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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 12:31:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362506000buzuvshuadbj3uk.htm/, Retrieved Sat, 04 May 2024 08:06:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207426, Retrieved Sat, 04 May 2024 08:06:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrumaten eigen...] [2013-03-05 17:31:20] [09688f513f3d2798cb35a3603f8bd204] [Current]
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Dataseries X:
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207426&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207426&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207426&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean40.48852777777781.5548410033710126.040301027562
Geometric Mean37.5035046112504
Harmonic Mean32.6347645950498
Quadratic Mean42.5554409019706
Winsorized Mean ( 1 / 24 )40.40761111111111.5218099559667926.5523372039189
Winsorized Mean ( 2 / 24 )40.41847222222221.515316750534126.6732828024081
Winsorized Mean ( 3 / 24 )40.47972222222221.4811128195918227.330613635076
Winsorized Mean ( 4 / 24 )40.30861111111111.3885720241521729.0288227113914
Winsorized Mean ( 5 / 24 )40.20340277777781.2134373686018833.1318317846928
Winsorized Mean ( 6 / 24 )41.00023611111110.99877383266470841.0505709803423
Winsorized Mean ( 7 / 24 )40.58140277777780.90313029777831644.9341616349349
Winsorized Mean ( 8 / 24 )40.71884722222220.84582564016476948.1409468910047
Winsorized Mean ( 9 / 24 )40.72922222222220.82771217753213349.206986834069
Winsorized Mean ( 10 / 24 )40.82172222222220.80649071341365550.6164814340329
Winsorized Mean ( 11 / 24 )41.14331944444440.74482427894426755.2389611986898
Winsorized Mean ( 12 / 24 )41.15298611111110.73577259743627955.9316645584578
Winsorized Mean ( 13 / 24 )41.1331250.71805590836245757.2840144074645
Winsorized Mean ( 14 / 24 )41.32873611111110.68251458478774460.5536306948868
Winsorized Mean ( 15 / 24 )41.00519444444440.62163208051120765.963768167697
Winsorized Mean ( 16 / 24 )40.99563888888890.60325650831966167.9572260282447
Winsorized Mean ( 17 / 24 )40.93472222222220.5709590167735271.694676885118
Winsorized Mean ( 18 / 24 )40.91547222222220.54771482518103574.702144877489
Winsorized Mean ( 19 / 24 )40.75238888888890.48136382829817984.6602642183678
Winsorized Mean ( 20 / 24 )40.68655555555560.45445122880442389.5289812783526
Winsorized Mean ( 21 / 24 )40.62180555555560.44275083588359591.7486817940997
Winsorized Mean ( 22 / 24 )40.530750.380116528726124106.627170714806
Winsorized Mean ( 23 / 24 )40.415750.334371442619253120.870818642312
Winsorized Mean ( 24 / 24 )40.276750.310802393550087129.589574713199
Trimmed Mean ( 1 / 24 )40.45802857142861.4371077489095128.1523974817675
Trimmed Mean ( 2 / 24 )40.51141176470591.3343001617048530.3615430226314
Trimmed Mean ( 3 / 24 )40.56210606060611.2115826152708233.4786134675096
Trimmed Mean ( 4 / 24 )40.5931.0748630579073637.7657411345311
Trimmed Mean ( 5 / 24 )40.6755645161290.94211564734791143.1747043270454
Trimmed Mean ( 6 / 24 )40.78888333333330.84352104052862948.3555019656311
Trimmed Mean ( 7 / 24 )40.74515517241380.79472907291452951.2692394943954
Trimmed Mean ( 8 / 24 )40.77523214285710.7624217745656753.4812009613519
Trimmed Mean ( 9 / 24 )40.78462962962960.73757395834083655.2956475325867
Trimmed Mean ( 10 / 24 )40.79315384615380.7110418250085457.3709624545137
Trimmed Mean ( 11 / 24 )40.789040.68284346188327459.7341005323596
Trimmed Mean ( 12 / 24 )40.74072916666670.66159839609267261.5792441566923
Trimmed Mean ( 13 / 24 )40.68695652173910.63626192989699863.9468662353031
Trimmed Mean ( 14 / 24 )40.63079545454550.60759161132436666.8718835106736
Trimmed Mean ( 15 / 24 )40.54533333333330.5780792153083470.1380230591875
Trimmed Mean ( 16 / 24 )40.490150.55526772077149372.9200500683574
Trimmed Mean ( 17 / 24 )40.43028947368420.52901998944167476.4248804971514
Trimmed Mean ( 18 / 24 )40.37094444444440.50190082170928180.4360995205319
Trimmed Mean ( 19 / 24 )40.30688235294120.47062529756014585.6453797998183
Trimmed Mean ( 20 / 24 )40.2541250.44721980494098490.0097101140502
Trimmed Mean ( 21 / 24 )40.20223333333330.42179663804934795.3118865983706
Trimmed Mean ( 22 / 24 )40.15085714285710.387909339058494103.505775963807
Trimmed Mean ( 23 / 24 )40.10303846153850.361244104474732111.013682894148
Trimmed Mean ( 24 / 24 )40.062250.338676699379952118.290541018457
Median39.9975
Midrange41.556
Midmean - Weighted Average at Xnp40.2373783783784
Midmean - Weighted Average at X(n+1)p40.3709444444444
Midmean - Empirical Distribution Function40.2373783783784
Midmean - Empirical Distribution Function - Averaging40.3709444444444
Midmean - Empirical Distribution Function - Interpolation40.3709444444444
Midmean - Closest Observation40.2373783783784
Midmean - True Basic - Statistics Graphics Toolkit40.3709444444444
Midmean - MS Excel (old versions)40.4302894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 40.4885277777778 & 1.55484100337101 & 26.040301027562 \tabularnewline
Geometric Mean & 37.5035046112504 &  &  \tabularnewline
Harmonic Mean & 32.6347645950498 &  &  \tabularnewline
Quadratic Mean & 42.5554409019706 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 40.4076111111111 & 1.52180995596679 & 26.5523372039189 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 40.4184722222222 & 1.5153167505341 & 26.6732828024081 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 40.4797222222222 & 1.48111281959182 & 27.330613635076 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 40.3086111111111 & 1.38857202415217 & 29.0288227113914 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 40.2034027777778 & 1.21343736860188 & 33.1318317846928 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 41.0002361111111 & 0.998773832664708 & 41.0505709803423 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 40.5814027777778 & 0.903130297778316 & 44.9341616349349 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 40.7188472222222 & 0.845825640164769 & 48.1409468910047 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 40.7292222222222 & 0.827712177532133 & 49.206986834069 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 40.8217222222222 & 0.806490713413655 & 50.6164814340329 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 41.1433194444444 & 0.744824278944267 & 55.2389611986898 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 41.1529861111111 & 0.735772597436279 & 55.9316645584578 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 41.133125 & 0.718055908362457 & 57.2840144074645 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 41.3287361111111 & 0.682514584787744 & 60.5536306948868 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 41.0051944444444 & 0.621632080511207 & 65.963768167697 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 40.9956388888889 & 0.603256508319661 & 67.9572260282447 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 40.9347222222222 & 0.57095901677352 & 71.694676885118 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 40.9154722222222 & 0.547714825181035 & 74.702144877489 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 40.7523888888889 & 0.481363828298179 & 84.6602642183678 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 40.6865555555556 & 0.454451228804423 & 89.5289812783526 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 40.6218055555556 & 0.442750835883595 & 91.7486817940997 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 40.53075 & 0.380116528726124 & 106.627170714806 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 40.41575 & 0.334371442619253 & 120.870818642312 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 40.27675 & 0.310802393550087 & 129.589574713199 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 40.4580285714286 & 1.43710774890951 & 28.1523974817675 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 40.5114117647059 & 1.33430016170485 & 30.3615430226314 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 40.5621060606061 & 1.21158261527082 & 33.4786134675096 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 40.593 & 1.07486305790736 & 37.7657411345311 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 40.675564516129 & 0.942115647347911 & 43.1747043270454 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 40.7888833333333 & 0.843521040528629 & 48.3555019656311 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 40.7451551724138 & 0.794729072914529 & 51.2692394943954 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 40.7752321428571 & 0.76242177456567 & 53.4812009613519 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 40.7846296296296 & 0.737573958340836 & 55.2956475325867 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 40.7931538461538 & 0.71104182500854 & 57.3709624545137 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 40.78904 & 0.682843461883274 & 59.7341005323596 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 40.7407291666667 & 0.661598396092672 & 61.5792441566923 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 40.6869565217391 & 0.636261929896998 & 63.9468662353031 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 40.6307954545455 & 0.607591611324366 & 66.8718835106736 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 40.5453333333333 & 0.57807921530834 & 70.1380230591875 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 40.49015 & 0.555267720771493 & 72.9200500683574 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 40.4302894736842 & 0.529019989441674 & 76.4248804971514 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 40.3709444444444 & 0.501900821709281 & 80.4360995205319 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 40.3068823529412 & 0.470625297560145 & 85.6453797998183 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 40.254125 & 0.447219804940984 & 90.0097101140502 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 40.2022333333333 & 0.421796638049347 & 95.3118865983706 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 40.1508571428571 & 0.387909339058494 & 103.505775963807 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 40.1030384615385 & 0.361244104474732 & 111.013682894148 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 40.06225 & 0.338676699379952 & 118.290541018457 \tabularnewline
Median & 39.9975 &  &  \tabularnewline
Midrange & 41.556 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 40.2373783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 40.3709444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 40.2373783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 40.3709444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 40.3709444444444 &  &  \tabularnewline
Midmean - Closest Observation & 40.2373783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 40.3709444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 40.4302894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207426&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]40.4885277777778[/C][C]1.55484100337101[/C][C]26.040301027562[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]37.5035046112504[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32.6347645950498[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]42.5554409019706[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]40.4076111111111[/C][C]1.52180995596679[/C][C]26.5523372039189[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]40.4184722222222[/C][C]1.5153167505341[/C][C]26.6732828024081[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]40.4797222222222[/C][C]1.48111281959182[/C][C]27.330613635076[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]40.3086111111111[/C][C]1.38857202415217[/C][C]29.0288227113914[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]40.2034027777778[/C][C]1.21343736860188[/C][C]33.1318317846928[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]41.0002361111111[/C][C]0.998773832664708[/C][C]41.0505709803423[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]40.5814027777778[/C][C]0.903130297778316[/C][C]44.9341616349349[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]40.7188472222222[/C][C]0.845825640164769[/C][C]48.1409468910047[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]40.7292222222222[/C][C]0.827712177532133[/C][C]49.206986834069[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]40.8217222222222[/C][C]0.806490713413655[/C][C]50.6164814340329[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]41.1433194444444[/C][C]0.744824278944267[/C][C]55.2389611986898[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]41.1529861111111[/C][C]0.735772597436279[/C][C]55.9316645584578[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]41.133125[/C][C]0.718055908362457[/C][C]57.2840144074645[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]41.3287361111111[/C][C]0.682514584787744[/C][C]60.5536306948868[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]41.0051944444444[/C][C]0.621632080511207[/C][C]65.963768167697[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]40.9956388888889[/C][C]0.603256508319661[/C][C]67.9572260282447[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]40.9347222222222[/C][C]0.57095901677352[/C][C]71.694676885118[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]40.9154722222222[/C][C]0.547714825181035[/C][C]74.702144877489[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]40.7523888888889[/C][C]0.481363828298179[/C][C]84.6602642183678[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]40.6865555555556[/C][C]0.454451228804423[/C][C]89.5289812783526[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]40.6218055555556[/C][C]0.442750835883595[/C][C]91.7486817940997[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]40.53075[/C][C]0.380116528726124[/C][C]106.627170714806[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]40.41575[/C][C]0.334371442619253[/C][C]120.870818642312[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]40.27675[/C][C]0.310802393550087[/C][C]129.589574713199[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]40.4580285714286[/C][C]1.43710774890951[/C][C]28.1523974817675[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]40.5114117647059[/C][C]1.33430016170485[/C][C]30.3615430226314[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]40.5621060606061[/C][C]1.21158261527082[/C][C]33.4786134675096[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]40.593[/C][C]1.07486305790736[/C][C]37.7657411345311[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]40.675564516129[/C][C]0.942115647347911[/C][C]43.1747043270454[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]40.7888833333333[/C][C]0.843521040528629[/C][C]48.3555019656311[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]40.7451551724138[/C][C]0.794729072914529[/C][C]51.2692394943954[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]40.7752321428571[/C][C]0.76242177456567[/C][C]53.4812009613519[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]40.7846296296296[/C][C]0.737573958340836[/C][C]55.2956475325867[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]40.7931538461538[/C][C]0.71104182500854[/C][C]57.3709624545137[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]40.78904[/C][C]0.682843461883274[/C][C]59.7341005323596[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]40.7407291666667[/C][C]0.661598396092672[/C][C]61.5792441566923[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]40.6869565217391[/C][C]0.636261929896998[/C][C]63.9468662353031[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]40.6307954545455[/C][C]0.607591611324366[/C][C]66.8718835106736[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]40.5453333333333[/C][C]0.57807921530834[/C][C]70.1380230591875[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]40.49015[/C][C]0.555267720771493[/C][C]72.9200500683574[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]40.4302894736842[/C][C]0.529019989441674[/C][C]76.4248804971514[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]40.3709444444444[/C][C]0.501900821709281[/C][C]80.4360995205319[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]40.3068823529412[/C][C]0.470625297560145[/C][C]85.6453797998183[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]40.254125[/C][C]0.447219804940984[/C][C]90.0097101140502[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]40.2022333333333[/C][C]0.421796638049347[/C][C]95.3118865983706[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]40.1508571428571[/C][C]0.387909339058494[/C][C]103.505775963807[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]40.1030384615385[/C][C]0.361244104474732[/C][C]111.013682894148[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]40.06225[/C][C]0.338676699379952[/C][C]118.290541018457[/C][/ROW]
[ROW][C]Median[/C][C]39.9975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41.556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]40.2373783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]40.3709444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]40.2373783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]40.3709444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]40.3709444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]40.2373783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]40.3709444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]40.4302894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207426&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207426&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 Mean40.48852777777781.5548410033710126.040301027562
Geometric Mean37.5035046112504
Harmonic Mean32.6347645950498
Quadratic Mean42.5554409019706
Winsorized Mean ( 1 / 24 )40.40761111111111.5218099559667926.5523372039189
Winsorized Mean ( 2 / 24 )40.41847222222221.515316750534126.6732828024081
Winsorized Mean ( 3 / 24 )40.47972222222221.4811128195918227.330613635076
Winsorized Mean ( 4 / 24 )40.30861111111111.3885720241521729.0288227113914
Winsorized Mean ( 5 / 24 )40.20340277777781.2134373686018833.1318317846928
Winsorized Mean ( 6 / 24 )41.00023611111110.99877383266470841.0505709803423
Winsorized Mean ( 7 / 24 )40.58140277777780.90313029777831644.9341616349349
Winsorized Mean ( 8 / 24 )40.71884722222220.84582564016476948.1409468910047
Winsorized Mean ( 9 / 24 )40.72922222222220.82771217753213349.206986834069
Winsorized Mean ( 10 / 24 )40.82172222222220.80649071341365550.6164814340329
Winsorized Mean ( 11 / 24 )41.14331944444440.74482427894426755.2389611986898
Winsorized Mean ( 12 / 24 )41.15298611111110.73577259743627955.9316645584578
Winsorized Mean ( 13 / 24 )41.1331250.71805590836245757.2840144074645
Winsorized Mean ( 14 / 24 )41.32873611111110.68251458478774460.5536306948868
Winsorized Mean ( 15 / 24 )41.00519444444440.62163208051120765.963768167697
Winsorized Mean ( 16 / 24 )40.99563888888890.60325650831966167.9572260282447
Winsorized Mean ( 17 / 24 )40.93472222222220.5709590167735271.694676885118
Winsorized Mean ( 18 / 24 )40.91547222222220.54771482518103574.702144877489
Winsorized Mean ( 19 / 24 )40.75238888888890.48136382829817984.6602642183678
Winsorized Mean ( 20 / 24 )40.68655555555560.45445122880442389.5289812783526
Winsorized Mean ( 21 / 24 )40.62180555555560.44275083588359591.7486817940997
Winsorized Mean ( 22 / 24 )40.530750.380116528726124106.627170714806
Winsorized Mean ( 23 / 24 )40.415750.334371442619253120.870818642312
Winsorized Mean ( 24 / 24 )40.276750.310802393550087129.589574713199
Trimmed Mean ( 1 / 24 )40.45802857142861.4371077489095128.1523974817675
Trimmed Mean ( 2 / 24 )40.51141176470591.3343001617048530.3615430226314
Trimmed Mean ( 3 / 24 )40.56210606060611.2115826152708233.4786134675096
Trimmed Mean ( 4 / 24 )40.5931.0748630579073637.7657411345311
Trimmed Mean ( 5 / 24 )40.6755645161290.94211564734791143.1747043270454
Trimmed Mean ( 6 / 24 )40.78888333333330.84352104052862948.3555019656311
Trimmed Mean ( 7 / 24 )40.74515517241380.79472907291452951.2692394943954
Trimmed Mean ( 8 / 24 )40.77523214285710.7624217745656753.4812009613519
Trimmed Mean ( 9 / 24 )40.78462962962960.73757395834083655.2956475325867
Trimmed Mean ( 10 / 24 )40.79315384615380.7110418250085457.3709624545137
Trimmed Mean ( 11 / 24 )40.789040.68284346188327459.7341005323596
Trimmed Mean ( 12 / 24 )40.74072916666670.66159839609267261.5792441566923
Trimmed Mean ( 13 / 24 )40.68695652173910.63626192989699863.9468662353031
Trimmed Mean ( 14 / 24 )40.63079545454550.60759161132436666.8718835106736
Trimmed Mean ( 15 / 24 )40.54533333333330.5780792153083470.1380230591875
Trimmed Mean ( 16 / 24 )40.490150.55526772077149372.9200500683574
Trimmed Mean ( 17 / 24 )40.43028947368420.52901998944167476.4248804971514
Trimmed Mean ( 18 / 24 )40.37094444444440.50190082170928180.4360995205319
Trimmed Mean ( 19 / 24 )40.30688235294120.47062529756014585.6453797998183
Trimmed Mean ( 20 / 24 )40.2541250.44721980494098490.0097101140502
Trimmed Mean ( 21 / 24 )40.20223333333330.42179663804934795.3118865983706
Trimmed Mean ( 22 / 24 )40.15085714285710.387909339058494103.505775963807
Trimmed Mean ( 23 / 24 )40.10303846153850.361244104474732111.013682894148
Trimmed Mean ( 24 / 24 )40.062250.338676699379952118.290541018457
Median39.9975
Midrange41.556
Midmean - Weighted Average at Xnp40.2373783783784
Midmean - Weighted Average at X(n+1)p40.3709444444444
Midmean - Empirical Distribution Function40.2373783783784
Midmean - Empirical Distribution Function - Averaging40.3709444444444
Midmean - Empirical Distribution Function - Interpolation40.3709444444444
Midmean - Closest Observation40.2373783783784
Midmean - True Basic - Statistics Graphics Toolkit40.3709444444444
Midmean - MS Excel (old versions)40.4302894736842
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')