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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 computationTue, 20 Oct 2009 13:57:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256068791nmjs19goec3ed6w.htm/, Retrieved Fri, 03 May 2024 02:55:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49105, Retrieved Fri, 03 May 2024 02:55:53 +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] [Workshop 3, vraag 3] [2009-10-20 19:57:48] [0875edf2b3e9b91e51327d1913579f76] [Current]
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Dataseries X:
107.3
107.2
107.2
105.7
105.7
104.9
104.8
104
104
103.6
103.6
103.6
103.6
104.2
104.2
104.7
104.7
104.7
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.1
106.2
106.4
106.4
106.4
107
107
107
107
106.1
106.3
106.2
106.2
106.3
106.3
106.2
107.1
105.2
103.4
102.4
100.6
100.6
100.6
99.8
100.2
101.4
101
100.6
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49105&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49105&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.9032786885250.273681311347624383.304501765116
Geometric Mean104.881516441380
Harmonic Mean104.859409228034
Quadratic Mean104.924696650565
Winsorized Mean ( 1 / 20 )104.9049180327870.272445174005418385.049646835369
Winsorized Mean ( 2 / 20 )104.9114754098360.270509520863685387.829142112536
Winsorized Mean ( 3 / 20 )104.9262295081970.264284802903226397.019534818345
Winsorized Mean ( 4 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 5 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 6 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 7 / 20 )104.9655737704920.251083828183774418.049917948779
Winsorized Mean ( 8 / 20 )104.9393442622950.227810662067210460.642813246974
Winsorized Mean ( 9 / 20 )105.0868852459020.19127806283395549.393295231814
Winsorized Mean ( 10 / 20 )105.2508196721310.155528764068151676.728965878052
Winsorized Mean ( 11 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 12 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 13 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 14 / 20 )105.2459016393440.143731948650245732.237353126323
Winsorized Mean ( 15 / 20 )105.3442622950820.125526750031909839.2176350324
Winsorized Mean ( 16 / 20 )105.3442622950820.125526750031909839.2176350324
Winsorized Mean ( 17 / 20 )105.40.115730042007038910.740186144495
Winsorized Mean ( 18 / 20 )105.3704918032790.112433204512823937.18303467248
Winsorized Mean ( 19 / 20 )105.5262295081970.08636248551032141221.89894008533
Winsorized Mean ( 20 / 20 )105.5262295081970.08636248551032141221.89894008533
Trimmed Mean ( 1 / 20 )104.9491525423730.266055157921124394.463889978357
Trimmed Mean ( 2 / 20 )104.9964912280700.258040681259208406.898984748063
Trimmed Mean ( 3 / 20 )105.0436363636360.249278604110131421.390502962013
Trimmed Mean ( 4 / 20 )105.0886792452830.241302410361839435.506131446014
Trimmed Mean ( 5 / 20 )105.1392156862750.231399466696092454.362394120636
Trimmed Mean ( 6 / 20 )105.1938775510200.218537348791647481.35423135984
Trimmed Mean ( 7 / 20 )105.2531914893620.201517165591489522.303850296945
Trimmed Mean ( 8 / 20 )105.3088888888890.183287107732187574.556989806193
Trimmed Mean ( 9 / 20 )105.3744186046510.166159572639672634.17603289798
Trimmed Mean ( 10 / 20 )105.4219512195120.155920249906019676.127387450028
Trimmed Mean ( 11 / 20 )105.4487179487180.153232017583939688.163737653287
Trimmed Mean ( 12 / 20 )105.4756756756760.151637973991468695.575606157927
Trimmed Mean ( 13 / 20 )105.5057142857140.148942651934985708.36468207756
Trimmed Mean ( 14 / 20 )105.5393939393940.144661268005549729.562206902165
Trimmed Mean ( 15 / 20 )105.5806451612900.138534523071156762.125157113799
Trimmed Mean ( 16 / 20 )105.6137931034480.135617919708586778.759866914268
Trimmed Mean ( 17 / 20 )105.6518518518520.130457268371488809.857918770758
Trimmed Mean ( 18 / 20 )105.6880.125872951820476839.640275940583
Trimmed Mean ( 19 / 20 )105.7347826086960.118222790893495894.36885908023
Trimmed Mean ( 20 / 20 )105.7666666666670.117985740327527896.436013140734
Median106.1
Midrange103.55
Midmean - Weighted Average at Xnp105.6
Midmean - Weighted Average at X(n+1)p105.6
Midmean - Empirical Distribution Function105.6
Midmean - Empirical Distribution Function - Averaging105.6
Midmean - Empirical Distribution Function - Interpolation105.6
Midmean - Closest Observation105.377777777778
Midmean - True Basic - Statistics Graphics Toolkit105.6
Midmean - MS Excel (old versions)105.6
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.903278688525 & 0.273681311347624 & 383.304501765116 \tabularnewline
Geometric Mean & 104.881516441380 &  &  \tabularnewline
Harmonic Mean & 104.859409228034 &  &  \tabularnewline
Quadratic Mean & 104.924696650565 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.904918032787 & 0.272445174005418 & 385.049646835369 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.911475409836 & 0.270509520863685 & 387.829142112536 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.926229508197 & 0.264284802903226 & 397.019534818345 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.919672131148 & 0.263403736235862 & 398.322642003826 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.919672131148 & 0.263403736235862 & 398.322642003826 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.919672131148 & 0.263403736235862 & 398.322642003826 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.965573770492 & 0.251083828183774 & 418.049917948779 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.939344262295 & 0.227810662067210 & 460.642813246974 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.086885245902 & 0.19127806283395 & 549.393295231814 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.250819672131 & 0.155528764068151 & 676.728965878052 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.268852459016 & 0.146349775336416 & 719.296303783409 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.268852459016 & 0.146349775336416 & 719.296303783409 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.268852459016 & 0.146349775336416 & 719.296303783409 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.245901639344 & 0.143731948650245 & 732.237353126323 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.344262295082 & 0.125526750031909 & 839.2176350324 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.344262295082 & 0.125526750031909 & 839.2176350324 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.4 & 0.115730042007038 & 910.740186144495 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.370491803279 & 0.112433204512823 & 937.18303467248 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.526229508197 & 0.0863624855103214 & 1221.89894008533 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.526229508197 & 0.0863624855103214 & 1221.89894008533 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.949152542373 & 0.266055157921124 & 394.463889978357 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.996491228070 & 0.258040681259208 & 406.898984748063 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.043636363636 & 0.249278604110131 & 421.390502962013 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.088679245283 & 0.241302410361839 & 435.506131446014 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.139215686275 & 0.231399466696092 & 454.362394120636 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.193877551020 & 0.218537348791647 & 481.35423135984 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.253191489362 & 0.201517165591489 & 522.303850296945 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.308888888889 & 0.183287107732187 & 574.556989806193 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.374418604651 & 0.166159572639672 & 634.17603289798 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.421951219512 & 0.155920249906019 & 676.127387450028 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.448717948718 & 0.153232017583939 & 688.163737653287 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.475675675676 & 0.151637973991468 & 695.575606157927 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.505714285714 & 0.148942651934985 & 708.36468207756 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.539393939394 & 0.144661268005549 & 729.562206902165 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.580645161290 & 0.138534523071156 & 762.125157113799 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.613793103448 & 0.135617919708586 & 778.759866914268 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.651851851852 & 0.130457268371488 & 809.857918770758 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.688 & 0.125872951820476 & 839.640275940583 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.734782608696 & 0.118222790893495 & 894.36885908023 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.766666666667 & 0.117985740327527 & 896.436013140734 \tabularnewline
Median & 106.1 &  &  \tabularnewline
Midrange & 103.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.6 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.6 &  &  \tabularnewline
Midmean - Closest Observation & 105.377777777778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.6 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49105&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]104.903278688525[/C][C]0.273681311347624[/C][C]383.304501765116[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.881516441380[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.859409228034[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.924696650565[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.904918032787[/C][C]0.272445174005418[/C][C]385.049646835369[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.911475409836[/C][C]0.270509520863685[/C][C]387.829142112536[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.926229508197[/C][C]0.264284802903226[/C][C]397.019534818345[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.919672131148[/C][C]0.263403736235862[/C][C]398.322642003826[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.919672131148[/C][C]0.263403736235862[/C][C]398.322642003826[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.919672131148[/C][C]0.263403736235862[/C][C]398.322642003826[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.965573770492[/C][C]0.251083828183774[/C][C]418.049917948779[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.939344262295[/C][C]0.227810662067210[/C][C]460.642813246974[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.086885245902[/C][C]0.19127806283395[/C][C]549.393295231814[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.250819672131[/C][C]0.155528764068151[/C][C]676.728965878052[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.268852459016[/C][C]0.146349775336416[/C][C]719.296303783409[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.268852459016[/C][C]0.146349775336416[/C][C]719.296303783409[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.268852459016[/C][C]0.146349775336416[/C][C]719.296303783409[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.245901639344[/C][C]0.143731948650245[/C][C]732.237353126323[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.344262295082[/C][C]0.125526750031909[/C][C]839.2176350324[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.344262295082[/C][C]0.125526750031909[/C][C]839.2176350324[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.4[/C][C]0.115730042007038[/C][C]910.740186144495[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.370491803279[/C][C]0.112433204512823[/C][C]937.18303467248[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.526229508197[/C][C]0.0863624855103214[/C][C]1221.89894008533[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.526229508197[/C][C]0.0863624855103214[/C][C]1221.89894008533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.949152542373[/C][C]0.266055157921124[/C][C]394.463889978357[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.996491228070[/C][C]0.258040681259208[/C][C]406.898984748063[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.043636363636[/C][C]0.249278604110131[/C][C]421.390502962013[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.088679245283[/C][C]0.241302410361839[/C][C]435.506131446014[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.139215686275[/C][C]0.231399466696092[/C][C]454.362394120636[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.193877551020[/C][C]0.218537348791647[/C][C]481.35423135984[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.253191489362[/C][C]0.201517165591489[/C][C]522.303850296945[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.308888888889[/C][C]0.183287107732187[/C][C]574.556989806193[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.374418604651[/C][C]0.166159572639672[/C][C]634.17603289798[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.421951219512[/C][C]0.155920249906019[/C][C]676.127387450028[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.448717948718[/C][C]0.153232017583939[/C][C]688.163737653287[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.475675675676[/C][C]0.151637973991468[/C][C]695.575606157927[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.505714285714[/C][C]0.148942651934985[/C][C]708.36468207756[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.539393939394[/C][C]0.144661268005549[/C][C]729.562206902165[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.580645161290[/C][C]0.138534523071156[/C][C]762.125157113799[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.613793103448[/C][C]0.135617919708586[/C][C]778.759866914268[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.651851851852[/C][C]0.130457268371488[/C][C]809.857918770758[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.688[/C][C]0.125872951820476[/C][C]839.640275940583[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.734782608696[/C][C]0.118222790893495[/C][C]894.36885908023[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.766666666667[/C][C]0.117985740327527[/C][C]896.436013140734[/C][/ROW]
[ROW][C]Median[/C][C]106.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.377777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49105&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 Mean104.9032786885250.273681311347624383.304501765116
Geometric Mean104.881516441380
Harmonic Mean104.859409228034
Quadratic Mean104.924696650565
Winsorized Mean ( 1 / 20 )104.9049180327870.272445174005418385.049646835369
Winsorized Mean ( 2 / 20 )104.9114754098360.270509520863685387.829142112536
Winsorized Mean ( 3 / 20 )104.9262295081970.264284802903226397.019534818345
Winsorized Mean ( 4 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 5 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 6 / 20 )104.9196721311480.263403736235862398.322642003826
Winsorized Mean ( 7 / 20 )104.9655737704920.251083828183774418.049917948779
Winsorized Mean ( 8 / 20 )104.9393442622950.227810662067210460.642813246974
Winsorized Mean ( 9 / 20 )105.0868852459020.19127806283395549.393295231814
Winsorized Mean ( 10 / 20 )105.2508196721310.155528764068151676.728965878052
Winsorized Mean ( 11 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 12 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 13 / 20 )105.2688524590160.146349775336416719.296303783409
Winsorized Mean ( 14 / 20 )105.2459016393440.143731948650245732.237353126323
Winsorized Mean ( 15 / 20 )105.3442622950820.125526750031909839.2176350324
Winsorized Mean ( 16 / 20 )105.3442622950820.125526750031909839.2176350324
Winsorized Mean ( 17 / 20 )105.40.115730042007038910.740186144495
Winsorized Mean ( 18 / 20 )105.3704918032790.112433204512823937.18303467248
Winsorized Mean ( 19 / 20 )105.5262295081970.08636248551032141221.89894008533
Winsorized Mean ( 20 / 20 )105.5262295081970.08636248551032141221.89894008533
Trimmed Mean ( 1 / 20 )104.9491525423730.266055157921124394.463889978357
Trimmed Mean ( 2 / 20 )104.9964912280700.258040681259208406.898984748063
Trimmed Mean ( 3 / 20 )105.0436363636360.249278604110131421.390502962013
Trimmed Mean ( 4 / 20 )105.0886792452830.241302410361839435.506131446014
Trimmed Mean ( 5 / 20 )105.1392156862750.231399466696092454.362394120636
Trimmed Mean ( 6 / 20 )105.1938775510200.218537348791647481.35423135984
Trimmed Mean ( 7 / 20 )105.2531914893620.201517165591489522.303850296945
Trimmed Mean ( 8 / 20 )105.3088888888890.183287107732187574.556989806193
Trimmed Mean ( 9 / 20 )105.3744186046510.166159572639672634.17603289798
Trimmed Mean ( 10 / 20 )105.4219512195120.155920249906019676.127387450028
Trimmed Mean ( 11 / 20 )105.4487179487180.153232017583939688.163737653287
Trimmed Mean ( 12 / 20 )105.4756756756760.151637973991468695.575606157927
Trimmed Mean ( 13 / 20 )105.5057142857140.148942651934985708.36468207756
Trimmed Mean ( 14 / 20 )105.5393939393940.144661268005549729.562206902165
Trimmed Mean ( 15 / 20 )105.5806451612900.138534523071156762.125157113799
Trimmed Mean ( 16 / 20 )105.6137931034480.135617919708586778.759866914268
Trimmed Mean ( 17 / 20 )105.6518518518520.130457268371488809.857918770758
Trimmed Mean ( 18 / 20 )105.6880.125872951820476839.640275940583
Trimmed Mean ( 19 / 20 )105.7347826086960.118222790893495894.36885908023
Trimmed Mean ( 20 / 20 )105.7666666666670.117985740327527896.436013140734
Median106.1
Midrange103.55
Midmean - Weighted Average at Xnp105.6
Midmean - Weighted Average at X(n+1)p105.6
Midmean - Empirical Distribution Function105.6
Midmean - Empirical Distribution Function - Averaging105.6
Midmean - Empirical Distribution Function - Interpolation105.6
Midmean - Closest Observation105.377777777778
Midmean - True Basic - Statistics Graphics Toolkit105.6
Midmean - MS Excel (old versions)105.6
Number of observations61



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')