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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 12:36:59 -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/t1256063893tb3drtbi6rad2mk.htm/, Retrieved Mon, 06 May 2024 15:38:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48972, Retrieved Mon, 06 May 2024 15:38:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [ws3v3] [2009-10-20 18:36:59] [f47dffd5f5a8c03c3681db4cc9472742] [Current]
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Dataseries X:
57
65
69
70
71
71
73
68
65
57
41
21
21
17
9
11
6
-2
0
5
3
7
4
8
9
14
12
12
7
15
14
19
39
12
11
17
16
25
24
28
25
31
24
24
33
37
35
37
38
42
43
44
32
32
37
38
39
38
39
30




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48972&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48972&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean29.81666666666672.6734192400641211.1530081851104
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean36.2038211611242
Winsorized Mean ( 1 / 20 )29.81666666666672.6579474331594311.2179294047303
Winsorized Mean ( 2 / 20 )29.91666666666672.6397966522723711.3329436344705
Winsorized Mean ( 3 / 20 )29.91666666666672.6181991985550911.4264287771446
Winsorized Mean ( 4 / 20 )29.91666666666672.5899950555835611.5508586019003
Winsorized Mean ( 5 / 20 )29.91666666666672.5554076555908611.7071992804019
Winsorized Mean ( 6 / 20 )29.71666666666672.4653636427050912.0536646813126
Winsorized Mean ( 7 / 20 )29.71666666666672.4653636427050912.0536646813126
Winsorized Mean ( 8 / 20 )28.78333333333332.1981105993912813.0945791996564
Winsorized Mean ( 9 / 20 )28.93333333333332.1744363081046513.3061305247212
Winsorized Mean ( 10 / 20 )26.76666666666671.7506038775148015.2899619442550
Winsorized Mean ( 11 / 20 )26.951.658810580618816.2465807216799
Winsorized Mean ( 12 / 20 )26.751.6265149392051816.4462061523221
Winsorized Mean ( 13 / 20 )26.751.5573091743153617.1770644141746
Winsorized Mean ( 14 / 20 )26.28333333333331.4872512215012217.6724234301204
Winsorized Mean ( 15 / 20 )26.28333333333331.4872512215012217.6724234301204
Winsorized Mean ( 16 / 20 )26.81666666666671.4024779657607619.1209183469205
Winsorized Mean ( 17 / 20 )26.53333333333331.3613856904333819.4899458102038
Winsorized Mean ( 18 / 20 )26.83333333333331.3150941764877620.4041153957487
Winsorized Mean ( 19 / 20 )27.151.2673262481338621.4230550657169
Winsorized Mean ( 20 / 20 )27.151.1699690951541523.2057411708152
Trimmed Mean ( 1 / 20 )29.62068965517242.6042484237328011.3739877445008
Trimmed Mean ( 2 / 20 )29.41071428571432.5373542803420911.5910949107781
Trimmed Mean ( 3 / 20 )29.12962962962962.4655624329185711.814598259898
Trimmed Mean ( 4 / 20 )28.82692307692312.3854955681083712.0842492697574
Trimmed Mean ( 5 / 20 )28.52.2950256767938012.4181617173953
Trimmed Mean ( 6 / 20 )28.14583333333332.1912118120078512.8448711252349
Trimmed Mean ( 7 / 20 )27.80434782608702.0876030600767813.3187905104260
Trimmed Mean ( 8 / 20 )27.43181818181821.9506050796665814.0632352841546
Trimmed Mean ( 9 / 20 )27.19047619047621.8579765245195214.6344562655375
Trimmed Mean ( 10 / 20 )26.91.7397317800933215.4621535962038
Trimmed Mean ( 11 / 20 )26.92105263157891.7094755498942215.7481355221751
Trimmed Mean ( 12 / 20 )26.91666666666671.6895453506974915.9313075884911
Trimmed Mean ( 13 / 20 )26.94117647058821.6664569439193116.1667402022556
Trimmed Mean ( 14 / 20 )26.968751.6482422057912516.3621280326658
Trimmed Mean ( 15 / 20 )27.06666666666671.635056562228316.5539635092376
Trimmed Mean ( 16 / 20 )27.17857142857141.6085531730899016.8962841162183
Trimmed Mean ( 17 / 20 )27.23076923076921.5896856895990417.1296561382757
Trimmed Mean ( 18 / 20 )27.33333333333331.5646301904444517.4695167588253
Trimmed Mean ( 19 / 20 )27.40909090909091.5327013909170317.8828642496969
Trimmed Mean ( 20 / 20 )27.451.4893923169145918.4303354383250
Median26.5
Midrange35.5
Midmean - Weighted Average at Xnp26.5151515151515
Midmean - Weighted Average at X(n+1)p26.5151515151515
Midmean - Empirical Distribution Function26.5151515151515
Midmean - Empirical Distribution Function - Averaging26.5151515151515
Midmean - Empirical Distribution Function - Interpolation26.5151515151515
Midmean - Closest Observation26.5151515151515
Midmean - True Basic - Statistics Graphics Toolkit26.5151515151515
Midmean - MS Excel (old versions)26.5151515151515
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 29.8166666666667 & 2.67341924006412 & 11.1530081851104 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 36.2038211611242 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 29.8166666666667 & 2.65794743315943 & 11.2179294047303 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 29.9166666666667 & 2.63979665227237 & 11.3329436344705 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 29.9166666666667 & 2.61819919855509 & 11.4264287771446 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 29.9166666666667 & 2.58999505558356 & 11.5508586019003 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 29.9166666666667 & 2.55540765559086 & 11.7071992804019 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 29.7166666666667 & 2.46536364270509 & 12.0536646813126 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 29.7166666666667 & 2.46536364270509 & 12.0536646813126 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 28.7833333333333 & 2.19811059939128 & 13.0945791996564 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 28.9333333333333 & 2.17443630810465 & 13.3061305247212 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 26.7666666666667 & 1.75060387751480 & 15.2899619442550 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 26.95 & 1.6588105806188 & 16.2465807216799 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 26.75 & 1.62651493920518 & 16.4462061523221 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 26.75 & 1.55730917431536 & 17.1770644141746 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 26.2833333333333 & 1.48725122150122 & 17.6724234301204 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 26.2833333333333 & 1.48725122150122 & 17.6724234301204 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 26.8166666666667 & 1.40247796576076 & 19.1209183469205 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 26.5333333333333 & 1.36138569043338 & 19.4899458102038 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 26.8333333333333 & 1.31509417648776 & 20.4041153957487 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 27.15 & 1.26732624813386 & 21.4230550657169 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 27.15 & 1.16996909515415 & 23.2057411708152 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 29.6206896551724 & 2.60424842373280 & 11.3739877445008 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 29.4107142857143 & 2.53735428034209 & 11.5910949107781 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 29.1296296296296 & 2.46556243291857 & 11.814598259898 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 28.8269230769231 & 2.38549556810837 & 12.0842492697574 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 28.5 & 2.29502567679380 & 12.4181617173953 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 28.1458333333333 & 2.19121181200785 & 12.8448711252349 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 27.8043478260870 & 2.08760306007678 & 13.3187905104260 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 27.4318181818182 & 1.95060507966658 & 14.0632352841546 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 27.1904761904762 & 1.85797652451952 & 14.6344562655375 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 26.9 & 1.73973178009332 & 15.4621535962038 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 26.9210526315789 & 1.70947554989422 & 15.7481355221751 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 26.9166666666667 & 1.68954535069749 & 15.9313075884911 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 26.9411764705882 & 1.66645694391931 & 16.1667402022556 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 26.96875 & 1.64824220579125 & 16.3621280326658 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 27.0666666666667 & 1.6350565622283 & 16.5539635092376 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 27.1785714285714 & 1.60855317308990 & 16.8962841162183 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 27.2307692307692 & 1.58968568959904 & 17.1296561382757 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 27.3333333333333 & 1.56463019044445 & 17.4695167588253 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 27.4090909090909 & 1.53270139091703 & 17.8828642496969 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 27.45 & 1.48939231691459 & 18.4303354383250 \tabularnewline
Median & 26.5 &  &  \tabularnewline
Midrange & 35.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.5151515151515 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.5151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.5151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.5151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.5151515151515 &  &  \tabularnewline
Midmean - Closest Observation & 26.5151515151515 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.5151515151515 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.5151515151515 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48972&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]29.8166666666667[/C][C]2.67341924006412[/C][C]11.1530081851104[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]36.2038211611242[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]29.8166666666667[/C][C]2.65794743315943[/C][C]11.2179294047303[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]29.9166666666667[/C][C]2.63979665227237[/C][C]11.3329436344705[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]29.9166666666667[/C][C]2.61819919855509[/C][C]11.4264287771446[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]29.9166666666667[/C][C]2.58999505558356[/C][C]11.5508586019003[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]29.9166666666667[/C][C]2.55540765559086[/C][C]11.7071992804019[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]29.7166666666667[/C][C]2.46536364270509[/C][C]12.0536646813126[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]29.7166666666667[/C][C]2.46536364270509[/C][C]12.0536646813126[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]28.7833333333333[/C][C]2.19811059939128[/C][C]13.0945791996564[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]28.9333333333333[/C][C]2.17443630810465[/C][C]13.3061305247212[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]26.7666666666667[/C][C]1.75060387751480[/C][C]15.2899619442550[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]26.95[/C][C]1.6588105806188[/C][C]16.2465807216799[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]26.75[/C][C]1.62651493920518[/C][C]16.4462061523221[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]26.75[/C][C]1.55730917431536[/C][C]17.1770644141746[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]26.2833333333333[/C][C]1.48725122150122[/C][C]17.6724234301204[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]26.2833333333333[/C][C]1.48725122150122[/C][C]17.6724234301204[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]26.8166666666667[/C][C]1.40247796576076[/C][C]19.1209183469205[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]26.5333333333333[/C][C]1.36138569043338[/C][C]19.4899458102038[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]26.8333333333333[/C][C]1.31509417648776[/C][C]20.4041153957487[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]27.15[/C][C]1.26732624813386[/C][C]21.4230550657169[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]27.15[/C][C]1.16996909515415[/C][C]23.2057411708152[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]29.6206896551724[/C][C]2.60424842373280[/C][C]11.3739877445008[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]29.4107142857143[/C][C]2.53735428034209[/C][C]11.5910949107781[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]29.1296296296296[/C][C]2.46556243291857[/C][C]11.814598259898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]28.8269230769231[/C][C]2.38549556810837[/C][C]12.0842492697574[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]28.5[/C][C]2.29502567679380[/C][C]12.4181617173953[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]28.1458333333333[/C][C]2.19121181200785[/C][C]12.8448711252349[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]27.8043478260870[/C][C]2.08760306007678[/C][C]13.3187905104260[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]27.4318181818182[/C][C]1.95060507966658[/C][C]14.0632352841546[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]27.1904761904762[/C][C]1.85797652451952[/C][C]14.6344562655375[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]26.9[/C][C]1.73973178009332[/C][C]15.4621535962038[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]26.9210526315789[/C][C]1.70947554989422[/C][C]15.7481355221751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]26.9166666666667[/C][C]1.68954535069749[/C][C]15.9313075884911[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]26.9411764705882[/C][C]1.66645694391931[/C][C]16.1667402022556[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]26.96875[/C][C]1.64824220579125[/C][C]16.3621280326658[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]27.0666666666667[/C][C]1.6350565622283[/C][C]16.5539635092376[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]27.1785714285714[/C][C]1.60855317308990[/C][C]16.8962841162183[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]27.2307692307692[/C][C]1.58968568959904[/C][C]17.1296561382757[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]27.3333333333333[/C][C]1.56463019044445[/C][C]17.4695167588253[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]27.4090909090909[/C][C]1.53270139091703[/C][C]17.8828642496969[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]27.45[/C][C]1.48939231691459[/C][C]18.4303354383250[/C][/ROW]
[ROW][C]Median[/C][C]26.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]35.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.5151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48972&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 Mean29.81666666666672.6734192400641211.1530081851104
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean36.2038211611242
Winsorized Mean ( 1 / 20 )29.81666666666672.6579474331594311.2179294047303
Winsorized Mean ( 2 / 20 )29.91666666666672.6397966522723711.3329436344705
Winsorized Mean ( 3 / 20 )29.91666666666672.6181991985550911.4264287771446
Winsorized Mean ( 4 / 20 )29.91666666666672.5899950555835611.5508586019003
Winsorized Mean ( 5 / 20 )29.91666666666672.5554076555908611.7071992804019
Winsorized Mean ( 6 / 20 )29.71666666666672.4653636427050912.0536646813126
Winsorized Mean ( 7 / 20 )29.71666666666672.4653636427050912.0536646813126
Winsorized Mean ( 8 / 20 )28.78333333333332.1981105993912813.0945791996564
Winsorized Mean ( 9 / 20 )28.93333333333332.1744363081046513.3061305247212
Winsorized Mean ( 10 / 20 )26.76666666666671.7506038775148015.2899619442550
Winsorized Mean ( 11 / 20 )26.951.658810580618816.2465807216799
Winsorized Mean ( 12 / 20 )26.751.6265149392051816.4462061523221
Winsorized Mean ( 13 / 20 )26.751.5573091743153617.1770644141746
Winsorized Mean ( 14 / 20 )26.28333333333331.4872512215012217.6724234301204
Winsorized Mean ( 15 / 20 )26.28333333333331.4872512215012217.6724234301204
Winsorized Mean ( 16 / 20 )26.81666666666671.4024779657607619.1209183469205
Winsorized Mean ( 17 / 20 )26.53333333333331.3613856904333819.4899458102038
Winsorized Mean ( 18 / 20 )26.83333333333331.3150941764877620.4041153957487
Winsorized Mean ( 19 / 20 )27.151.2673262481338621.4230550657169
Winsorized Mean ( 20 / 20 )27.151.1699690951541523.2057411708152
Trimmed Mean ( 1 / 20 )29.62068965517242.6042484237328011.3739877445008
Trimmed Mean ( 2 / 20 )29.41071428571432.5373542803420911.5910949107781
Trimmed Mean ( 3 / 20 )29.12962962962962.4655624329185711.814598259898
Trimmed Mean ( 4 / 20 )28.82692307692312.3854955681083712.0842492697574
Trimmed Mean ( 5 / 20 )28.52.2950256767938012.4181617173953
Trimmed Mean ( 6 / 20 )28.14583333333332.1912118120078512.8448711252349
Trimmed Mean ( 7 / 20 )27.80434782608702.0876030600767813.3187905104260
Trimmed Mean ( 8 / 20 )27.43181818181821.9506050796665814.0632352841546
Trimmed Mean ( 9 / 20 )27.19047619047621.8579765245195214.6344562655375
Trimmed Mean ( 10 / 20 )26.91.7397317800933215.4621535962038
Trimmed Mean ( 11 / 20 )26.92105263157891.7094755498942215.7481355221751
Trimmed Mean ( 12 / 20 )26.91666666666671.6895453506974915.9313075884911
Trimmed Mean ( 13 / 20 )26.94117647058821.6664569439193116.1667402022556
Trimmed Mean ( 14 / 20 )26.968751.6482422057912516.3621280326658
Trimmed Mean ( 15 / 20 )27.06666666666671.635056562228316.5539635092376
Trimmed Mean ( 16 / 20 )27.17857142857141.6085531730899016.8962841162183
Trimmed Mean ( 17 / 20 )27.23076923076921.5896856895990417.1296561382757
Trimmed Mean ( 18 / 20 )27.33333333333331.5646301904444517.4695167588253
Trimmed Mean ( 19 / 20 )27.40909090909091.5327013909170317.8828642496969
Trimmed Mean ( 20 / 20 )27.451.4893923169145918.4303354383250
Median26.5
Midrange35.5
Midmean - Weighted Average at Xnp26.5151515151515
Midmean - Weighted Average at X(n+1)p26.5151515151515
Midmean - Empirical Distribution Function26.5151515151515
Midmean - Empirical Distribution Function - Averaging26.5151515151515
Midmean - Empirical Distribution Function - Interpolation26.5151515151515
Midmean - Closest Observation26.5151515151515
Midmean - True Basic - Statistics Graphics Toolkit26.5151515151515
Midmean - MS Excel (old versions)26.5151515151515
Number of observations60



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')