9285.51351351351
Midmean - Empirical Distribution Function - Averaging9328.58333333333
Midmean - Empirical Distribution Function - Interpolation9328.58333333333
Midmean - Closest Observation9285.51351351351
Midmean - True Basic - Statistics Graphics Toolkit9328.58333333333
Midmean - MS Excel (old versions)9334.05263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9973.88888888889 & 336.483544161106 & 29.6415354092724 \tabularnewline
Geometric Mean & 9626.74897555659 &  &  \tabularnewline
Harmonic Mean & 9327.40621658677 &  &  \tabularnewline
Quadratic Mean & 10369.0483183259 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9978.69444444445 & 334.723171561456 & 29.811782667733 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9971.11111111111 & 330.387384398647 & 30.1800600808653 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9944.73611111111 & 313.638424033387 & 31.707645967678 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9923.23611111111 & 304.444824574365 & 32.5945304702896 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9799.34722222222 & 270.630026371059 & 36.2093864957408 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9782.68055555555 & 261.728051789002 & 37.3772718999265 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9782.68055555555 & 259.641389129876 & 37.6776622107123 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9754.125 & 248.621284309171 & 39.2328638599998 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9720.5 & 241.299560900485 & 40.2839522945044 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9655.36111111111 & 227.63902810118 & 42.4152272641911 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9655.36111111111 & 221.041585131432 & 43.6811973881295 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9603.52777777778 & 210.123182788844 & 45.7042752271106 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9557.125 & 197.120578012589 & 48.4836494310078 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9497.23611111111 & 186.598232648766 & 50.8967098792825 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9473.90277777778 & 181.4146356156 & 52.2223730496148 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9403.68055555555 & 166.135219389013 & 56.6025710270164 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9380.54166666667 & 162.449151714023 & 57.7444792274463 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9406.04166666667 & 156.743745944154 & 60.0090396590235 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9429.52777777778 & 149.88669686922 & 62.9110386361057 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9458.41666666667 & 139.791497082242 & 67.6608868499497 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 9408.25 & 129.082655929506 & 72.8854696415447 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 9410.38888888889 & 126.614012646998 & 74.3234393425727 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 9359.59722222222 & 116.768653712027 & 80.1550495332827 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 9327.26388888889 & 105.57986910854 & 88.3432037531715 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9913.24285714286 & 319.210295264392 & 31.0555235974831 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9843.94117647059 & 300.324043519739 & 32.7777325488213 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9774.57575757576 & 280.063004117539 & 34.9013458181484 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9710.765625 & 263.55770348552 & 36.8449318558185 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9649.08064516129 & 246.921705314593 & 39.0774907085135 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9613.01666666667 & 238.535639109202 & 40.3001274885629 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9577.91379310345 & 230.870461874297 & 41.4860944762971 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9540.30357142857 & 221.890735834371 & 42.9955019778287 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9504.66666666667 & 213.636063376768 & 44.4899916073827 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9471.46153846154 & 205.169145282917 & 46.1641614064383 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9444.98 & 197.978577464063 & 47.7070808416858 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9416.29166666667 & 190.328467379361 & 49.4739005484566 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9391.86956521739 & 183.217738547736 & 51.2607001901752 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9371.06818181818 & 177.161368605401 & 52.8956637419682 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9355.61904761905 & 171.788514718128 & 54.4600962582967 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9341.425 & 165.860166186954 & 56.321087906487 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 9334.05263157895 & 161.692585177923 & 57.7271531734617 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 9328.58333333333 & 156.792458997277 & 59.4963775234583 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 9319.47058823529 & 151.322890453534 & 61.5866546052857 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 9306.4375 & 145.318732956854 & 64.0415541110115 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 9288.2 & 139.407798393324 & 66.6261149451222 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 9273.5 & 134.132717779205 & 69.1367486884521 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 9256.26923076923 & 126.647925765058 & 73.0866232103977 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 9242.79166666667 & 118.953833133996 & 77.7006627121893 \tabularnewline
Median & 9237 &  &  \tabularnewline
Midrange & 12096.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9285.51351351351 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9328.58333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9285.51351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9328.58333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9328.58333333333 &  &  \tabularnewline
Midmean - Closest Observation & 9285.51351351351 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9328.58333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9334.05263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213623&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]9973.88888888889[/C][C]336.483544161106[/C][C]29.6415354092724[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9626.74897555659[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9327.40621658677[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10369.0483183259[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9978.69444444445[/C][C]334.723171561456[/C][C]29.811782667733[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9971.11111111111[/C][C]330.387384398647[/C][C]30.1800600808653[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9944.73611111111[/C][C]313.638424033387[/C][C]31.707645967678[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9923.23611111111[/C][C]304.444824574365[/C][C]32.5945304702896[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9799.34722222222[/C][C]270.630026371059[/C][C]36.2093864957408[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9782.68055555555[/C][C]261.728051789002[/C][C]37.3772718999265[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9782.68055555555[/C][C]259.641389129876[/C][C]37.6776622107123[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9754.125[/C][C]248.621284309171[/C][C]39.2328638599998[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9720.5[/C][C]241.299560900485[/C][C]40.2839522945044[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9655.36111111111[/C][C]227.63902810118[/C][C]42.4152272641911[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9655.36111111111[/C][C]221.041585131432[/C][C]43.6811973881295[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9603.52777777778[/C][C]210.123182788844[/C][C]45.7042752271106[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9557.125[/C][C]197.120578012589[/C][C]48.4836494310078[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9497.23611111111[/C][C]186.598232648766[/C][C]50.8967098792825[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9473.90277777778[/C][C]181.4146356156[/C][C]52.2223730496148[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9403.68055555555[/C][C]166.135219389013[/C][C]56.6025710270164[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9380.54166666667[/C][C]162.449151714023[/C][C]57.7444792274463[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9406.04166666667[/C][C]156.743745944154[/C][C]60.0090396590235[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9429.52777777778[/C][C]149.88669686922[/C][C]62.9110386361057[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9458.41666666667[/C][C]139.791497082242[/C][C]67.6608868499497[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]9408.25[/C][C]129.082655929506[/C][C]72.8854696415447[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]9410.38888888889[/C][C]126.614012646998[/C][C]74.3234393425727[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]9359.59722222222[/C][C]116.768653712027[/C][C]80.1550495332827[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]9327.26388888889[/C][C]105.57986910854[/C][C]88.3432037531715[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9913.24285714286[/C][C]319.210295264392[/C][C]31.0555235974831[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9843.94117647059[/C][C]300.324043519739[/C][C]32.7777325488213[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9774.57575757576[/C][C]280.063004117539[/C][C]34.9013458181484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9710.765625[/C][C]263.55770348552[/C][C]36.8449318558185[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9649.08064516129[/C][C]246.921705314593[/C][C]39.0774907085135[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9613.01666666667[/C][C]238.535639109202[/C][C]40.3001274885629[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9577.91379310345[/C][C]230.870461874297[/C][C]41.4860944762971[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9540.30357142857[/C][C]221.890735834371[/C][C]42.9955019778287[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9504.66666666667[/C][C]213.636063376768[/C][C]44.4899916073827[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9471.46153846154[/C][C]205.169145282917[/C][C]46.1641614064383[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9444.98[/C][C]197.978577464063[/C][C]47.7070808416858[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9416.29166666667[/C][C]190.328467379361[/C][C]49.4739005484566[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9391.86956521739[/C][C]183.217738547736[/C][C]51.2607001901752[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9371.06818181818[/C][C]177.161368605401[/C][C]52.8956637419682[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9355.61904761905[/C][C]171.788514718128[/C][C]54.4600962582967[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9341.425[/C][C]165.860166186954[/C][C]56.321087906487[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]9334.05263157895[/C][C]161.692585177923[/C][C]57.7271531734617[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]9328.58333333333[/C][C]156.792458997277[/C][C]59.4963775234583[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]9319.47058823529[/C][C]151.322890453534[/C][C]61.5866546052857[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]9306.4375[/C][C]145.318732956854[/C][C]64.0415541110115[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]9288.2[/C][C]139.407798393324[/C][C]66.6261149451222[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]9273.5[/C][C]134.132717779205[/C][C]69.1367486884521[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]9256.26923076923[/C][C]126.647925765058[/C][C]73.0866232103977[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]9242.79166666667[/C][C]118.953833133996[/C][C]77.7006627121893[/C][/ROW]
[ROW][C]Median[/C][C]9237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12096.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9285.51351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9328.58333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9285.51351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9328.58333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9328.58333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9285.51351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9328.58333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9334.05263157895[/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=213623&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213623&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 Mean9973.88888888889336.48354416110629.6415354092724
Geometric Mean9626.74897555659
Harmonic Mean9327.40621658677
Quadratic Mean10369.0483183259
Winsorized Mean ( 1 / 24 )9978.69444444445334.72317156145629.811782667733
Winsorized Mean ( 2 / 24 )9971.11111111111330.38738439864730.1800600808653
Winsorized Mean ( 3 / 24 )9944.73611111111313.63842403338731.707645967678
Winsorized Mean ( 4 / 24 )9923.23611111111304.44482457436532.5945304702896
Winsorized Mean ( 5 / 24 )9799.34722222222270.63002637105936.2093864957408
Winsorized Mean ( 6 / 24 )9782.68055555555261.72805178900237.3772718999265
Winsorized Mean ( 7 / 24 )9782.68055555555259.64138912987637.6776622107123
Winsorized Mean ( 8 / 24 )9754.125248.62128430917139.2328638599998
Winsorized Mean ( 9 / 24 )9720.5241.29956090048540.2839522945044
Winsorized Mean ( 10 / 24 )9655.36111111111227.6390281011842.4152272641911
Winsorized Mean ( 11 / 24 )9655.36111111111221.04158513143243.6811973881295
Winsorized Mean ( 12 / 24 )9603.52777777778210.12318278884445.7042752271106
Winsorized Mean ( 13 / 24 )9557.125197.12057801258948.4836494310078
Winsorized Mean ( 14 / 24 )9497.23611111111186.59823264876650.8967098792825
Winsorized Mean ( 15 / 24 )9473.90277777778181.414635615652.2223730496148
Winsorized Mean ( 16 / 24 )9403.68055555555166.13521938901356.6025710270164
Winsorized Mean ( 17 / 24 )9380.54166666667162.44915171402357.7444792274463
Winsorized Mean ( 18 / 24 )9406.04166666667156.74374594415460.0090396590235
Winsorized Mean ( 19 / 24 )9429.52777777778149.8866968692262.9110386361057
Winsorized Mean ( 20 / 24 )9458.41666666667139.79149708224267.6608868499497
Winsorized Mean ( 21 / 24 )9408.25129.08265592950672.8854696415447
Winsorized Mean ( 22 / 24 )9410.38888888889126.61401264699874.3234393425727
Winsorized Mean ( 23 / 24 )9359.59722222222116.76865371202780.1550495332827
Winsorized Mean ( 24 / 24 )9327.26388888889105.5798691085488.3432037531715
Trimmed Mean ( 1 / 24 )9913.24285714286319.21029526439231.0555235974831
Trimmed Mean ( 2 / 24 )9843.94117647059300.32404351973932.7777325488213
Trimmed Mean ( 3 / 24 )9774.57575757576280.06300411753934.9013458181484
Trimmed Mean ( 4 / 24 )9710.765625263.5577034855236.8449318558185
Trimmed Mean ( 5 / 24 )9649.08064516129246.92170531459339.0774907085135
Trimmed Mean ( 6 / 24 )9613.01666666667238.53563910920240.3001274885629
Trimmed Mean ( 7 / 24 )9577.91379310345230.87046187429741.4860944762971
Trimmed Mean ( 8 / 24 )9540.30357142857221.89073583437142.9955019778287
Trimmed Mean ( 9 / 24 )9504.66666666667213.63606337676844.4899916073827
Trimmed Mean ( 10 / 24 )9471.46153846154205.16914528291746.1641614064383
Trimmed Mean ( 11 / 24 )9444.98197.97857746406347.7070808416858
Trimmed Mean ( 12 / 24 )9416.29166666667190.32846737936149.4739005484566
Trimmed Mean ( 13 / 24 )9391.86956521739183.21773854773651.2607001901752
Trimmed Mean ( 14 / 24 )9371.06818181818177.16136860540152.8956637419682
Trimmed Mean ( 15 / 24 )9355.61904761905171.78851471812854.4600962582967
Trimmed Mean ( 16 / 24 )9341.425165.86016618695456.321087906487
Trimmed Mean ( 17 / 24 )9334.05263157895161.69258517792357.7271531734617
Trimmed Mean ( 18 / 24 )9328.58333333333156.79245899727759.4963775234583
Trimmed Mean ( 19 / 24 )9319.47058823529151.32289045353461.5866546052857
Trimmed Mean ( 20 / 24 )9306.4375145.31873295685464.0415541110115
Trimmed Mean ( 21 / 24 )9288.2139.40779839332466.6261149451222
Trimmed Mean ( 22 / 24 )9273.5134.13271777920569.1367486884521
Trimmed Mean ( 23 / 24 )9256.26923076923126.64792576505873.0866232103977
Trimmed Mean ( 24 / 24 )9242.79166666667118.95383313399677.7006627121893
Median9237
Midrange12096.5
Midmean - Weighted Average at Xnp9285.51351351351
Midmean - Weighted Average at X(n+1)p9328.58333333333
Midmean - Empirical Distribution Function9285.51351351351
Midmean - Empirical Distribution Function - Averaging9328.58333333333
Midmean - Empirical Distribution Function - Interpolation9328.58333333333
Midmean - Closest Observation9285.51351351351
Midmean - True Basic - Statistics Graphics Toolkit9328.58333333333
Midmean - MS Excel (old versions)9334.05263157895
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')