Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Mar 2010 07:01:34 -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/2010/Mar/17/t1268831032639tgks8y5iielj.htm/, Retrieved Fri, 21 Jan 2022 10:23:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74503, Retrieved Fri, 21 Jan 2022 10:23:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten eige...] [2010-03-17 13:01:34] [0e5311d1fc10a1511b42f76588fb6510] [Current]
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Dataseries X:
81.28
69.39
67.63
51.25
103.97
133.83
162.37
172.91
163.01
151.50
111.73
88.58
74.29
63.98
61.18
76.48
107.98
124.97
145.57
140.20
143.84
138.80
104.06
74.70
60.18
55.16
35.62
56.18
85.44
114.08
133.64
67.14
95.58
89.37
75.24
69.18
54.49
57.50
62.16
76.67
110.04
127.38
156.47
167.56
153.54
124.08
100.97
79.17
68.13
61.77
54.31
60.30
84.18
104.05
114.66
105.55
96.61
70.94
63.91
58.61
44.53
49.58
57.39
76.76
104.57
125.41
143.11
136.35
135.15
131.70
96.87
70.63
66.29
63.49
62.97
66.43
101.49
127.69
133.21
158.72
148.61
134.31
100.99
75.16
59.74
52.87
52.07
57.38
79.43
101.40
120.19
134.38
135.97
113.83
84.38
70.28
65.96
56.36
49.57
68.33
90.32
117.06
134.69
131.67
129.25
118.77
88.44
76.79
75.28
73.89
76.24
88.58
105.83
115.84
127.76
131.75
119.63
93.38
75.55
51.79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74503&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74503&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.82853.0820934413304931.0920164570456
Geometric Mean89.942250300139
Harmonic Mean84.2851805274835
Quadratic Mean101.555492761347
Winsorized Mean ( 1 / 40 )95.85816666666673.0616931704196931.3088743159481
Winsorized Mean ( 2 / 40 )95.86633333333333.0358810389308231.5777634577854
Winsorized Mean ( 3 / 40 )95.85058333333333.0328876845713531.6037365382623
Winsorized Mean ( 4 / 40 )95.78458333333333.0039265034812331.8864603452611
Winsorized Mean ( 5 / 40 )95.71333333333332.9848622594266832.0662479586972
Winsorized Mean ( 6 / 40 )95.58083333333332.9585412234131432.3067438022939
Winsorized Mean ( 7 / 40 )95.50852.9334674792267032.5582269707579
Winsorized Mean ( 8 / 40 )95.41183333333332.8915208723003632.9971103606207
Winsorized Mean ( 9 / 40 )95.19733333333332.8553763058143133.3396803564861
Winsorized Mean ( 10 / 40 )95.1092.8275905511459733.6360580783006
Winsorized Mean ( 11 / 40 )95.13558333333332.8069364082468433.8930312257246
Winsorized Mean ( 12 / 40 )94.86258333333332.7638728118547234.3223403502692
Winsorized Mean ( 13 / 40 )94.82141666666672.7303185480619734.7290673221894
Winsorized Mean ( 14 / 40 )94.536752.6921811785380035.1153000970532
Winsorized Mean ( 15 / 40 )94.5032.6844048983458735.2044507362629
Winsorized Mean ( 16 / 40 )94.54166666666672.6532834088739535.6319518489696
Winsorized Mean ( 17 / 40 )94.63658333333332.6268726800080136.0263304931265
Winsorized Mean ( 18 / 40 )94.65608333333332.6135820217730836.2169935914686
Winsorized Mean ( 19 / 40 )94.6642.6100627223432436.2688602038702
Winsorized Mean ( 20 / 40 )94.73066666666672.5837540564605636.6639643699047
Winsorized Mean ( 21 / 40 )94.80066666666672.5683144172482136.9116281207656
Winsorized Mean ( 22 / 40 )94.79333333333332.5506089412246437.1649811937927
Winsorized Mean ( 23 / 40 )94.668752.4988278276183537.885263223689
Winsorized Mean ( 24 / 40 )94.762752.4865410823263438.1102691902209
Winsorized Mean ( 25 / 40 )94.8442.4765444022812538.2969107731867
Winsorized Mean ( 26 / 40 )94.33483333333332.4102609026439839.1388472633194
Winsorized Mean ( 27 / 40 )94.44508333333332.3231141051614140.65451762507
Winsorized Mean ( 28 / 40 )94.505752.3132321618222440.8544164134193
Winsorized Mean ( 29 / 40 )94.46466666666672.3007470864762741.0582576511462
Winsorized Mean ( 30 / 40 )94.14966666666672.2239002315667542.3353823747469
Winsorized Mean ( 31 / 40 )94.16258333333332.1976105163869142.8477123817854
Winsorized Mean ( 32 / 40 )94.05858333333332.156245596904843.6214610563613
Winsorized Mean ( 33 / 40 )93.04383333333332.0278267098134145.8835229278022
Winsorized Mean ( 34 / 40 )93.1261.9854645238205946.9038851526792
Winsorized Mean ( 35 / 40 )92.93641666666671.9512317477109147.629614870553
Winsorized Mean ( 36 / 40 )92.69041666666661.8675572407722049.6319013110092
Winsorized Mean ( 37 / 40 )92.42216666666671.815661110635550.9027627046095
Winsorized Mean ( 38 / 40 )92.14666666666671.7654823153430352.1934804250717
Winsorized Mean ( 39 / 40 )92.91691666666671.6503308971141756.3019918182134
Winsorized Mean ( 40 / 40 )92.96691666666671.628470690512357.0884801355683
Trimmed Mean ( 1 / 40 )95.68550847457633.0219747830065231.6632385593172
Trimmed Mean ( 2 / 40 )95.50689655172412.9778598399846832.0723276728214
Trimmed Mean ( 3 / 40 )95.31771929824562.9436499090531432.3807933155018
Trimmed Mean ( 4 / 40 )95.12741071428572.9066267227101432.7277699509997
Trimmed Mean ( 5 / 40 )94.94818181818182.8743307831399733.0331437060485
Trimmed Mean ( 6 / 40 )94.77814814814812.8430750983794033.3364912527893
Trimmed Mean ( 7 / 40 )94.62669811320762.8139150758859533.6281286255288
Trimmed Mean ( 8 / 40 )94.48134615384612.7860654011167333.9121063403521
Trimmed Mean ( 9 / 40 )94.34450980392162.7622181291421534.1553437827959
Trimmed Mean ( 10 / 40 )94.23082.7411746088054334.376066266375
Trimmed Mean ( 11 / 40 )94.12326530612242.7213736838268434.5866743202150
Trimmed Mean ( 12 / 40 )94.00822916666672.7015180754839534.7982973054238
Trimmed Mean ( 13 / 40 )93.9173404255322.6846739121427334.9827738857765
Trimmed Mean ( 14 / 40 )93.82663043478262.6694273069498835.1485991735022
Trimmed Mean ( 15 / 40 )93.7592.6563770068923935.2958182354114
Trimmed Mean ( 16 / 40 )93.69136363636362.6416106938838035.4675137609377
Trimmed Mean ( 17 / 40 )93.61720930232562.627706581466235.6269645791614
Trimmed Mean ( 18 / 40 )93.53154761904762.6139860131707735.7811966658512
Trimmed Mean ( 19 / 40 )93.44012195121952.5987724124301535.9554847913143
Trimmed Mean ( 20 / 40 )93.34352.5806046790420436.1711736625427
Trimmed Mean ( 21 / 40 )93.23679487179492.5617136139336836.3962600521233
Trimmed Mean ( 22 / 40 )93.11921052631582.5405485370058836.6531909034337
Trimmed Mean ( 23 / 40 )92.99581081081082.5169964338493336.9471364997483
Trimmed Mean ( 24 / 40 )92.87458333333332.4948554103758337.2264392345457
Trimmed Mean ( 25 / 40 )92.73971428571432.4691261140194637.5597316634201
Trimmed Mean ( 26 / 40 )92.59117647058822.4388158165168037.9656289923648
Trimmed Mean ( 27 / 40 )92.46924242424242.4108742411322638.3550667416043
Trimmed Mean ( 28 / 40 )92.332031252.3876255491348138.6710685364619
Trimmed Mean ( 29 / 40 )92.18177419354842.3595208142729939.0680063663482
Trimmed Mean ( 30 / 40 )92.02433333333332.3259842624311139.563609616666
Trimmed Mean ( 31 / 40 )91.87775862068972.2952803444975740.0289920318215
Trimmed Mean ( 32 / 40 )91.71982142857142.2600850387844140.5824647544693
Trimmed Mean ( 33 / 40 )91.55740740740742.2217641013922241.209328816698
Trimmed Mean ( 34 / 40 )91.45346153846152.1941584808901341.6804266122839
Trimmed Mean ( 35 / 40 )91.33542.1643574379440442.1997764319193
Trimmed Mean ( 36 / 40 )91.22104166666672.1307026161013042.8126576544878
Trimmed Mean ( 37 / 40 )91.11456521739132.1007589543317443.372213184913
Trimmed Mean ( 38 / 40 )91.01818181818182.0696036141586743.9785576307966
Trimmed Mean ( 39 / 40 )90.93333333333332.0364784419297144.6522445124279
Trimmed Mean ( 40 / 40 )90.780752.0118846053052145.1222449640586
Median88.975
Midrange104.265
Midmean - Weighted Average at Xnp91.6047540983607
Midmean - Weighted Average at X(n+1)p92.0243333333333
Midmean - Empirical Distribution Function91.6047540983607
Midmean - Empirical Distribution Function - Averaging92.0243333333333
Midmean - Empirical Distribution Function - Interpolation92.0243333333333
Midmean - Closest Observation91.6047540983607
Midmean - True Basic - Statistics Graphics Toolkit92.0243333333333
Midmean - MS Excel (old versions)92.1817741935484
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.8285 & 3.08209344133049 & 31.0920164570456 \tabularnewline
Geometric Mean & 89.942250300139 &  &  \tabularnewline
Harmonic Mean & 84.2851805274835 &  &  \tabularnewline
Quadratic Mean & 101.555492761347 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 95.8581666666667 & 3.06169317041969 & 31.3088743159481 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 95.8663333333333 & 3.03588103893082 & 31.5777634577854 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 95.8505833333333 & 3.03288768457135 & 31.6037365382623 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 95.7845833333333 & 3.00392650348123 & 31.8864603452611 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 95.7133333333333 & 2.98486225942668 & 32.0662479586972 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 95.5808333333333 & 2.95854122341314 & 32.3067438022939 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 95.5085 & 2.93346747922670 & 32.5582269707579 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 95.4118333333333 & 2.89152087230036 & 32.9971103606207 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 95.1973333333333 & 2.85537630581431 & 33.3396803564861 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 95.109 & 2.82759055114597 & 33.6360580783006 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 95.1355833333333 & 2.80693640824684 & 33.8930312257246 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 94.8625833333333 & 2.76387281185472 & 34.3223403502692 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 94.8214166666667 & 2.73031854806197 & 34.7290673221894 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 94.53675 & 2.69218117853800 & 35.1153000970532 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 94.503 & 2.68440489834587 & 35.2044507362629 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 94.5416666666667 & 2.65328340887395 & 35.6319518489696 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 94.6365833333333 & 2.62687268000801 & 36.0263304931265 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 94.6560833333333 & 2.61358202177308 & 36.2169935914686 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 94.664 & 2.61006272234324 & 36.2688602038702 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 94.7306666666667 & 2.58375405646056 & 36.6639643699047 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 94.8006666666667 & 2.56831441724821 & 36.9116281207656 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 94.7933333333333 & 2.55060894122464 & 37.1649811937927 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 94.66875 & 2.49882782761835 & 37.885263223689 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 94.76275 & 2.48654108232634 & 38.1102691902209 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 94.844 & 2.47654440228125 & 38.2969107731867 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 94.3348333333333 & 2.41026090264398 & 39.1388472633194 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 94.4450833333333 & 2.32311410516141 & 40.65451762507 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 94.50575 & 2.31323216182224 & 40.8544164134193 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 94.4646666666667 & 2.30074708647627 & 41.0582576511462 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 94.1496666666667 & 2.22390023156675 & 42.3353823747469 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 94.1625833333333 & 2.19761051638691 & 42.8477123817854 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 94.0585833333333 & 2.1562455969048 & 43.6214610563613 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 93.0438333333333 & 2.02782670981341 & 45.8835229278022 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 93.126 & 1.98546452382059 & 46.9038851526792 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 92.9364166666667 & 1.95123174771091 & 47.629614870553 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 92.6904166666666 & 1.86755724077220 & 49.6319013110092 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 92.4221666666667 & 1.8156611106355 & 50.9027627046095 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 92.1466666666667 & 1.76548231534303 & 52.1934804250717 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 92.9169166666667 & 1.65033089711417 & 56.3019918182134 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 92.9669166666667 & 1.6284706905123 & 57.0884801355683 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 95.6855084745763 & 3.02197478300652 & 31.6632385593172 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 95.5068965517241 & 2.97785983998468 & 32.0723276728214 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 95.3177192982456 & 2.94364990905314 & 32.3807933155018 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 95.1274107142857 & 2.90662672271014 & 32.7277699509997 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 94.9481818181818 & 2.87433078313997 & 33.0331437060485 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 94.7781481481481 & 2.84307509837940 & 33.3364912527893 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 94.6266981132076 & 2.81391507588595 & 33.6281286255288 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 94.4813461538461 & 2.78606540111673 & 33.9121063403521 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 94.3445098039216 & 2.76221812914215 & 34.1553437827959 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 94.2308 & 2.74117460880543 & 34.376066266375 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 94.1232653061224 & 2.72137368382684 & 34.5866743202150 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 94.0082291666667 & 2.70151807548395 & 34.7982973054238 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 93.917340425532 & 2.68467391214273 & 34.9827738857765 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 93.8266304347826 & 2.66942730694988 & 35.1485991735022 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 93.759 & 2.65637700689239 & 35.2958182354114 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 93.6913636363636 & 2.64161069388380 & 35.4675137609377 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 93.6172093023256 & 2.6277065814662 & 35.6269645791614 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 93.5315476190476 & 2.61398601317077 & 35.7811966658512 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 93.4401219512195 & 2.59877241243015 & 35.9554847913143 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 93.3435 & 2.58060467904204 & 36.1711736625427 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 93.2367948717949 & 2.56171361393368 & 36.3962600521233 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 93.1192105263158 & 2.54054853700588 & 36.6531909034337 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 92.9958108108108 & 2.51699643384933 & 36.9471364997483 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 92.8745833333333 & 2.49485541037583 & 37.2264392345457 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 92.7397142857143 & 2.46912611401946 & 37.5597316634201 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 92.5911764705882 & 2.43881581651680 & 37.9656289923648 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 92.4692424242424 & 2.41087424113226 & 38.3550667416043 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 92.33203125 & 2.38762554913481 & 38.6710685364619 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 92.1817741935484 & 2.35952081427299 & 39.0680063663482 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 92.0243333333333 & 2.32598426243111 & 39.563609616666 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 91.8777586206897 & 2.29528034449757 & 40.0289920318215 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 91.7198214285714 & 2.26008503878441 & 40.5824647544693 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 91.5574074074074 & 2.22176410139222 & 41.209328816698 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 91.4534615384615 & 2.19415848089013 & 41.6804266122839 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 91.3354 & 2.16435743794404 & 42.1997764319193 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 91.2210416666667 & 2.13070261610130 & 42.8126576544878 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 91.1145652173913 & 2.10075895433174 & 43.372213184913 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 91.0181818181818 & 2.06960361415867 & 43.9785576307966 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 90.9333333333333 & 2.03647844192971 & 44.6522445124279 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 90.78075 & 2.01188460530521 & 45.1222449640586 \tabularnewline
Median & 88.975 &  &  \tabularnewline
Midrange & 104.265 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 91.6047540983607 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 92.0243333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 91.6047540983607 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 92.0243333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 92.0243333333333 &  &  \tabularnewline
Midmean - Closest Observation & 91.6047540983607 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 92.0243333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 92.1817741935484 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74503&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]95.8285[/C][C]3.08209344133049[/C][C]31.0920164570456[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]89.942250300139[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]84.2851805274835[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.555492761347[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]95.8581666666667[/C][C]3.06169317041969[/C][C]31.3088743159481[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]95.8663333333333[/C][C]3.03588103893082[/C][C]31.5777634577854[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]95.8505833333333[/C][C]3.03288768457135[/C][C]31.6037365382623[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]95.7845833333333[/C][C]3.00392650348123[/C][C]31.8864603452611[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]95.7133333333333[/C][C]2.98486225942668[/C][C]32.0662479586972[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]95.5808333333333[/C][C]2.95854122341314[/C][C]32.3067438022939[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]95.5085[/C][C]2.93346747922670[/C][C]32.5582269707579[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]95.4118333333333[/C][C]2.89152087230036[/C][C]32.9971103606207[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]95.1973333333333[/C][C]2.85537630581431[/C][C]33.3396803564861[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]95.109[/C][C]2.82759055114597[/C][C]33.6360580783006[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]95.1355833333333[/C][C]2.80693640824684[/C][C]33.8930312257246[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]94.8625833333333[/C][C]2.76387281185472[/C][C]34.3223403502692[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]94.8214166666667[/C][C]2.73031854806197[/C][C]34.7290673221894[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]94.53675[/C][C]2.69218117853800[/C][C]35.1153000970532[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]94.503[/C][C]2.68440489834587[/C][C]35.2044507362629[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]94.5416666666667[/C][C]2.65328340887395[/C][C]35.6319518489696[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]94.6365833333333[/C][C]2.62687268000801[/C][C]36.0263304931265[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]94.6560833333333[/C][C]2.61358202177308[/C][C]36.2169935914686[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]94.664[/C][C]2.61006272234324[/C][C]36.2688602038702[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]94.7306666666667[/C][C]2.58375405646056[/C][C]36.6639643699047[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]94.8006666666667[/C][C]2.56831441724821[/C][C]36.9116281207656[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]94.7933333333333[/C][C]2.55060894122464[/C][C]37.1649811937927[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]94.66875[/C][C]2.49882782761835[/C][C]37.885263223689[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]94.76275[/C][C]2.48654108232634[/C][C]38.1102691902209[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]94.844[/C][C]2.47654440228125[/C][C]38.2969107731867[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]94.3348333333333[/C][C]2.41026090264398[/C][C]39.1388472633194[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]94.4450833333333[/C][C]2.32311410516141[/C][C]40.65451762507[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]94.50575[/C][C]2.31323216182224[/C][C]40.8544164134193[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]94.4646666666667[/C][C]2.30074708647627[/C][C]41.0582576511462[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]94.1496666666667[/C][C]2.22390023156675[/C][C]42.3353823747469[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]94.1625833333333[/C][C]2.19761051638691[/C][C]42.8477123817854[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]94.0585833333333[/C][C]2.1562455969048[/C][C]43.6214610563613[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]93.0438333333333[/C][C]2.02782670981341[/C][C]45.8835229278022[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]93.126[/C][C]1.98546452382059[/C][C]46.9038851526792[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]92.9364166666667[/C][C]1.95123174771091[/C][C]47.629614870553[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]92.6904166666666[/C][C]1.86755724077220[/C][C]49.6319013110092[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]92.4221666666667[/C][C]1.8156611106355[/C][C]50.9027627046095[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]92.1466666666667[/C][C]1.76548231534303[/C][C]52.1934804250717[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]92.9169166666667[/C][C]1.65033089711417[/C][C]56.3019918182134[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]92.9669166666667[/C][C]1.6284706905123[/C][C]57.0884801355683[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]95.6855084745763[/C][C]3.02197478300652[/C][C]31.6632385593172[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]95.5068965517241[/C][C]2.97785983998468[/C][C]32.0723276728214[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]95.3177192982456[/C][C]2.94364990905314[/C][C]32.3807933155018[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]95.1274107142857[/C][C]2.90662672271014[/C][C]32.7277699509997[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]94.9481818181818[/C][C]2.87433078313997[/C][C]33.0331437060485[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]94.7781481481481[/C][C]2.84307509837940[/C][C]33.3364912527893[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]94.6266981132076[/C][C]2.81391507588595[/C][C]33.6281286255288[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]94.4813461538461[/C][C]2.78606540111673[/C][C]33.9121063403521[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]94.3445098039216[/C][C]2.76221812914215[/C][C]34.1553437827959[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]94.2308[/C][C]2.74117460880543[/C][C]34.376066266375[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]94.1232653061224[/C][C]2.72137368382684[/C][C]34.5866743202150[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]94.0082291666667[/C][C]2.70151807548395[/C][C]34.7982973054238[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]93.917340425532[/C][C]2.68467391214273[/C][C]34.9827738857765[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]93.8266304347826[/C][C]2.66942730694988[/C][C]35.1485991735022[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]93.759[/C][C]2.65637700689239[/C][C]35.2958182354114[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]93.6913636363636[/C][C]2.64161069388380[/C][C]35.4675137609377[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]93.6172093023256[/C][C]2.6277065814662[/C][C]35.6269645791614[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]93.5315476190476[/C][C]2.61398601317077[/C][C]35.7811966658512[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]93.4401219512195[/C][C]2.59877241243015[/C][C]35.9554847913143[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]93.3435[/C][C]2.58060467904204[/C][C]36.1711736625427[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]93.2367948717949[/C][C]2.56171361393368[/C][C]36.3962600521233[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]93.1192105263158[/C][C]2.54054853700588[/C][C]36.6531909034337[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]92.9958108108108[/C][C]2.51699643384933[/C][C]36.9471364997483[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]92.8745833333333[/C][C]2.49485541037583[/C][C]37.2264392345457[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]92.7397142857143[/C][C]2.46912611401946[/C][C]37.5597316634201[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]92.5911764705882[/C][C]2.43881581651680[/C][C]37.9656289923648[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]92.4692424242424[/C][C]2.41087424113226[/C][C]38.3550667416043[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]92.33203125[/C][C]2.38762554913481[/C][C]38.6710685364619[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]92.1817741935484[/C][C]2.35952081427299[/C][C]39.0680063663482[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]92.0243333333333[/C][C]2.32598426243111[/C][C]39.563609616666[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]91.8777586206897[/C][C]2.29528034449757[/C][C]40.0289920318215[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]91.7198214285714[/C][C]2.26008503878441[/C][C]40.5824647544693[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]91.5574074074074[/C][C]2.22176410139222[/C][C]41.209328816698[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]91.4534615384615[/C][C]2.19415848089013[/C][C]41.6804266122839[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]91.3354[/C][C]2.16435743794404[/C][C]42.1997764319193[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]91.2210416666667[/C][C]2.13070261610130[/C][C]42.8126576544878[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]91.1145652173913[/C][C]2.10075895433174[/C][C]43.372213184913[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]91.0181818181818[/C][C]2.06960361415867[/C][C]43.9785576307966[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]90.9333333333333[/C][C]2.03647844192971[/C][C]44.6522445124279[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]90.78075[/C][C]2.01188460530521[/C][C]45.1222449640586[/C][/ROW]
[ROW][C]Median[/C][C]88.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]91.6047540983607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]92.0243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]91.6047540983607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]92.0243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]92.0243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]91.6047540983607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]92.0243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]92.1817741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74503&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 Mean95.82853.0820934413304931.0920164570456
Geometric Mean89.942250300139
Harmonic Mean84.2851805274835
Quadratic Mean101.555492761347
Winsorized Mean ( 1 / 40 )95.85816666666673.0616931704196931.3088743159481
Winsorized Mean ( 2 / 40 )95.86633333333333.0358810389308231.5777634577854
Winsorized Mean ( 3 / 40 )95.85058333333333.0328876845713531.6037365382623
Winsorized Mean ( 4 / 40 )95.78458333333333.0039265034812331.8864603452611
Winsorized Mean ( 5 / 40 )95.71333333333332.9848622594266832.0662479586972
Winsorized Mean ( 6 / 40 )95.58083333333332.9585412234131432.3067438022939
Winsorized Mean ( 7 / 40 )95.50852.9334674792267032.5582269707579
Winsorized Mean ( 8 / 40 )95.41183333333332.8915208723003632.9971103606207
Winsorized Mean ( 9 / 40 )95.19733333333332.8553763058143133.3396803564861
Winsorized Mean ( 10 / 40 )95.1092.8275905511459733.6360580783006
Winsorized Mean ( 11 / 40 )95.13558333333332.8069364082468433.8930312257246
Winsorized Mean ( 12 / 40 )94.86258333333332.7638728118547234.3223403502692
Winsorized Mean ( 13 / 40 )94.82141666666672.7303185480619734.7290673221894
Winsorized Mean ( 14 / 40 )94.536752.6921811785380035.1153000970532
Winsorized Mean ( 15 / 40 )94.5032.6844048983458735.2044507362629
Winsorized Mean ( 16 / 40 )94.54166666666672.6532834088739535.6319518489696
Winsorized Mean ( 17 / 40 )94.63658333333332.6268726800080136.0263304931265
Winsorized Mean ( 18 / 40 )94.65608333333332.6135820217730836.2169935914686
Winsorized Mean ( 19 / 40 )94.6642.6100627223432436.2688602038702
Winsorized Mean ( 20 / 40 )94.73066666666672.5837540564605636.6639643699047
Winsorized Mean ( 21 / 40 )94.80066666666672.5683144172482136.9116281207656
Winsorized Mean ( 22 / 40 )94.79333333333332.5506089412246437.1649811937927
Winsorized Mean ( 23 / 40 )94.668752.4988278276183537.885263223689
Winsorized Mean ( 24 / 40 )94.762752.4865410823263438.1102691902209
Winsorized Mean ( 25 / 40 )94.8442.4765444022812538.2969107731867
Winsorized Mean ( 26 / 40 )94.33483333333332.4102609026439839.1388472633194
Winsorized Mean ( 27 / 40 )94.44508333333332.3231141051614140.65451762507
Winsorized Mean ( 28 / 40 )94.505752.3132321618222440.8544164134193
Winsorized Mean ( 29 / 40 )94.46466666666672.3007470864762741.0582576511462
Winsorized Mean ( 30 / 40 )94.14966666666672.2239002315667542.3353823747469
Winsorized Mean ( 31 / 40 )94.16258333333332.1976105163869142.8477123817854
Winsorized Mean ( 32 / 40 )94.05858333333332.156245596904843.6214610563613
Winsorized Mean ( 33 / 40 )93.04383333333332.0278267098134145.8835229278022
Winsorized Mean ( 34 / 40 )93.1261.9854645238205946.9038851526792
Winsorized Mean ( 35 / 40 )92.93641666666671.9512317477109147.629614870553
Winsorized Mean ( 36 / 40 )92.69041666666661.8675572407722049.6319013110092
Winsorized Mean ( 37 / 40 )92.42216666666671.815661110635550.9027627046095
Winsorized Mean ( 38 / 40 )92.14666666666671.7654823153430352.1934804250717
Winsorized Mean ( 39 / 40 )92.91691666666671.6503308971141756.3019918182134
Winsorized Mean ( 40 / 40 )92.96691666666671.628470690512357.0884801355683
Trimmed Mean ( 1 / 40 )95.68550847457633.0219747830065231.6632385593172
Trimmed Mean ( 2 / 40 )95.50689655172412.9778598399846832.0723276728214
Trimmed Mean ( 3 / 40 )95.31771929824562.9436499090531432.3807933155018
Trimmed Mean ( 4 / 40 )95.12741071428572.9066267227101432.7277699509997
Trimmed Mean ( 5 / 40 )94.94818181818182.8743307831399733.0331437060485
Trimmed Mean ( 6 / 40 )94.77814814814812.8430750983794033.3364912527893
Trimmed Mean ( 7 / 40 )94.62669811320762.8139150758859533.6281286255288
Trimmed Mean ( 8 / 40 )94.48134615384612.7860654011167333.9121063403521
Trimmed Mean ( 9 / 40 )94.34450980392162.7622181291421534.1553437827959
Trimmed Mean ( 10 / 40 )94.23082.7411746088054334.376066266375
Trimmed Mean ( 11 / 40 )94.12326530612242.7213736838268434.5866743202150
Trimmed Mean ( 12 / 40 )94.00822916666672.7015180754839534.7982973054238
Trimmed Mean ( 13 / 40 )93.9173404255322.6846739121427334.9827738857765
Trimmed Mean ( 14 / 40 )93.82663043478262.6694273069498835.1485991735022
Trimmed Mean ( 15 / 40 )93.7592.6563770068923935.2958182354114
Trimmed Mean ( 16 / 40 )93.69136363636362.6416106938838035.4675137609377
Trimmed Mean ( 17 / 40 )93.61720930232562.627706581466235.6269645791614
Trimmed Mean ( 18 / 40 )93.53154761904762.6139860131707735.7811966658512
Trimmed Mean ( 19 / 40 )93.44012195121952.5987724124301535.9554847913143
Trimmed Mean ( 20 / 40 )93.34352.5806046790420436.1711736625427
Trimmed Mean ( 21 / 40 )93.23679487179492.5617136139336836.3962600521233
Trimmed Mean ( 22 / 40 )93.11921052631582.5405485370058836.6531909034337
Trimmed Mean ( 23 / 40 )92.99581081081082.5169964338493336.9471364997483
Trimmed Mean ( 24 / 40 )92.87458333333332.4948554103758337.2264392345457
Trimmed Mean ( 25 / 40 )92.73971428571432.4691261140194637.5597316634201
Trimmed Mean ( 26 / 40 )92.59117647058822.4388158165168037.9656289923648
Trimmed Mean ( 27 / 40 )92.46924242424242.4108742411322638.3550667416043
Trimmed Mean ( 28 / 40 )92.332031252.3876255491348138.6710685364619
Trimmed Mean ( 29 / 40 )92.18177419354842.3595208142729939.0680063663482
Trimmed Mean ( 30 / 40 )92.02433333333332.3259842624311139.563609616666
Trimmed Mean ( 31 / 40 )91.87775862068972.2952803444975740.0289920318215
Trimmed Mean ( 32 / 40 )91.71982142857142.2600850387844140.5824647544693
Trimmed Mean ( 33 / 40 )91.55740740740742.2217641013922241.209328816698
Trimmed Mean ( 34 / 40 )91.45346153846152.1941584808901341.6804266122839
Trimmed Mean ( 35 / 40 )91.33542.1643574379440442.1997764319193
Trimmed Mean ( 36 / 40 )91.22104166666672.1307026161013042.8126576544878
Trimmed Mean ( 37 / 40 )91.11456521739132.1007589543317443.372213184913
Trimmed Mean ( 38 / 40 )91.01818181818182.0696036141586743.9785576307966
Trimmed Mean ( 39 / 40 )90.93333333333332.0364784419297144.6522445124279
Trimmed Mean ( 40 / 40 )90.780752.0118846053052145.1222449640586
Median88.975
Midrange104.265
Midmean - Weighted Average at Xnp91.6047540983607
Midmean - Weighted Average at X(n+1)p92.0243333333333
Midmean - Empirical Distribution Function91.6047540983607
Midmean - Empirical Distribution Function - Averaging92.0243333333333
Midmean - Empirical Distribution Function - Interpolation92.0243333333333
Midmean - Closest Observation91.6047540983607
Midmean - True Basic - Statistics Graphics Toolkit92.0243333333333
Midmean - MS Excel (old versions)92.1817741935484
Number of observations120



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')