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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 26 Nov 2011 03:28:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/26/t13222962908p16d9cuhqjub61.htm/, Retrieved Sun, 05 Feb 2023 14:07:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147368, Retrieved Sun, 05 Feb 2023 14:07:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS8-births] [2011-11-26 08:28:43] [01668b8db120351c61467eadc96b2965] [Current]
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Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147368&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147368&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9605.5066666666758.0892428469724165.357752931485
Geometric Mean9592.4687602401
Harmonic Mean9579.39088375951
Quadratic Mean9618.49577498131
Winsorized Mean ( 1 / 25 )9604.9333333333357.6930627501218166.483332232402
Winsorized Mean ( 2 / 25 )9605.9257.2648022014498167.745624375121
Winsorized Mean ( 3 / 25 )9602.455.4455499477551173.18612601098
Winsorized Mean ( 4 / 25 )9603.3066666666754.7592337791909175.373284173235
Winsorized Mean ( 5 / 25 )9609.1066666666753.4873886738467179.651818959806
Winsorized Mean ( 6 / 25 )9615.3466666666751.0786762628865188.24580764739
Winsorized Mean ( 7 / 25 )9616.8448.9059072317666196.639640165052
Winsorized Mean ( 8 / 25 )9605.5333333333346.2580982277877207.650848204633
Winsorized Mean ( 9 / 25 )9604.8133333333345.5736160962029210.753812316719
Winsorized Mean ( 10 / 25 )9605.2133333333344.7605975909247214.590819834827
Winsorized Mean ( 11 / 25 )9600.9643.5011460551111220.705909399183
Winsorized Mean ( 12 / 25 )9600.3243.2464430032394221.990973900001
Winsorized Mean ( 13 / 25 )9604.3066666666742.1727890295927227.737052437469
Winsorized Mean ( 14 / 25 )9601.3241.2387387194513232.82283353325
Winsorized Mean ( 15 / 25 )9596.3239.8595650066897240.753254542277
Winsorized Mean ( 16 / 25 )9598.8836.8826088073015260.254909031808
Winsorized Mean ( 17 / 25 )9602.7333333333336.0347146604585266.48562154068
Winsorized Mean ( 18 / 25 )9593.3733333333334.1294291826912281.088010056688
Winsorized Mean ( 19 / 25 )9602.7466666666732.671866252855293.914849930789
Winsorized Mean ( 20 / 25 )9599.0133333333331.082699880027308.821735897576
Winsorized Mean ( 21 / 25 )9595.3733333333329.6357026789188323.777486813531
Winsorized Mean ( 22 / 25 )9588.0428.2461920577937339.445401361791
Winsorized Mean ( 23 / 25 )9578.5333333333326.0106030585888368.254950173885
Winsorized Mean ( 24 / 25 )9575.6533333333323.6627848104357404.671445480513
Winsorized Mean ( 25 / 25 )9604.9866666666717.4507749726809550.404591297705
Trimmed Mean ( 1 / 25 )9605.2876712328855.9488564276353171.679785513694
Trimmed Mean ( 2 / 25 )9605.6619718309953.8877100014464178.253296931214
Trimmed Mean ( 3 / 25 )9605.5217391304351.7150885848444185.73924945273
Trimmed Mean ( 4 / 25 )9606.6865671641849.9745308671686192.231650812262
Trimmed Mean ( 5 / 25 )9607.6615384615448.1481052273321199.54391752487
Trimmed Mean ( 6 / 25 )9607.3174603174646.3656509941688207.207647349235
Trimmed Mean ( 7 / 25 )9605.6721311475444.9109423624806213.882667026206
Trimmed Mean ( 8 / 25 )9603.644067796643.7130658173422219.697335069703
Trimmed Mean ( 9 / 25 )9603.3333333333342.8894242805979223.909121990188
Trimmed Mean ( 10 / 25 )9603.1090909090942.0168851157863228.553569938508
Trimmed Mean ( 11 / 25 )9602.8113207547241.100765203254233.640694358519
Trimmed Mean ( 12 / 25 )9603.0588235294140.2154629490649238.790209519463
Trimmed Mean ( 13 / 25 )9603.408163265339.1377073251118245.374826979288
Trimmed Mean ( 14 / 25 )9603.2978723404237.9914532831502252.775217646113
Trimmed Mean ( 15 / 25 )9603.5333333333336.716324500806261.560313127817
Trimmed Mean ( 16 / 25 )9604.3720930232635.3672556491853271.561135200618
Trimmed Mean ( 17 / 25 )960534.2888554745722280.120169281324
Trimmed Mean ( 18 / 25 )9605.256410256433.0384946613106290.729238989952
Trimmed Mean ( 19 / 25 )9606.594594594631.8089373869495302.009289959367
Trimmed Mean ( 20 / 25 )9607.0285714285730.4971271746432315.014214827956
Trimmed Mean ( 21 / 25 )9607.939393939429.0922949875055330.257183149896
Trimmed Mean ( 22 / 25 )9609.387096774227.5050993285587349.367474808451
Trimmed Mean ( 23 / 25 )9611.8965517241425.6093879428397375.32707041566
Trimmed Mean ( 24 / 25 )9615.9259259259323.5210353769146408.82239118452
Trimmed Mean ( 25 / 25 )9620.9621.1884780010269454.065648298747
Median9655
Midrange9613.5
Midmean - Weighted Average at Xnp9596.26315789474
Midmean - Weighted Average at X(n+1)p9605.2564102564
Midmean - Empirical Distribution Function9605.2564102564
Midmean - Empirical Distribution Function - Averaging9605.2564102564
Midmean - Empirical Distribution Function - Interpolation9606.5945945946
Midmean - Closest Observation9596.26315789474
Midmean - True Basic - Statistics Graphics Toolkit9605.2564102564
Midmean - MS Excel (old versions)9605.2564102564
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9605.50666666667 & 58.0892428469724 & 165.357752931485 \tabularnewline
Geometric Mean & 9592.4687602401 &  &  \tabularnewline
Harmonic Mean & 9579.39088375951 &  &  \tabularnewline
Quadratic Mean & 9618.49577498131 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 9604.93333333333 & 57.6930627501218 & 166.483332232402 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 9605.92 & 57.2648022014498 & 167.745624375121 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 9602.4 & 55.4455499477551 & 173.18612601098 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 9603.30666666667 & 54.7592337791909 & 175.373284173235 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 9609.10666666667 & 53.4873886738467 & 179.651818959806 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 9615.34666666667 & 51.0786762628865 & 188.24580764739 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 9616.84 & 48.9059072317666 & 196.639640165052 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 9605.53333333333 & 46.2580982277877 & 207.650848204633 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 9604.81333333333 & 45.5736160962029 & 210.753812316719 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 9605.21333333333 & 44.7605975909247 & 214.590819834827 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 9600.96 & 43.5011460551111 & 220.705909399183 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 9600.32 & 43.2464430032394 & 221.990973900001 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 9604.30666666667 & 42.1727890295927 & 227.737052437469 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 9601.32 & 41.2387387194513 & 232.82283353325 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 9596.32 & 39.8595650066897 & 240.753254542277 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 9598.88 & 36.8826088073015 & 260.254909031808 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 9602.73333333333 & 36.0347146604585 & 266.48562154068 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 9593.37333333333 & 34.1294291826912 & 281.088010056688 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 9602.74666666667 & 32.671866252855 & 293.914849930789 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 9599.01333333333 & 31.082699880027 & 308.821735897576 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 9595.37333333333 & 29.6357026789188 & 323.777486813531 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 9588.04 & 28.2461920577937 & 339.445401361791 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 9578.53333333333 & 26.0106030585888 & 368.254950173885 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 9575.65333333333 & 23.6627848104357 & 404.671445480513 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 9604.98666666667 & 17.4507749726809 & 550.404591297705 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 9605.28767123288 & 55.9488564276353 & 171.679785513694 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 9605.66197183099 & 53.8877100014464 & 178.253296931214 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 9605.52173913043 & 51.7150885848444 & 185.73924945273 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 9606.68656716418 & 49.9745308671686 & 192.231650812262 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 9607.66153846154 & 48.1481052273321 & 199.54391752487 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 9607.31746031746 & 46.3656509941688 & 207.207647349235 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 9605.67213114754 & 44.9109423624806 & 213.882667026206 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 9603.6440677966 & 43.7130658173422 & 219.697335069703 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 9603.33333333333 & 42.8894242805979 & 223.909121990188 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 9603.10909090909 & 42.0168851157863 & 228.553569938508 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 9602.81132075472 & 41.100765203254 & 233.640694358519 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 9603.05882352941 & 40.2154629490649 & 238.790209519463 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 9603.4081632653 & 39.1377073251118 & 245.374826979288 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 9603.29787234042 & 37.9914532831502 & 252.775217646113 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 9603.53333333333 & 36.716324500806 & 261.560313127817 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 9604.37209302326 & 35.3672556491853 & 271.561135200618 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 9605 & 34.2888554745722 & 280.120169281324 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 9605.2564102564 & 33.0384946613106 & 290.729238989952 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 9606.5945945946 & 31.8089373869495 & 302.009289959367 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 9607.02857142857 & 30.4971271746432 & 315.014214827956 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 9607.9393939394 & 29.0922949875055 & 330.257183149896 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 9609.3870967742 & 27.5050993285587 & 349.367474808451 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 9611.89655172414 & 25.6093879428397 & 375.32707041566 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 9615.92592592593 & 23.5210353769146 & 408.82239118452 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 9620.96 & 21.1884780010269 & 454.065648298747 \tabularnewline
Median & 9655 &  &  \tabularnewline
Midrange & 9613.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9596.26315789474 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9605.2564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9605.2564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9605.2564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9606.5945945946 &  &  \tabularnewline
Midmean - Closest Observation & 9596.26315789474 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9605.2564102564 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9605.2564102564 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147368&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]9605.50666666667[/C][C]58.0892428469724[/C][C]165.357752931485[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9592.4687602401[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9579.39088375951[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9618.49577498131[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]9604.93333333333[/C][C]57.6930627501218[/C][C]166.483332232402[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]9605.92[/C][C]57.2648022014498[/C][C]167.745624375121[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]9602.4[/C][C]55.4455499477551[/C][C]173.18612601098[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]9603.30666666667[/C][C]54.7592337791909[/C][C]175.373284173235[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]9609.10666666667[/C][C]53.4873886738467[/C][C]179.651818959806[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]9615.34666666667[/C][C]51.0786762628865[/C][C]188.24580764739[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]9616.84[/C][C]48.9059072317666[/C][C]196.639640165052[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]9605.53333333333[/C][C]46.2580982277877[/C][C]207.650848204633[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]9604.81333333333[/C][C]45.5736160962029[/C][C]210.753812316719[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]9605.21333333333[/C][C]44.7605975909247[/C][C]214.590819834827[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]9600.96[/C][C]43.5011460551111[/C][C]220.705909399183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]9600.32[/C][C]43.2464430032394[/C][C]221.990973900001[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]9604.30666666667[/C][C]42.1727890295927[/C][C]227.737052437469[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]9601.32[/C][C]41.2387387194513[/C][C]232.82283353325[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]9596.32[/C][C]39.8595650066897[/C][C]240.753254542277[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]9598.88[/C][C]36.8826088073015[/C][C]260.254909031808[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]9602.73333333333[/C][C]36.0347146604585[/C][C]266.48562154068[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]9593.37333333333[/C][C]34.1294291826912[/C][C]281.088010056688[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]9602.74666666667[/C][C]32.671866252855[/C][C]293.914849930789[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]9599.01333333333[/C][C]31.082699880027[/C][C]308.821735897576[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]9595.37333333333[/C][C]29.6357026789188[/C][C]323.777486813531[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]9588.04[/C][C]28.2461920577937[/C][C]339.445401361791[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]9578.53333333333[/C][C]26.0106030585888[/C][C]368.254950173885[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]9575.65333333333[/C][C]23.6627848104357[/C][C]404.671445480513[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]9604.98666666667[/C][C]17.4507749726809[/C][C]550.404591297705[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]9605.28767123288[/C][C]55.9488564276353[/C][C]171.679785513694[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]9605.66197183099[/C][C]53.8877100014464[/C][C]178.253296931214[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]9605.52173913043[/C][C]51.7150885848444[/C][C]185.73924945273[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]9606.68656716418[/C][C]49.9745308671686[/C][C]192.231650812262[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]9607.66153846154[/C][C]48.1481052273321[/C][C]199.54391752487[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]9607.31746031746[/C][C]46.3656509941688[/C][C]207.207647349235[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]9605.67213114754[/C][C]44.9109423624806[/C][C]213.882667026206[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]9603.6440677966[/C][C]43.7130658173422[/C][C]219.697335069703[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]9603.33333333333[/C][C]42.8894242805979[/C][C]223.909121990188[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]9603.10909090909[/C][C]42.0168851157863[/C][C]228.553569938508[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]9602.81132075472[/C][C]41.100765203254[/C][C]233.640694358519[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]9603.05882352941[/C][C]40.2154629490649[/C][C]238.790209519463[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]9603.4081632653[/C][C]39.1377073251118[/C][C]245.374826979288[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]9603.29787234042[/C][C]37.9914532831502[/C][C]252.775217646113[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]9603.53333333333[/C][C]36.716324500806[/C][C]261.560313127817[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]9604.37209302326[/C][C]35.3672556491853[/C][C]271.561135200618[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]9605[/C][C]34.2888554745722[/C][C]280.120169281324[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]9605.2564102564[/C][C]33.0384946613106[/C][C]290.729238989952[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]9606.5945945946[/C][C]31.8089373869495[/C][C]302.009289959367[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]9607.02857142857[/C][C]30.4971271746432[/C][C]315.014214827956[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]9607.9393939394[/C][C]29.0922949875055[/C][C]330.257183149896[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]9609.3870967742[/C][C]27.5050993285587[/C][C]349.367474808451[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]9611.89655172414[/C][C]25.6093879428397[/C][C]375.32707041566[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]9615.92592592593[/C][C]23.5210353769146[/C][C]408.82239118452[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]9620.96[/C][C]21.1884780010269[/C][C]454.065648298747[/C][/ROW]
[ROW][C]Median[/C][C]9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9613.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9596.26315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9605.2564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9605.2564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9605.2564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9606.5945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9596.26315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9605.2564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9605.2564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147368&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 Mean9605.5066666666758.0892428469724165.357752931485
Geometric Mean9592.4687602401
Harmonic Mean9579.39088375951
Quadratic Mean9618.49577498131
Winsorized Mean ( 1 / 25 )9604.9333333333357.6930627501218166.483332232402
Winsorized Mean ( 2 / 25 )9605.9257.2648022014498167.745624375121
Winsorized Mean ( 3 / 25 )9602.455.4455499477551173.18612601098
Winsorized Mean ( 4 / 25 )9603.3066666666754.7592337791909175.373284173235
Winsorized Mean ( 5 / 25 )9609.1066666666753.4873886738467179.651818959806
Winsorized Mean ( 6 / 25 )9615.3466666666751.0786762628865188.24580764739
Winsorized Mean ( 7 / 25 )9616.8448.9059072317666196.639640165052
Winsorized Mean ( 8 / 25 )9605.5333333333346.2580982277877207.650848204633
Winsorized Mean ( 9 / 25 )9604.8133333333345.5736160962029210.753812316719
Winsorized Mean ( 10 / 25 )9605.2133333333344.7605975909247214.590819834827
Winsorized Mean ( 11 / 25 )9600.9643.5011460551111220.705909399183
Winsorized Mean ( 12 / 25 )9600.3243.2464430032394221.990973900001
Winsorized Mean ( 13 / 25 )9604.3066666666742.1727890295927227.737052437469
Winsorized Mean ( 14 / 25 )9601.3241.2387387194513232.82283353325
Winsorized Mean ( 15 / 25 )9596.3239.8595650066897240.753254542277
Winsorized Mean ( 16 / 25 )9598.8836.8826088073015260.254909031808
Winsorized Mean ( 17 / 25 )9602.7333333333336.0347146604585266.48562154068
Winsorized Mean ( 18 / 25 )9593.3733333333334.1294291826912281.088010056688
Winsorized Mean ( 19 / 25 )9602.7466666666732.671866252855293.914849930789
Winsorized Mean ( 20 / 25 )9599.0133333333331.082699880027308.821735897576
Winsorized Mean ( 21 / 25 )9595.3733333333329.6357026789188323.777486813531
Winsorized Mean ( 22 / 25 )9588.0428.2461920577937339.445401361791
Winsorized Mean ( 23 / 25 )9578.5333333333326.0106030585888368.254950173885
Winsorized Mean ( 24 / 25 )9575.6533333333323.6627848104357404.671445480513
Winsorized Mean ( 25 / 25 )9604.9866666666717.4507749726809550.404591297705
Trimmed Mean ( 1 / 25 )9605.2876712328855.9488564276353171.679785513694
Trimmed Mean ( 2 / 25 )9605.6619718309953.8877100014464178.253296931214
Trimmed Mean ( 3 / 25 )9605.5217391304351.7150885848444185.73924945273
Trimmed Mean ( 4 / 25 )9606.6865671641849.9745308671686192.231650812262
Trimmed Mean ( 5 / 25 )9607.6615384615448.1481052273321199.54391752487
Trimmed Mean ( 6 / 25 )9607.3174603174646.3656509941688207.207647349235
Trimmed Mean ( 7 / 25 )9605.6721311475444.9109423624806213.882667026206
Trimmed Mean ( 8 / 25 )9603.644067796643.7130658173422219.697335069703
Trimmed Mean ( 9 / 25 )9603.3333333333342.8894242805979223.909121990188
Trimmed Mean ( 10 / 25 )9603.1090909090942.0168851157863228.553569938508
Trimmed Mean ( 11 / 25 )9602.8113207547241.100765203254233.640694358519
Trimmed Mean ( 12 / 25 )9603.0588235294140.2154629490649238.790209519463
Trimmed Mean ( 13 / 25 )9603.408163265339.1377073251118245.374826979288
Trimmed Mean ( 14 / 25 )9603.2978723404237.9914532831502252.775217646113
Trimmed Mean ( 15 / 25 )9603.5333333333336.716324500806261.560313127817
Trimmed Mean ( 16 / 25 )9604.3720930232635.3672556491853271.561135200618
Trimmed Mean ( 17 / 25 )960534.2888554745722280.120169281324
Trimmed Mean ( 18 / 25 )9605.256410256433.0384946613106290.729238989952
Trimmed Mean ( 19 / 25 )9606.594594594631.8089373869495302.009289959367
Trimmed Mean ( 20 / 25 )9607.0285714285730.4971271746432315.014214827956
Trimmed Mean ( 21 / 25 )9607.939393939429.0922949875055330.257183149896
Trimmed Mean ( 22 / 25 )9609.387096774227.5050993285587349.367474808451
Trimmed Mean ( 23 / 25 )9611.8965517241425.6093879428397375.32707041566
Trimmed Mean ( 24 / 25 )9615.9259259259323.5210353769146408.82239118452
Trimmed Mean ( 25 / 25 )9620.9621.1884780010269454.065648298747
Median9655
Midrange9613.5
Midmean - Weighted Average at Xnp9596.26315789474
Midmean - Weighted Average at X(n+1)p9605.2564102564
Midmean - Empirical Distribution Function9605.2564102564
Midmean - Empirical Distribution Function - Averaging9605.2564102564
Midmean - Empirical Distribution Function - Interpolation9606.5945945946
Midmean - Closest Observation9596.26315789474
Midmean - True Basic - Statistics Graphics Toolkit9605.2564102564
Midmean - MS Excel (old versions)9605.2564102564
Number of observations75



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')