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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 computationThu, 19 Mar 2009 10:52:49 -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/Mar/19/t1237481605qgwb7jmnxhlqs6b.htm/, Retrieved Sat, 03 Dec 2022 16:46:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39125, Retrieved Sat, 03 Dec 2022 16:46:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [eigencijferreekso...] [2009-03-19 16:52:49] [1f24ecf252e89ff3a946a11432983a6a] [Current]
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Dataseries X:
76284
74250
71362
72008
73454
76207
75091
67610
66466
69848
70483
73302
74988
74291
72932
75576
77304
81329
79357
72187
75728
77828
78665
81640
83614
82719
83324
86625
91790
92134
90951
84957
84831
84816
85220
86629
87184
86858
86285
89664
92194
92729
91378
84915
85159
86587
88521
89488
89587
89955
89528
92159
94118
93571
92603
87175
87032
88219
90390
90269
90398
89168
87888
91301
92472
91995
90580
82880
82387
83903
83823
84757
84886




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=39125&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=39125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39125&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 Mean83668.5753424658858.58996582814897.4488157007097
Geometric Mean83338.3383110892
Harmonic Mean82995.2798242791
Quadratic Mean83985.160739003
Winsorized Mean ( 1 / 24 )83676.7534246575853.12265405051598.0829110883075
Winsorized Mean ( 2 / 24 )83715834.427115745665100.326317805708
Winsorized Mean ( 3 / 24 )83735.9178082192827.73982687004101.162122553475
Winsorized Mean ( 4 / 24 )83776.904109589816.230277397177102.638809695641
Winsorized Mean ( 5 / 24 )83802.1095890411804.260991359675104.197655349871
Winsorized Mean ( 6 / 24 )83813.9452054795800.862796936466104.654561962539
Winsorized Mean ( 7 / 24 )83882.9863013699786.401194587236106.666911086520
Winsorized Mean ( 8 / 24 )83908.301369863776.421262375357108.070586723961
Winsorized Mean ( 9 / 24 )83901.7671232877769.248017218192109.069851654216
Winsorized Mean ( 10 / 24 )83954.3698630137741.094099061101113.284358854532
Winsorized Mean ( 11 / 24 )83948.9452054795738.361671609093113.696239164923
Winsorized Mean ( 12 / 24 )84005.9863013699709.953447916806118.32604876822
Winsorized Mean ( 13 / 24 )83958.2602739726697.874214554969120.305720605414
Winsorized Mean ( 14 / 24 )84016.3698630137677.027084353212124.096024818974
Winsorized Mean ( 15 / 24 )84045.9589041096671.420537247734125.176330245465
Winsorized Mean ( 16 / 24 )84124.4246575342650.024581819985129.417297453577
Winsorized Mean ( 17 / 24 )84069.2328767123637.497607814937131.873801322745
Winsorized Mean ( 18 / 24 )84248.9863013699586.247597215481143.708881198882
Winsorized Mean ( 19 / 24 )84365.3287671233561.415283586846150.272590065804
Winsorized Mean ( 20 / 24 )84578.4794520548522.731922234212161.800869345337
Winsorized Mean ( 21 / 24 )84766.0410958904490.304020492174172.884654322845
Winsorized Mean ( 22 / 24 )85263.904109589389.509241807846218.900849987153
Winsorized Mean ( 23 / 24 )85158.0410958904347.850256800463244.812356555883
Winsorized Mean ( 24 / 24 )85304.3424657534300.652902682845283.730313941921
Trimmed Mean ( 1 / 24 )83763.690140845835.437389652146100.263276672022
Trimmed Mean ( 2 / 24 )83855.6666666667814.291927379345102.979857526700
Trimmed Mean ( 3 / 24 )83932.2985074627800.806146016864104.809758172979
Trimmed Mean ( 4 / 24 )84005.8153846154787.426815247806106.683965745031
Trimmed Mean ( 5 / 24 )84072.126984127775.249351390618108.445272264106
Trimmed Mean ( 6 / 24 )84136.7540983607763.903618665138110.140536112897
Trimmed Mean ( 7 / 24 )84203.3220338983750.681335734668112.169196202928
Trimmed Mean ( 8 / 24 )84261.9298245614737.943983795743114.184723603471
Trimmed Mean ( 9 / 24 )84320.6724.308560844845116.415302204418
Trimmed Mean ( 10 / 24 )84384.6981132075708.654078339119119.077418295512
Trimmed Mean ( 11 / 24 )84446.294117647695.144342914177121.480229219204
Trimmed Mean ( 12 / 24 )84513.6530612245678.222376109008124.610534889873
Trimmed Mean ( 13 / 24 )84579.3617021277662.706055383762127.627265535018
Trimmed Mean ( 14 / 24 )84656.8666666667644.792150834498131.293264902655
Trimmed Mean ( 15 / 24 )84734.534883721625.906454387825135.378912119698
Trimmed Mean ( 16 / 24 )84816.268292683601.897762998763140.914742513933
Trimmed Mean ( 17 / 24 )84897.2051282051575.027688331167147.640203856256
Trimmed Mean ( 18 / 24 )84993.2972972973541.050031359144157.089534000747
Trimmed Mean ( 19 / 24 )85079.5428571429509.343047534791167.037801475697
Trimmed Mean ( 20 / 24 )85162.696969697472.332901920304180.302275415204
Trimmed Mean ( 21 / 24 )85231.4838709677432.757179104631196.949901668438
Trimmed Mean ( 22 / 24 )85287.275862069386.743862286316220.526514261598
Trimmed Mean ( 23 / 24 )85290.1481481481359.49337453608237.250959793664
Trimmed Mean ( 24 / 24 )85306.92334.051627347231255.370466767185
Median84957
Midrange80292
Midmean - Weighted Average at Xnp84863.5555555556
Midmean - Weighted Average at X(n+1)p84993.2972972973
Midmean - Empirical Distribution Function84993.2972972973
Midmean - Empirical Distribution Function - Averaging84993.2972972973
Midmean - Empirical Distribution Function - Interpolation84993.2972972973
Midmean - Closest Observation84764.1052631579
Midmean - True Basic - Statistics Graphics Toolkit84993.2972972973
Midmean - MS Excel (old versions)84993.2972972973
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 83668.5753424658 & 858.589965828148 & 97.4488157007097 \tabularnewline
Geometric Mean & 83338.3383110892 &  &  \tabularnewline
Harmonic Mean & 82995.2798242791 &  &  \tabularnewline
Quadratic Mean & 83985.160739003 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 83676.7534246575 & 853.122654050515 & 98.0829110883075 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 83715 & 834.427115745665 & 100.326317805708 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 83735.9178082192 & 827.73982687004 & 101.162122553475 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 83776.904109589 & 816.230277397177 & 102.638809695641 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 83802.1095890411 & 804.260991359675 & 104.197655349871 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 83813.9452054795 & 800.862796936466 & 104.654561962539 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 83882.9863013699 & 786.401194587236 & 106.666911086520 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 83908.301369863 & 776.421262375357 & 108.070586723961 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 83901.7671232877 & 769.248017218192 & 109.069851654216 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 83954.3698630137 & 741.094099061101 & 113.284358854532 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 83948.9452054795 & 738.361671609093 & 113.696239164923 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 84005.9863013699 & 709.953447916806 & 118.32604876822 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 83958.2602739726 & 697.874214554969 & 120.305720605414 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 84016.3698630137 & 677.027084353212 & 124.096024818974 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 84045.9589041096 & 671.420537247734 & 125.176330245465 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 84124.4246575342 & 650.024581819985 & 129.417297453577 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 84069.2328767123 & 637.497607814937 & 131.873801322745 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 84248.9863013699 & 586.247597215481 & 143.708881198882 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 84365.3287671233 & 561.415283586846 & 150.272590065804 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 84578.4794520548 & 522.731922234212 & 161.800869345337 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 84766.0410958904 & 490.304020492174 & 172.884654322845 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 85263.904109589 & 389.509241807846 & 218.900849987153 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 85158.0410958904 & 347.850256800463 & 244.812356555883 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 85304.3424657534 & 300.652902682845 & 283.730313941921 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 83763.690140845 & 835.437389652146 & 100.263276672022 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 83855.6666666667 & 814.291927379345 & 102.979857526700 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 83932.2985074627 & 800.806146016864 & 104.809758172979 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 84005.8153846154 & 787.426815247806 & 106.683965745031 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 84072.126984127 & 775.249351390618 & 108.445272264106 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 84136.7540983607 & 763.903618665138 & 110.140536112897 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 84203.3220338983 & 750.681335734668 & 112.169196202928 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 84261.9298245614 & 737.943983795743 & 114.184723603471 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 84320.6 & 724.308560844845 & 116.415302204418 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 84384.6981132075 & 708.654078339119 & 119.077418295512 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 84446.294117647 & 695.144342914177 & 121.480229219204 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 84513.6530612245 & 678.222376109008 & 124.610534889873 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 84579.3617021277 & 662.706055383762 & 127.627265535018 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 84656.8666666667 & 644.792150834498 & 131.293264902655 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 84734.534883721 & 625.906454387825 & 135.378912119698 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 84816.268292683 & 601.897762998763 & 140.914742513933 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 84897.2051282051 & 575.027688331167 & 147.640203856256 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 84993.2972972973 & 541.050031359144 & 157.089534000747 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 85079.5428571429 & 509.343047534791 & 167.037801475697 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 85162.696969697 & 472.332901920304 & 180.302275415204 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 85231.4838709677 & 432.757179104631 & 196.949901668438 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 85287.275862069 & 386.743862286316 & 220.526514261598 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 85290.1481481481 & 359.49337453608 & 237.250959793664 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 85306.92 & 334.051627347231 & 255.370466767185 \tabularnewline
Median & 84957 &  &  \tabularnewline
Midrange & 80292 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 84863.5555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 84993.2972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 84993.2972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 84993.2972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 84993.2972972973 &  &  \tabularnewline
Midmean - Closest Observation & 84764.1052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 84993.2972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 84993.2972972973 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39125&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]83668.5753424658[/C][C]858.589965828148[/C][C]97.4488157007097[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]83338.3383110892[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]82995.2798242791[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]83985.160739003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]83676.7534246575[/C][C]853.122654050515[/C][C]98.0829110883075[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]83715[/C][C]834.427115745665[/C][C]100.326317805708[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]83735.9178082192[/C][C]827.73982687004[/C][C]101.162122553475[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]83776.904109589[/C][C]816.230277397177[/C][C]102.638809695641[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]83802.1095890411[/C][C]804.260991359675[/C][C]104.197655349871[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]83813.9452054795[/C][C]800.862796936466[/C][C]104.654561962539[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]83882.9863013699[/C][C]786.401194587236[/C][C]106.666911086520[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]83908.301369863[/C][C]776.421262375357[/C][C]108.070586723961[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]83901.7671232877[/C][C]769.248017218192[/C][C]109.069851654216[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]83954.3698630137[/C][C]741.094099061101[/C][C]113.284358854532[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]83948.9452054795[/C][C]738.361671609093[/C][C]113.696239164923[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]84005.9863013699[/C][C]709.953447916806[/C][C]118.32604876822[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]83958.2602739726[/C][C]697.874214554969[/C][C]120.305720605414[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]84016.3698630137[/C][C]677.027084353212[/C][C]124.096024818974[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]84045.9589041096[/C][C]671.420537247734[/C][C]125.176330245465[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]84124.4246575342[/C][C]650.024581819985[/C][C]129.417297453577[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]84069.2328767123[/C][C]637.497607814937[/C][C]131.873801322745[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]84248.9863013699[/C][C]586.247597215481[/C][C]143.708881198882[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]84365.3287671233[/C][C]561.415283586846[/C][C]150.272590065804[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]84578.4794520548[/C][C]522.731922234212[/C][C]161.800869345337[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]84766.0410958904[/C][C]490.304020492174[/C][C]172.884654322845[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]85263.904109589[/C][C]389.509241807846[/C][C]218.900849987153[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]85158.0410958904[/C][C]347.850256800463[/C][C]244.812356555883[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]85304.3424657534[/C][C]300.652902682845[/C][C]283.730313941921[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]83763.690140845[/C][C]835.437389652146[/C][C]100.263276672022[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]83855.6666666667[/C][C]814.291927379345[/C][C]102.979857526700[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]83932.2985074627[/C][C]800.806146016864[/C][C]104.809758172979[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]84005.8153846154[/C][C]787.426815247806[/C][C]106.683965745031[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]84072.126984127[/C][C]775.249351390618[/C][C]108.445272264106[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]84136.7540983607[/C][C]763.903618665138[/C][C]110.140536112897[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]84203.3220338983[/C][C]750.681335734668[/C][C]112.169196202928[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]84261.9298245614[/C][C]737.943983795743[/C][C]114.184723603471[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]84320.6[/C][C]724.308560844845[/C][C]116.415302204418[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]84384.6981132075[/C][C]708.654078339119[/C][C]119.077418295512[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]84446.294117647[/C][C]695.144342914177[/C][C]121.480229219204[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]84513.6530612245[/C][C]678.222376109008[/C][C]124.610534889873[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]84579.3617021277[/C][C]662.706055383762[/C][C]127.627265535018[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]84656.8666666667[/C][C]644.792150834498[/C][C]131.293264902655[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]84734.534883721[/C][C]625.906454387825[/C][C]135.378912119698[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]84816.268292683[/C][C]601.897762998763[/C][C]140.914742513933[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]84897.2051282051[/C][C]575.027688331167[/C][C]147.640203856256[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]84993.2972972973[/C][C]541.050031359144[/C][C]157.089534000747[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]85079.5428571429[/C][C]509.343047534791[/C][C]167.037801475697[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]85162.696969697[/C][C]472.332901920304[/C][C]180.302275415204[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]85231.4838709677[/C][C]432.757179104631[/C][C]196.949901668438[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]85287.275862069[/C][C]386.743862286316[/C][C]220.526514261598[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]85290.1481481481[/C][C]359.49337453608[/C][C]237.250959793664[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]85306.92[/C][C]334.051627347231[/C][C]255.370466767185[/C][/ROW]
[ROW][C]Median[/C][C]84957[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]80292[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]84863.5555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]84764.1052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]84993.2972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39125&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 Mean83668.5753424658858.58996582814897.4488157007097
Geometric Mean83338.3383110892
Harmonic Mean82995.2798242791
Quadratic Mean83985.160739003
Winsorized Mean ( 1 / 24 )83676.7534246575853.12265405051598.0829110883075
Winsorized Mean ( 2 / 24 )83715834.427115745665100.326317805708
Winsorized Mean ( 3 / 24 )83735.9178082192827.73982687004101.162122553475
Winsorized Mean ( 4 / 24 )83776.904109589816.230277397177102.638809695641
Winsorized Mean ( 5 / 24 )83802.1095890411804.260991359675104.197655349871
Winsorized Mean ( 6 / 24 )83813.9452054795800.862796936466104.654561962539
Winsorized Mean ( 7 / 24 )83882.9863013699786.401194587236106.666911086520
Winsorized Mean ( 8 / 24 )83908.301369863776.421262375357108.070586723961
Winsorized Mean ( 9 / 24 )83901.7671232877769.248017218192109.069851654216
Winsorized Mean ( 10 / 24 )83954.3698630137741.094099061101113.284358854532
Winsorized Mean ( 11 / 24 )83948.9452054795738.361671609093113.696239164923
Winsorized Mean ( 12 / 24 )84005.9863013699709.953447916806118.32604876822
Winsorized Mean ( 13 / 24 )83958.2602739726697.874214554969120.305720605414
Winsorized Mean ( 14 / 24 )84016.3698630137677.027084353212124.096024818974
Winsorized Mean ( 15 / 24 )84045.9589041096671.420537247734125.176330245465
Winsorized Mean ( 16 / 24 )84124.4246575342650.024581819985129.417297453577
Winsorized Mean ( 17 / 24 )84069.2328767123637.497607814937131.873801322745
Winsorized Mean ( 18 / 24 )84248.9863013699586.247597215481143.708881198882
Winsorized Mean ( 19 / 24 )84365.3287671233561.415283586846150.272590065804
Winsorized Mean ( 20 / 24 )84578.4794520548522.731922234212161.800869345337
Winsorized Mean ( 21 / 24 )84766.0410958904490.304020492174172.884654322845
Winsorized Mean ( 22 / 24 )85263.904109589389.509241807846218.900849987153
Winsorized Mean ( 23 / 24 )85158.0410958904347.850256800463244.812356555883
Winsorized Mean ( 24 / 24 )85304.3424657534300.652902682845283.730313941921
Trimmed Mean ( 1 / 24 )83763.690140845835.437389652146100.263276672022
Trimmed Mean ( 2 / 24 )83855.6666666667814.291927379345102.979857526700
Trimmed Mean ( 3 / 24 )83932.2985074627800.806146016864104.809758172979
Trimmed Mean ( 4 / 24 )84005.8153846154787.426815247806106.683965745031
Trimmed Mean ( 5 / 24 )84072.126984127775.249351390618108.445272264106
Trimmed Mean ( 6 / 24 )84136.7540983607763.903618665138110.140536112897
Trimmed Mean ( 7 / 24 )84203.3220338983750.681335734668112.169196202928
Trimmed Mean ( 8 / 24 )84261.9298245614737.943983795743114.184723603471
Trimmed Mean ( 9 / 24 )84320.6724.308560844845116.415302204418
Trimmed Mean ( 10 / 24 )84384.6981132075708.654078339119119.077418295512
Trimmed Mean ( 11 / 24 )84446.294117647695.144342914177121.480229219204
Trimmed Mean ( 12 / 24 )84513.6530612245678.222376109008124.610534889873
Trimmed Mean ( 13 / 24 )84579.3617021277662.706055383762127.627265535018
Trimmed Mean ( 14 / 24 )84656.8666666667644.792150834498131.293264902655
Trimmed Mean ( 15 / 24 )84734.534883721625.906454387825135.378912119698
Trimmed Mean ( 16 / 24 )84816.268292683601.897762998763140.914742513933
Trimmed Mean ( 17 / 24 )84897.2051282051575.027688331167147.640203856256
Trimmed Mean ( 18 / 24 )84993.2972972973541.050031359144157.089534000747
Trimmed Mean ( 19 / 24 )85079.5428571429509.343047534791167.037801475697
Trimmed Mean ( 20 / 24 )85162.696969697472.332901920304180.302275415204
Trimmed Mean ( 21 / 24 )85231.4838709677432.757179104631196.949901668438
Trimmed Mean ( 22 / 24 )85287.275862069386.743862286316220.526514261598
Trimmed Mean ( 23 / 24 )85290.1481481481359.49337453608237.250959793664
Trimmed Mean ( 24 / 24 )85306.92334.051627347231255.370466767185
Median84957
Midrange80292
Midmean - Weighted Average at Xnp84863.5555555556
Midmean - Weighted Average at X(n+1)p84993.2972972973
Midmean - Empirical Distribution Function84993.2972972973
Midmean - Empirical Distribution Function - Averaging84993.2972972973
Midmean - Empirical Distribution Function - Interpolation84993.2972972973
Midmean - Closest Observation84764.1052631579
Midmean - True Basic - Statistics Graphics Toolkit84993.2972972973
Midmean - MS Excel (old versions)84993.2972972973
Number of observations73



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')