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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 computationMon, 20 Oct 2008 16:18:20 -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/2008/Oct/21/t1224541155pyv0if3mlfu3tjg.htm/, Retrieved Sun, 19 May 2024 21:00:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18253, Retrieved Sun, 19 May 2024 21:00:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [central tendency] [2008-10-20 22:18:20] [0d500ce70fb61d771562626855e78bdd] [Current]
Feedback Forum
2008-10-24 09:51:29 [Siem Van Opstal] [reply
de gegevens vertonen een normaalverdeling. de mediaan en het gemiddelde liggen dicht bij elkaar, respectievelijk 46 en 49. De midrange bedraagt 46,78.

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Dataseries X:
26.599
35.324
38.546
42.065
44.148
54.424
58.397
64.864
70.639
66.642
57.794
27.860
31.060
41.303
45.844
48.614
50.883
53.511
58.078
64.496
71.660
69.447
60.190
28.893
30.744
37.817
45.343
51.175
52.913
54.078
55.568
61.765
69.153
66.083
58.032
26.054
27.643
35.243
42.103
45.870
49.092
51.814
54.871
60.769
67.197
64.020
54.200
23.779
26.485
33.354
39.072
41.666
43.651
45.712
48.585
55.810
61.266
58.464
44.524
21.912
25.199




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' @ 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18253&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18253&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' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean48.23454098360661.7640444972538827.3431543584611
Geometric Mean46.070629766025
Harmonic Mean43.7084525053948
Quadratic Mean50.1326452842529
Winsorized Mean ( 1 / 20 )48.24840983606561.7530438149532727.5226491343296
Winsorized Mean ( 2 / 20 )48.25588524590161.7343288741670627.8239530948692
Winsorized Mean ( 3 / 20 )48.28347540983611.7222146053205928.0356903609282
Winsorized Mean ( 4 / 20 )48.18347540983611.6911750977531628.4911216312557
Winsorized Mean ( 5 / 20 )48.14732786885251.6807437227597628.6464421772732
Winsorized Mean ( 6 / 20 )48.19503278688521.6490921494775329.2251908434313
Winsorized Mean ( 7 / 20 )48.08004918032791.6191814474591029.6940464923047
Winsorized Mean ( 8 / 20 )48.1672622950821.5830156411624130.4275340322682
Winsorized Mean ( 9 / 20 )48.3701311475411.5167565858426131.8905034591754
Winsorized Mean ( 10 / 20 )48.0522622950821.445597620458133.2404132485045
Winsorized Mean ( 11 / 20 )48.37595081967211.3524542280723335.7690114870822
Winsorized Mean ( 12 / 20 )48.64978688524591.2697668625809338.3139522056517
Winsorized Mean ( 13 / 20 )48.54365573770491.2473059345937638.918804433906
Winsorized Mean ( 14 / 20 )48.71968852459021.0883541493438544.7645543998361
Winsorized Mean ( 15 / 20 )48.88247540983611.0563002001797446.2770672594005
Winsorized Mean ( 16 / 20 )48.93677049180331.0214216438532847.9104498972539
Winsorized Mean ( 17 / 20 )49.54570491803280.92298207222708453.680029557327
Winsorized Mean ( 18 / 20 )49.58259016393440.8963833240271855.3140479467811
Winsorized Mean ( 19 / 20 )49.08890163934430.78661297782831862.4054052284631
Winsorized Mean ( 20 / 20 )49.02201639344260.77351165405394563.3759247666407
Trimmed Mean ( 1 / 20 )48.28364406779661.7220347494786128.0387164558762
Trimmed Mean ( 2 / 20 )48.3213508771931.683557036022528.7019387186043
Trimmed Mean ( 3 / 20 )48.35765454545451.6480048315238829.3431509546845
Trimmed Mean ( 4 / 20 )48.38611320754721.6091560243755230.0692490191092
Trimmed Mean ( 5 / 20 )48.44670588235291.5721403403139430.8157641147218
Trimmed Mean ( 6 / 20 )48.52124489795921.5283574003283031.7473157047799
Trimmed Mean ( 7 / 20 )48.59180851063831.482152655937532.7846179109686
Trimmed Mean ( 8 / 20 )48.69091111111111.4309699902345034.0265075042781
Trimmed Mean ( 9 / 20 )48.78376744186051.3745567785954635.4905437167232
Trimmed Mean ( 10 / 20 )48.85214634146341.3192986290583937.0288767572891
Trimmed Mean ( 11 / 20 )48.97725641025641.2647476695513438.7249232312328
Trimmed Mean ( 12 / 20 )49.06737837837841.217732955157740.2940383361999
Trimmed Mean ( 13 / 20 )49.12802857142861.1764558072288841.7593489441383
Trimmed Mean ( 14 / 20 )49.21112121212121.1238930477915643.7863027169896
Trimmed Mean ( 15 / 20 )49.28019354838711.0965642878832944.9405421031113
Trimmed Mean ( 16 / 20 )49.33596551724141.0643415567687546.3535086114849
Trimmed Mean ( 17 / 20 )49.39233333333331.0253164975888848.1727675790684
Trimmed Mean ( 18 / 20 )49.370320.99824932042718349.4569031901498
Trimmed Mean ( 19 / 20 )49.33904347826090.9612693281583251.3269715707966
Trimmed Mean ( 20 / 20 )49.37728571428570.942069523121652.4136324362467
Median49.092
Midrange46.786
Midmean - Weighted Average at Xnp48.9763
Midmean - Weighted Average at X(n+1)p49.2801935483871
Midmean - Empirical Distribution Function49.2801935483871
Midmean - Empirical Distribution Function - Averaging49.2801935483871
Midmean - Empirical Distribution Function - Interpolation49.2801935483871
Midmean - Closest Observation48.92196875
Midmean - True Basic - Statistics Graphics Toolkit49.2801935483871
Midmean - MS Excel (old versions)49.2801935483871
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 48.2345409836066 & 1.76404449725388 & 27.3431543584611 \tabularnewline
Geometric Mean & 46.070629766025 &  &  \tabularnewline
Harmonic Mean & 43.7084525053948 &  &  \tabularnewline
Quadratic Mean & 50.1326452842529 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 48.2484098360656 & 1.75304381495327 & 27.5226491343296 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 48.2558852459016 & 1.73432887416706 & 27.8239530948692 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 48.2834754098361 & 1.72221460532059 & 28.0356903609282 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 48.1834754098361 & 1.69117509775316 & 28.4911216312557 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 48.1473278688525 & 1.68074372275976 & 28.6464421772732 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 48.1950327868852 & 1.64909214947753 & 29.2251908434313 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 48.0800491803279 & 1.61918144745910 & 29.6940464923047 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 48.167262295082 & 1.58301564116241 & 30.4275340322682 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 48.370131147541 & 1.51675658584261 & 31.8905034591754 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 48.052262295082 & 1.4455976204581 & 33.2404132485045 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 48.3759508196721 & 1.35245422807233 & 35.7690114870822 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 48.6497868852459 & 1.26976686258093 & 38.3139522056517 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 48.5436557377049 & 1.24730593459376 & 38.918804433906 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 48.7196885245902 & 1.08835414934385 & 44.7645543998361 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 48.8824754098361 & 1.05630020017974 & 46.2770672594005 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 48.9367704918033 & 1.02142164385328 & 47.9104498972539 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 49.5457049180328 & 0.922982072227084 & 53.680029557327 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 49.5825901639344 & 0.89638332402718 & 55.3140479467811 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 49.0889016393443 & 0.786612977828318 & 62.4054052284631 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 49.0220163934426 & 0.773511654053945 & 63.3759247666407 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 48.2836440677966 & 1.72203474947861 & 28.0387164558762 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 48.321350877193 & 1.6835570360225 & 28.7019387186043 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 48.3576545454545 & 1.64800483152388 & 29.3431509546845 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 48.3861132075472 & 1.60915602437552 & 30.0692490191092 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 48.4467058823529 & 1.57214034031394 & 30.8157641147218 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 48.5212448979592 & 1.52835740032830 & 31.7473157047799 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 48.5918085106383 & 1.4821526559375 & 32.7846179109686 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 48.6909111111111 & 1.43096999023450 & 34.0265075042781 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 48.7837674418605 & 1.37455677859546 & 35.4905437167232 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 48.8521463414634 & 1.31929862905839 & 37.0288767572891 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 48.9772564102564 & 1.26474766955134 & 38.7249232312328 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 49.0673783783784 & 1.2177329551577 & 40.2940383361999 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 49.1280285714286 & 1.17645580722888 & 41.7593489441383 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 49.2111212121212 & 1.12389304779156 & 43.7863027169896 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 49.2801935483871 & 1.09656428788329 & 44.9405421031113 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 49.3359655172414 & 1.06434155676875 & 46.3535086114849 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 49.3923333333333 & 1.02531649758888 & 48.1727675790684 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 49.37032 & 0.998249320427183 & 49.4569031901498 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 49.3390434782609 & 0.96126932815832 & 51.3269715707966 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 49.3772857142857 & 0.9420695231216 & 52.4136324362467 \tabularnewline
Median & 49.092 &  &  \tabularnewline
Midrange & 46.786 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.9763 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 49.2801935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 49.2801935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 49.2801935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 49.2801935483871 &  &  \tabularnewline
Midmean - Closest Observation & 48.92196875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 49.2801935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.2801935483871 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18253&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]48.2345409836066[/C][C]1.76404449725388[/C][C]27.3431543584611[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]46.070629766025[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]43.7084525053948[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]50.1326452842529[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]48.2484098360656[/C][C]1.75304381495327[/C][C]27.5226491343296[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]48.2558852459016[/C][C]1.73432887416706[/C][C]27.8239530948692[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]48.2834754098361[/C][C]1.72221460532059[/C][C]28.0356903609282[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]48.1834754098361[/C][C]1.69117509775316[/C][C]28.4911216312557[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]48.1473278688525[/C][C]1.68074372275976[/C][C]28.6464421772732[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]48.1950327868852[/C][C]1.64909214947753[/C][C]29.2251908434313[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]48.0800491803279[/C][C]1.61918144745910[/C][C]29.6940464923047[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]48.167262295082[/C][C]1.58301564116241[/C][C]30.4275340322682[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]48.370131147541[/C][C]1.51675658584261[/C][C]31.8905034591754[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]48.052262295082[/C][C]1.4455976204581[/C][C]33.2404132485045[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]48.3759508196721[/C][C]1.35245422807233[/C][C]35.7690114870822[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]48.6497868852459[/C][C]1.26976686258093[/C][C]38.3139522056517[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]48.5436557377049[/C][C]1.24730593459376[/C][C]38.918804433906[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]48.7196885245902[/C][C]1.08835414934385[/C][C]44.7645543998361[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]48.8824754098361[/C][C]1.05630020017974[/C][C]46.2770672594005[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]48.9367704918033[/C][C]1.02142164385328[/C][C]47.9104498972539[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]49.5457049180328[/C][C]0.922982072227084[/C][C]53.680029557327[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]49.5825901639344[/C][C]0.89638332402718[/C][C]55.3140479467811[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]49.0889016393443[/C][C]0.786612977828318[/C][C]62.4054052284631[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]49.0220163934426[/C][C]0.773511654053945[/C][C]63.3759247666407[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]48.2836440677966[/C][C]1.72203474947861[/C][C]28.0387164558762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]48.321350877193[/C][C]1.6835570360225[/C][C]28.7019387186043[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]48.3576545454545[/C][C]1.64800483152388[/C][C]29.3431509546845[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]48.3861132075472[/C][C]1.60915602437552[/C][C]30.0692490191092[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]48.4467058823529[/C][C]1.57214034031394[/C][C]30.8157641147218[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]48.5212448979592[/C][C]1.52835740032830[/C][C]31.7473157047799[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]48.5918085106383[/C][C]1.4821526559375[/C][C]32.7846179109686[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]48.6909111111111[/C][C]1.43096999023450[/C][C]34.0265075042781[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]48.7837674418605[/C][C]1.37455677859546[/C][C]35.4905437167232[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]48.8521463414634[/C][C]1.31929862905839[/C][C]37.0288767572891[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]48.9772564102564[/C][C]1.26474766955134[/C][C]38.7249232312328[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]49.0673783783784[/C][C]1.2177329551577[/C][C]40.2940383361999[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]49.1280285714286[/C][C]1.17645580722888[/C][C]41.7593489441383[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]49.2111212121212[/C][C]1.12389304779156[/C][C]43.7863027169896[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]49.2801935483871[/C][C]1.09656428788329[/C][C]44.9405421031113[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]49.3359655172414[/C][C]1.06434155676875[/C][C]46.3535086114849[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]49.3923333333333[/C][C]1.02531649758888[/C][C]48.1727675790684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]49.37032[/C][C]0.998249320427183[/C][C]49.4569031901498[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]49.3390434782609[/C][C]0.96126932815832[/C][C]51.3269715707966[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]49.3772857142857[/C][C]0.9420695231216[/C][C]52.4136324362467[/C][/ROW]
[ROW][C]Median[/C][C]49.092[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]46.786[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.9763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.92196875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.2801935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18253&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 Mean48.23454098360661.7640444972538827.3431543584611
Geometric Mean46.070629766025
Harmonic Mean43.7084525053948
Quadratic Mean50.1326452842529
Winsorized Mean ( 1 / 20 )48.24840983606561.7530438149532727.5226491343296
Winsorized Mean ( 2 / 20 )48.25588524590161.7343288741670627.8239530948692
Winsorized Mean ( 3 / 20 )48.28347540983611.7222146053205928.0356903609282
Winsorized Mean ( 4 / 20 )48.18347540983611.6911750977531628.4911216312557
Winsorized Mean ( 5 / 20 )48.14732786885251.6807437227597628.6464421772732
Winsorized Mean ( 6 / 20 )48.19503278688521.6490921494775329.2251908434313
Winsorized Mean ( 7 / 20 )48.08004918032791.6191814474591029.6940464923047
Winsorized Mean ( 8 / 20 )48.1672622950821.5830156411624130.4275340322682
Winsorized Mean ( 9 / 20 )48.3701311475411.5167565858426131.8905034591754
Winsorized Mean ( 10 / 20 )48.0522622950821.445597620458133.2404132485045
Winsorized Mean ( 11 / 20 )48.37595081967211.3524542280723335.7690114870822
Winsorized Mean ( 12 / 20 )48.64978688524591.2697668625809338.3139522056517
Winsorized Mean ( 13 / 20 )48.54365573770491.2473059345937638.918804433906
Winsorized Mean ( 14 / 20 )48.71968852459021.0883541493438544.7645543998361
Winsorized Mean ( 15 / 20 )48.88247540983611.0563002001797446.2770672594005
Winsorized Mean ( 16 / 20 )48.93677049180331.0214216438532847.9104498972539
Winsorized Mean ( 17 / 20 )49.54570491803280.92298207222708453.680029557327
Winsorized Mean ( 18 / 20 )49.58259016393440.8963833240271855.3140479467811
Winsorized Mean ( 19 / 20 )49.08890163934430.78661297782831862.4054052284631
Winsorized Mean ( 20 / 20 )49.02201639344260.77351165405394563.3759247666407
Trimmed Mean ( 1 / 20 )48.28364406779661.7220347494786128.0387164558762
Trimmed Mean ( 2 / 20 )48.3213508771931.683557036022528.7019387186043
Trimmed Mean ( 3 / 20 )48.35765454545451.6480048315238829.3431509546845
Trimmed Mean ( 4 / 20 )48.38611320754721.6091560243755230.0692490191092
Trimmed Mean ( 5 / 20 )48.44670588235291.5721403403139430.8157641147218
Trimmed Mean ( 6 / 20 )48.52124489795921.5283574003283031.7473157047799
Trimmed Mean ( 7 / 20 )48.59180851063831.482152655937532.7846179109686
Trimmed Mean ( 8 / 20 )48.69091111111111.4309699902345034.0265075042781
Trimmed Mean ( 9 / 20 )48.78376744186051.3745567785954635.4905437167232
Trimmed Mean ( 10 / 20 )48.85214634146341.3192986290583937.0288767572891
Trimmed Mean ( 11 / 20 )48.97725641025641.2647476695513438.7249232312328
Trimmed Mean ( 12 / 20 )49.06737837837841.217732955157740.2940383361999
Trimmed Mean ( 13 / 20 )49.12802857142861.1764558072288841.7593489441383
Trimmed Mean ( 14 / 20 )49.21112121212121.1238930477915643.7863027169896
Trimmed Mean ( 15 / 20 )49.28019354838711.0965642878832944.9405421031113
Trimmed Mean ( 16 / 20 )49.33596551724141.0643415567687546.3535086114849
Trimmed Mean ( 17 / 20 )49.39233333333331.0253164975888848.1727675790684
Trimmed Mean ( 18 / 20 )49.370320.99824932042718349.4569031901498
Trimmed Mean ( 19 / 20 )49.33904347826090.9612693281583251.3269715707966
Trimmed Mean ( 20 / 20 )49.37728571428570.942069523121652.4136324362467
Median49.092
Midrange46.786
Midmean - Weighted Average at Xnp48.9763
Midmean - Weighted Average at X(n+1)p49.2801935483871
Midmean - Empirical Distribution Function49.2801935483871
Midmean - Empirical Distribution Function - Averaging49.2801935483871
Midmean - Empirical Distribution Function - Interpolation49.2801935483871
Midmean - Closest Observation48.92196875
Midmean - True Basic - Statistics Graphics Toolkit49.2801935483871
Midmean - MS Excel (old versions)49.2801935483871
Number of observations61



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