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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 06:20:32 -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/t1381141246lecjkb13mbviv9c.htm/, Retrieved Fri, 03 May 2024 12:50:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=213606, Retrieved Fri, 03 May 2024 12:50:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-07 10:20:32] [3e2b14d12dd0cca2f2b67dfbdf2cdaf9] [Current]
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Dataseries X:
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811
104519
106758
109337
109078
108293
106534
99197
103493
130676
137448
134704
123725
118277
121225
120528
118240
112514
107304
100001
102082
130455
135574
132540
119920
112454
109415
109843
106365
102304
97968
92462
92286
120092
126656
124144
114045
108120
105698
111203
110030
104009
99772
96301
97680
121563
134210
133111
124527
117589
115699




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=213606&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=213606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213606&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 Mean113685.309523811506.4996177851375.4632182986881
Geometric Mean112867.878538931
Harmonic Mean112060.028563465
Quadratic Mean114510.792123234
Winsorized Mean ( 1 / 28 )113716.9285714291494.53374443376.0885654104592
Winsorized Mean ( 2 / 28 )113698.309523811436.479088743479.150688941299
Winsorized Mean ( 3 / 28 )113486.1309523811385.1268010391381.931943607793
Winsorized Mean ( 4 / 28 )113424.940476191361.9876527106783.27897852117
Winsorized Mean ( 5 / 28 )113384.8809523811349.8763535740183.9964939397426
Winsorized Mean ( 6 / 28 )113451.2380952381328.6936306351385.3855512508228
Winsorized Mean ( 7 / 28 )113440.7380952381326.6188436242985.511176507429
Winsorized Mean ( 8 / 28 )113503.309523811279.1660848484788.732269302821
Winsorized Mean ( 9 / 28 )113589.8809523811244.5487379840491.2699338206535
Winsorized Mean ( 10 / 28 )113402.2619047621199.628089255194.5311825560687
Winsorized Mean ( 11 / 28 )113534.2619047621170.2377434136597.018116655147
Winsorized Mean ( 12 / 28 )113604.8333333331156.235409711998.2540686603264
Winsorized Mean ( 13 / 28 )113064.8690476191055.89780800349107.079367141981
Winsorized Mean ( 14 / 28 )113056.535714286990.964420465991114.087381322048
Winsorized Mean ( 15 / 28 )113006.892857143956.742763612637118.1162765532
Winsorized Mean ( 16 / 28 )112987.273809524938.731966648032120.361591832195
Winsorized Mean ( 17 / 28 )113029.166666667932.038058239104121.270977796993
Winsorized Mean ( 18 / 28 )113244.738095238891.928619725117126.96614458917
Winsorized Mean ( 19 / 28 )113311.464285714869.497548218913130.318325241771
Winsorized Mean ( 20 / 28 )113192.654761905819.76887799999138.078741215528
Winsorized Mean ( 21 / 28 )113206.904761905815.751472856354138.776218650897
Winsorized Mean ( 22 / 28 )112958.880952381769.672137656687146.762336098447
Winsorized Mean ( 23 / 28 )112903.845238095752.475037658342150.043309861076
Winsorized Mean ( 24 / 28 )112879.55952381703.988332159118160.342940880299
Winsorized Mean ( 25 / 28 )112869.44047619689.939960626172163.593134065974
Winsorized Mean ( 26 / 28 )113003.154761905654.919491028205172.545108688845
Winsorized Mean ( 27 / 28 )113002.19047619641.102199317879176.262365963528
Winsorized Mean ( 28 / 28 )112529.19047619562.520011367426200.04477743404
Trimmed Mean ( 1 / 28 )113604.7439024391432.4335185088379.3089120259499
Trimmed Mean ( 2 / 28 )113486.951359.5618802752183.4731773863998
Trimmed Mean ( 3 / 28 )113373.1410256411311.2618380654686.461100090355
Trimmed Mean ( 4 / 28 )113331.5131578951278.0025355510488.6786293495336
Trimmed Mean ( 5 / 28 )1133051247.261070984390.8430501327069
Trimmed Mean ( 6 / 28 )113286.3611111111214.757556184593.2584123756666
Trimmed Mean ( 7 / 28 )113253.3857142861182.0614017347795.8100700590321
Trimmed Mean ( 8 / 28 )113220.3235294121143.7074781727598.9941271611682
Trimmed Mean ( 9 / 28 )113175.3030303031109.13940366804102.038844401363
Trimmed Mean ( 10 / 28 )113114.843751075.31212989337105.192567446642
Trimmed Mean ( 11 / 28 )113075.9032258061044.27009082218108.282238684801
Trimmed Mean ( 12 / 28 )113017.5666666671012.54977372717111.616801069098
Trimmed Mean ( 13 / 28 )112946.689655172976.497524693816115.665105951587
Trimmed Mean ( 14 / 28 )112933.053571429952.931443146584118.511204959848
Trimmed Mean ( 15 / 28 )112919.333333333936.024055324089120.637212997946
Trimmed Mean ( 16 / 28 )112909.903846154920.926885808116122.604634076977
Trimmed Mean ( 17 / 28 )112901.78904.800410188651124.780867392025
Trimmed Mean ( 18 / 28 )112888.666666667885.099916893093127.543415734273
Trimmed Mean ( 19 / 28 )112852.543478261867.210366082024130.132834998408
Trimmed Mean ( 20 / 28 )112806.431818182847.904791414786133.041389741361
Trimmed Mean ( 21 / 28 )112767.80952381832.448621593913135.465188599736
Trimmed Mean ( 22 / 28 )112723.9811.90708606974138.838423674402
Trimmed Mean ( 23 / 28 )112700.289473684794.324020749786141.882011030339
Trimmed Mean ( 24 / 28 )112679.638888889773.510912649936145.672978940743
Trimmed Mean ( 25 / 28 )112659.058823529755.943706631439149.031016245309
Trimmed Mean ( 26 / 28 )112636.96875733.624054262598153.534999425853
Trimmed Mean ( 27 / 28 )112597.533333333710.299339089592158.521241871986
Trimmed Mean ( 28 / 28 )112552.571428571678.94966623597165.77454416106
Median112273.5
Midrange116988.5
Midmean - Weighted Average at Xnp112575.976744186
Midmean - Weighted Average at X(n+1)p112767.80952381
Midmean - Empirical Distribution Function112575.976744186
Midmean - Empirical Distribution Function - Averaging112767.80952381
Midmean - Empirical Distribution Function - Interpolation112767.80952381
Midmean - Closest Observation112575.976744186
Midmean - True Basic - Statistics Graphics Toolkit112767.80952381
Midmean - MS Excel (old versions)112806.431818182
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113685.30952381 & 1506.49961778513 & 75.4632182986881 \tabularnewline
Geometric Mean & 112867.878538931 &  &  \tabularnewline
Harmonic Mean & 112060.028563465 &  &  \tabularnewline
Quadratic Mean & 114510.792123234 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 113716.928571429 & 1494.533744433 & 76.0885654104592 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 113698.30952381 & 1436.4790887434 & 79.150688941299 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 113486.130952381 & 1385.12680103913 & 81.931943607793 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 113424.94047619 & 1361.98765271067 & 83.27897852117 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 113384.880952381 & 1349.87635357401 & 83.9964939397426 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 113451.238095238 & 1328.69363063513 & 85.3855512508228 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 113440.738095238 & 1326.61884362429 & 85.511176507429 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 113503.30952381 & 1279.16608484847 & 88.732269302821 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 113589.880952381 & 1244.54873798404 & 91.2699338206535 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 113402.261904762 & 1199.6280892551 & 94.5311825560687 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 113534.261904762 & 1170.23774341365 & 97.018116655147 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 113604.833333333 & 1156.2354097119 & 98.2540686603264 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 113064.869047619 & 1055.89780800349 & 107.079367141981 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 113056.535714286 & 990.964420465991 & 114.087381322048 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 113006.892857143 & 956.742763612637 & 118.1162765532 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 112987.273809524 & 938.731966648032 & 120.361591832195 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 113029.166666667 & 932.038058239104 & 121.270977796993 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 113244.738095238 & 891.928619725117 & 126.96614458917 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 113311.464285714 & 869.497548218913 & 130.318325241771 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 113192.654761905 & 819.76887799999 & 138.078741215528 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 113206.904761905 & 815.751472856354 & 138.776218650897 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 112958.880952381 & 769.672137656687 & 146.762336098447 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 112903.845238095 & 752.475037658342 & 150.043309861076 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 112879.55952381 & 703.988332159118 & 160.342940880299 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 112869.44047619 & 689.939960626172 & 163.593134065974 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 113003.154761905 & 654.919491028205 & 172.545108688845 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 113002.19047619 & 641.102199317879 & 176.262365963528 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 112529.19047619 & 562.520011367426 & 200.04477743404 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 113604.743902439 & 1432.43351850883 & 79.3089120259499 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 113486.95 & 1359.56188027521 & 83.4731773863998 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 113373.141025641 & 1311.26183806546 & 86.461100090355 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 113331.513157895 & 1278.00253555104 & 88.6786293495336 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 113305 & 1247.2610709843 & 90.8430501327069 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 113286.361111111 & 1214.7575561845 & 93.2584123756666 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 113253.385714286 & 1182.06140173477 & 95.8100700590321 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 113220.323529412 & 1143.70747817275 & 98.9941271611682 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 113175.303030303 & 1109.13940366804 & 102.038844401363 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 113114.84375 & 1075.31212989337 & 105.192567446642 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 113075.903225806 & 1044.27009082218 & 108.282238684801 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 113017.566666667 & 1012.54977372717 & 111.616801069098 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 112946.689655172 & 976.497524693816 & 115.665105951587 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 112933.053571429 & 952.931443146584 & 118.511204959848 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 112919.333333333 & 936.024055324089 & 120.637212997946 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 112909.903846154 & 920.926885808116 & 122.604634076977 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 112901.78 & 904.800410188651 & 124.780867392025 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 112888.666666667 & 885.099916893093 & 127.543415734273 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 112852.543478261 & 867.210366082024 & 130.132834998408 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 112806.431818182 & 847.904791414786 & 133.041389741361 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 112767.80952381 & 832.448621593913 & 135.465188599736 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 112723.9 & 811.90708606974 & 138.838423674402 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 112700.289473684 & 794.324020749786 & 141.882011030339 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 112679.638888889 & 773.510912649936 & 145.672978940743 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 112659.058823529 & 755.943706631439 & 149.031016245309 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 112636.96875 & 733.624054262598 & 153.534999425853 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 112597.533333333 & 710.299339089592 & 158.521241871986 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 112552.571428571 & 678.94966623597 & 165.77454416106 \tabularnewline
Median & 112273.5 &  &  \tabularnewline
Midrange & 116988.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112575.976744186 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112767.80952381 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112575.976744186 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112767.80952381 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112767.80952381 &  &  \tabularnewline
Midmean - Closest Observation & 112575.976744186 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112767.80952381 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112806.431818182 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213606&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]113685.30952381[/C][C]1506.49961778513[/C][C]75.4632182986881[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112867.878538931[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112060.028563465[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114510.792123234[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]113716.928571429[/C][C]1494.533744433[/C][C]76.0885654104592[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]113698.30952381[/C][C]1436.4790887434[/C][C]79.150688941299[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]113486.130952381[/C][C]1385.12680103913[/C][C]81.931943607793[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]113424.94047619[/C][C]1361.98765271067[/C][C]83.27897852117[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]113384.880952381[/C][C]1349.87635357401[/C][C]83.9964939397426[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]113451.238095238[/C][C]1328.69363063513[/C][C]85.3855512508228[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]113440.738095238[/C][C]1326.61884362429[/C][C]85.511176507429[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]113503.30952381[/C][C]1279.16608484847[/C][C]88.732269302821[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]113589.880952381[/C][C]1244.54873798404[/C][C]91.2699338206535[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]113402.261904762[/C][C]1199.6280892551[/C][C]94.5311825560687[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]113534.261904762[/C][C]1170.23774341365[/C][C]97.018116655147[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]113604.833333333[/C][C]1156.2354097119[/C][C]98.2540686603264[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]113064.869047619[/C][C]1055.89780800349[/C][C]107.079367141981[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]113056.535714286[/C][C]990.964420465991[/C][C]114.087381322048[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]113006.892857143[/C][C]956.742763612637[/C][C]118.1162765532[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]112987.273809524[/C][C]938.731966648032[/C][C]120.361591832195[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]113029.166666667[/C][C]932.038058239104[/C][C]121.270977796993[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]113244.738095238[/C][C]891.928619725117[/C][C]126.96614458917[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]113311.464285714[/C][C]869.497548218913[/C][C]130.318325241771[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]113192.654761905[/C][C]819.76887799999[/C][C]138.078741215528[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]113206.904761905[/C][C]815.751472856354[/C][C]138.776218650897[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]112958.880952381[/C][C]769.672137656687[/C][C]146.762336098447[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]112903.845238095[/C][C]752.475037658342[/C][C]150.043309861076[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]112879.55952381[/C][C]703.988332159118[/C][C]160.342940880299[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]112869.44047619[/C][C]689.939960626172[/C][C]163.593134065974[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]113003.154761905[/C][C]654.919491028205[/C][C]172.545108688845[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]113002.19047619[/C][C]641.102199317879[/C][C]176.262365963528[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]112529.19047619[/C][C]562.520011367426[/C][C]200.04477743404[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]113604.743902439[/C][C]1432.43351850883[/C][C]79.3089120259499[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]113486.95[/C][C]1359.56188027521[/C][C]83.4731773863998[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]113373.141025641[/C][C]1311.26183806546[/C][C]86.461100090355[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]113331.513157895[/C][C]1278.00253555104[/C][C]88.6786293495336[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]113305[/C][C]1247.2610709843[/C][C]90.8430501327069[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]113286.361111111[/C][C]1214.7575561845[/C][C]93.2584123756666[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]113253.385714286[/C][C]1182.06140173477[/C][C]95.8100700590321[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]113220.323529412[/C][C]1143.70747817275[/C][C]98.9941271611682[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]113175.303030303[/C][C]1109.13940366804[/C][C]102.038844401363[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]113114.84375[/C][C]1075.31212989337[/C][C]105.192567446642[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]113075.903225806[/C][C]1044.27009082218[/C][C]108.282238684801[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]113017.566666667[/C][C]1012.54977372717[/C][C]111.616801069098[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]112946.689655172[/C][C]976.497524693816[/C][C]115.665105951587[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]112933.053571429[/C][C]952.931443146584[/C][C]118.511204959848[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]112919.333333333[/C][C]936.024055324089[/C][C]120.637212997946[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]112909.903846154[/C][C]920.926885808116[/C][C]122.604634076977[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]112901.78[/C][C]904.800410188651[/C][C]124.780867392025[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]112888.666666667[/C][C]885.099916893093[/C][C]127.543415734273[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]112852.543478261[/C][C]867.210366082024[/C][C]130.132834998408[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]112806.431818182[/C][C]847.904791414786[/C][C]133.041389741361[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]112767.80952381[/C][C]832.448621593913[/C][C]135.465188599736[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]112723.9[/C][C]811.90708606974[/C][C]138.838423674402[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]112700.289473684[/C][C]794.324020749786[/C][C]141.882011030339[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]112679.638888889[/C][C]773.510912649936[/C][C]145.672978940743[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]112659.058823529[/C][C]755.943706631439[/C][C]149.031016245309[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]112636.96875[/C][C]733.624054262598[/C][C]153.534999425853[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]112597.533333333[/C][C]710.299339089592[/C][C]158.521241871986[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]112552.571428571[/C][C]678.94966623597[/C][C]165.77454416106[/C][/ROW]
[ROW][C]Median[/C][C]112273.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]116988.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112575.976744186[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112767.80952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112575.976744186[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112767.80952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112767.80952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112575.976744186[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112767.80952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112806.431818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=213606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213606&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 Mean113685.309523811506.4996177851375.4632182986881
Geometric Mean112867.878538931
Harmonic Mean112060.028563465
Quadratic Mean114510.792123234
Winsorized Mean ( 1 / 28 )113716.9285714291494.53374443376.0885654104592
Winsorized Mean ( 2 / 28 )113698.309523811436.479088743479.150688941299
Winsorized Mean ( 3 / 28 )113486.1309523811385.1268010391381.931943607793
Winsorized Mean ( 4 / 28 )113424.940476191361.9876527106783.27897852117
Winsorized Mean ( 5 / 28 )113384.8809523811349.8763535740183.9964939397426
Winsorized Mean ( 6 / 28 )113451.2380952381328.6936306351385.3855512508228
Winsorized Mean ( 7 / 28 )113440.7380952381326.6188436242985.511176507429
Winsorized Mean ( 8 / 28 )113503.309523811279.1660848484788.732269302821
Winsorized Mean ( 9 / 28 )113589.8809523811244.5487379840491.2699338206535
Winsorized Mean ( 10 / 28 )113402.2619047621199.628089255194.5311825560687
Winsorized Mean ( 11 / 28 )113534.2619047621170.2377434136597.018116655147
Winsorized Mean ( 12 / 28 )113604.8333333331156.235409711998.2540686603264
Winsorized Mean ( 13 / 28 )113064.8690476191055.89780800349107.079367141981
Winsorized Mean ( 14 / 28 )113056.535714286990.964420465991114.087381322048
Winsorized Mean ( 15 / 28 )113006.892857143956.742763612637118.1162765532
Winsorized Mean ( 16 / 28 )112987.273809524938.731966648032120.361591832195
Winsorized Mean ( 17 / 28 )113029.166666667932.038058239104121.270977796993
Winsorized Mean ( 18 / 28 )113244.738095238891.928619725117126.96614458917
Winsorized Mean ( 19 / 28 )113311.464285714869.497548218913130.318325241771
Winsorized Mean ( 20 / 28 )113192.654761905819.76887799999138.078741215528
Winsorized Mean ( 21 / 28 )113206.904761905815.751472856354138.776218650897
Winsorized Mean ( 22 / 28 )112958.880952381769.672137656687146.762336098447
Winsorized Mean ( 23 / 28 )112903.845238095752.475037658342150.043309861076
Winsorized Mean ( 24 / 28 )112879.55952381703.988332159118160.342940880299
Winsorized Mean ( 25 / 28 )112869.44047619689.939960626172163.593134065974
Winsorized Mean ( 26 / 28 )113003.154761905654.919491028205172.545108688845
Winsorized Mean ( 27 / 28 )113002.19047619641.102199317879176.262365963528
Winsorized Mean ( 28 / 28 )112529.19047619562.520011367426200.04477743404
Trimmed Mean ( 1 / 28 )113604.7439024391432.4335185088379.3089120259499
Trimmed Mean ( 2 / 28 )113486.951359.5618802752183.4731773863998
Trimmed Mean ( 3 / 28 )113373.1410256411311.2618380654686.461100090355
Trimmed Mean ( 4 / 28 )113331.5131578951278.0025355510488.6786293495336
Trimmed Mean ( 5 / 28 )1133051247.261070984390.8430501327069
Trimmed Mean ( 6 / 28 )113286.3611111111214.757556184593.2584123756666
Trimmed Mean ( 7 / 28 )113253.3857142861182.0614017347795.8100700590321
Trimmed Mean ( 8 / 28 )113220.3235294121143.7074781727598.9941271611682
Trimmed Mean ( 9 / 28 )113175.3030303031109.13940366804102.038844401363
Trimmed Mean ( 10 / 28 )113114.843751075.31212989337105.192567446642
Trimmed Mean ( 11 / 28 )113075.9032258061044.27009082218108.282238684801
Trimmed Mean ( 12 / 28 )113017.5666666671012.54977372717111.616801069098
Trimmed Mean ( 13 / 28 )112946.689655172976.497524693816115.665105951587
Trimmed Mean ( 14 / 28 )112933.053571429952.931443146584118.511204959848
Trimmed Mean ( 15 / 28 )112919.333333333936.024055324089120.637212997946
Trimmed Mean ( 16 / 28 )112909.903846154920.926885808116122.604634076977
Trimmed Mean ( 17 / 28 )112901.78904.800410188651124.780867392025
Trimmed Mean ( 18 / 28 )112888.666666667885.099916893093127.543415734273
Trimmed Mean ( 19 / 28 )112852.543478261867.210366082024130.132834998408
Trimmed Mean ( 20 / 28 )112806.431818182847.904791414786133.041389741361
Trimmed Mean ( 21 / 28 )112767.80952381832.448621593913135.465188599736
Trimmed Mean ( 22 / 28 )112723.9811.90708606974138.838423674402
Trimmed Mean ( 23 / 28 )112700.289473684794.324020749786141.882011030339
Trimmed Mean ( 24 / 28 )112679.638888889773.510912649936145.672978940743
Trimmed Mean ( 25 / 28 )112659.058823529755.943706631439149.031016245309
Trimmed Mean ( 26 / 28 )112636.96875733.624054262598153.534999425853
Trimmed Mean ( 27 / 28 )112597.533333333710.299339089592158.521241871986
Trimmed Mean ( 28 / 28 )112552.571428571678.94966623597165.77454416106
Median112273.5
Midrange116988.5
Midmean - Weighted Average at Xnp112575.976744186
Midmean - Weighted Average at X(n+1)p112767.80952381
Midmean - Empirical Distribution Function112575.976744186
Midmean - Empirical Distribution Function - Averaging112767.80952381
Midmean - Empirical Distribution Function - Interpolation112767.80952381
Midmean - Closest Observation112575.976744186
Midmean - True Basic - Statistics Graphics Toolkit112767.80952381
Midmean - MS Excel (old versions)112806.431818182
Number of observations84



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')