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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 14 Dec 2007 13:01:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/14/t1197661639r9oyk5a8tupa3yi.htm/, Retrieved Thu, 02 May 2024 22:28:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3957, Retrieved Thu, 02 May 2024 22:28:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-14 20:01:45] [ba3202e2798d2e4685d19d988e9c69df] [Current]
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Dataseries X:
85.6
89
97.5
104
99.4
103.2
103
91.2
85.9
80.7
86.7
80.7
81.5
83.4
83.5
89.5
85.8
77.4
67.5
63.7
59.4
62
62.4
58.1
58
56.3
61.4
59.8
54.3
47
50.5
48.1
58.8
70.4
71.9
73.3
83.5
90.1
101.3
98.3
106.7
109.9
111.1
119
120.7
104.5
121.6
129.6
124.5
130.1
142.3
140
143.3
113.4
113.8
120.7
112.9
115.5
121.9
119.3
111
114.2
113.5
94
83.2
82.8
85.8
88.7
105.3
113.1
113.8
109.4
113.9




Summary of compuational 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 compuational 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=3957&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3957&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 compuational 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 Mean93.33698630136992.8706934570037532.5137419579411
Geometric Mean89.9201005053115
Harmonic Mean86.3021613941341
Quadratic Mean96.4631351260997
Winsorized Mean ( 1 / 24 )93.33835616438362.864069540149232.5894168615477
Winsorized Mean ( 2 / 24 )93.3410958904112.8352725271046732.9213840990902
Winsorized Mean ( 3 / 24 )93.09041095890412.7182588860008434.2463374030796
Winsorized Mean ( 4 / 24 )93.1726027397262.6918066253347834.6134086538025
Winsorized Mean ( 5 / 24 )92.93972602739732.6076501284222135.6411793953476
Winsorized Mean ( 6 / 24 )92.73424657534252.5713148174285436.0649135402572
Winsorized Mean ( 7 / 24 )92.7726027397262.5543157887550436.3199425647143
Winsorized Mean ( 8 / 24 )92.73972602739732.5269082634446136.7008677635876
Winsorized Mean ( 9 / 24 )92.78904109589042.5179028395574436.8517162926745
Winsorized Mean ( 10 / 24 )92.81643835616442.4492629383172837.8956611411972
Winsorized Mean ( 11 / 24 )92.86164383561642.4264474019506338.2706189142878
Winsorized Mean ( 12 / 24 )92.35205479452052.3320096617216639.6019177409151
Winsorized Mean ( 13 / 24 )92.35205479452062.2594593223118840.8735195551235
Winsorized Mean ( 14 / 24 )93.02328767123292.1266559673117543.7415779049684
Winsorized Mean ( 15 / 24 )93.59863013698632.0267479754465646.1816818227552
Winsorized Mean ( 16 / 24 )93.9273972602741.9751445049286847.5546963910195
Winsorized Mean ( 17 / 24 )94.18356164383561.9154274470178549.1710410595145
Winsorized Mean ( 18 / 24 )95.16986301369861.7644453651124853.9375516496265
Winsorized Mean ( 19 / 24 )95.95068493150681.6373728392278558.6003887646966
Winsorized Mean ( 20 / 24 )95.89589041095891.6294164178769358.8529054690068
Winsorized Mean ( 21 / 24 )95.60821917808221.5256567234109262.666927435898
Winsorized Mean ( 22 / 24 )95.96986301369861.4718770113611665.2023656004707
Winsorized Mean ( 23 / 24 )95.74931506849321.4074588261706268.0299226436384
Winsorized Mean ( 24 / 24 )95.65068493150691.3764422673697969.4912436206156
Trimmed Mean ( 1 / 24 )93.28591549295772.7894045691150333.4429492680418
Trimmed Mean ( 2 / 24 )93.23043478260872.7008455184805834.5189808690197
Trimmed Mean ( 3 / 24 )93.17014925373132.6138733429763735.6444773822286
Trimmed Mean ( 4 / 24 )93.22.5635115264328036.3563803162182
Trimmed Mean ( 5 / 24 )93.20793650793652.5121948363915437.1021925360766
Trimmed Mean ( 6 / 24 )93.2721311475412.4756851799241137.6752795161137
Trimmed Mean ( 7 / 24 )93.38305084745762.4400972383667138.2702170139597
Trimmed Mean ( 8 / 24 )93.49473684210532.3997407716264838.9603485291192
Trimmed Mean ( 9 / 24 )93.622.3554870392169839.7454957048379
Trimmed Mean ( 10 / 24 )93.74716981132082.3016788908945240.7299081475639
Trimmed Mean ( 11 / 24 )93.88039215686272.2492125325393641.7392268621552
Trimmed Mean ( 12 / 24 )94.01836734693882.1872440053696442.9848554235951
Trimmed Mean ( 13 / 24 )94.23404255319152.1278173392018044.2867161654681
Trimmed Mean ( 14 / 24 )94.46888888888892.0664756075473345.7149789447613
Trimmed Mean ( 15 / 24 )94.64418604651162.0172327962371246.9178303183737
Trimmed Mean ( 16 / 24 )94.76829268292681.9744818370113447.9965380823011
Trimmed Mean ( 17 / 24 )94.86666666666671.9278704988584949.2080078629961
Trimmed Mean ( 18 / 24 )94.9459459459461.8775526951438650.5689913212642
Trimmed Mean ( 19 / 24 )94.921.8441677314845151.4703724501195
Trimmed Mean ( 20 / 24 )94.81.8241695910659551.9688522735455
Trimmed Mean ( 21 / 24 )94.67096774193551.7921585084250152.8251085475327
Trimmed Mean ( 22 / 24 )94.55862068965521.7697688282520753.4299277850018
Trimmed Mean ( 23 / 24 )94.38518518518521.7434672833743454.1364819892178
Trimmed Mean ( 24 / 24 )94.2121.7162392995539254.8944427647632
Median91.2
Midrange95.15
Midmean - Weighted Average at Xnp94.4333333333333
Midmean - Weighted Average at X(n+1)p94.945945945946
Midmean - Empirical Distribution Function94.945945945946
Midmean - Empirical Distribution Function - Averaging94.945945945946
Midmean - Empirical Distribution Function - Interpolation94.945945945946
Midmean - Closest Observation94.3763157894737
Midmean - True Basic - Statistics Graphics Toolkit94.945945945946
Midmean - MS Excel (old versions)94.945945945946
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.3369863013699 & 2.87069345700375 & 32.5137419579411 \tabularnewline
Geometric Mean & 89.9201005053115 &  &  \tabularnewline
Harmonic Mean & 86.3021613941341 &  &  \tabularnewline
Quadratic Mean & 96.4631351260997 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 93.3383561643836 & 2.8640695401492 & 32.5894168615477 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 93.341095890411 & 2.83527252710467 & 32.9213840990902 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 93.0904109589041 & 2.71825888600084 & 34.2463374030796 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 93.172602739726 & 2.69180662533478 & 34.6134086538025 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 92.9397260273973 & 2.60765012842221 & 35.6411793953476 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 92.7342465753425 & 2.57131481742854 & 36.0649135402572 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 92.772602739726 & 2.55431578875504 & 36.3199425647143 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 92.7397260273973 & 2.52690826344461 & 36.7008677635876 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 92.7890410958904 & 2.51790283955744 & 36.8517162926745 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 92.8164383561644 & 2.44926293831728 & 37.8956611411972 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 92.8616438356164 & 2.42644740195063 & 38.2706189142878 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 92.3520547945205 & 2.33200966172166 & 39.6019177409151 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 92.3520547945206 & 2.25945932231188 & 40.8735195551235 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.0232876712329 & 2.12665596731175 & 43.7415779049684 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.5986301369863 & 2.02674797544656 & 46.1816818227552 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 93.927397260274 & 1.97514450492868 & 47.5546963910195 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 94.1835616438356 & 1.91542744701785 & 49.1710410595145 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 95.1698630136986 & 1.76444536511248 & 53.9375516496265 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 95.9506849315068 & 1.63737283922785 & 58.6003887646966 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 95.8958904109589 & 1.62941641787693 & 58.8529054690068 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 95.6082191780822 & 1.52565672341092 & 62.666927435898 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 95.9698630136986 & 1.47187701136116 & 65.2023656004707 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 95.7493150684932 & 1.40745882617062 & 68.0299226436384 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 95.6506849315069 & 1.37644226736979 & 69.4912436206156 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.2859154929577 & 2.78940456911503 & 33.4429492680418 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.2304347826087 & 2.70084551848058 & 34.5189808690197 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.1701492537313 & 2.61387334297637 & 35.6444773822286 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.2 & 2.56351152643280 & 36.3563803162182 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.2079365079365 & 2.51219483639154 & 37.1021925360766 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.272131147541 & 2.47568517992411 & 37.6752795161137 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.3830508474576 & 2.44009723836671 & 38.2702170139597 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.4947368421053 & 2.39974077162648 & 38.9603485291192 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.62 & 2.35548703921698 & 39.7454957048379 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.7471698113208 & 2.30167889089452 & 40.7299081475639 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.8803921568627 & 2.24921253253936 & 41.7392268621552 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 94.0183673469388 & 2.18724400536964 & 42.9848554235951 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 94.2340425531915 & 2.12781733920180 & 44.2867161654681 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 94.4688888888889 & 2.06647560754733 & 45.7149789447613 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 94.6441860465116 & 2.01723279623712 & 46.9178303183737 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 94.7682926829268 & 1.97448183701134 & 47.9965380823011 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 94.8666666666667 & 1.92787049885849 & 49.2080078629961 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 94.945945945946 & 1.87755269514386 & 50.5689913212642 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 94.92 & 1.84416773148451 & 51.4703724501195 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 94.8 & 1.82416959106595 & 51.9688522735455 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 94.6709677419355 & 1.79215850842501 & 52.8251085475327 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 94.5586206896552 & 1.76976882825207 & 53.4299277850018 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 94.3851851851852 & 1.74346728337434 & 54.1364819892178 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 94.212 & 1.71623929955392 & 54.8944427647632 \tabularnewline
Median & 91.2 &  &  \tabularnewline
Midrange & 95.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 94.4333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 94.945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 94.945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 94.945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 94.945945945946 &  &  \tabularnewline
Midmean - Closest Observation & 94.3763157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 94.945945945946 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 94.945945945946 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3957&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]93.3369863013699[/C][C]2.87069345700375[/C][C]32.5137419579411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]89.9201005053115[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.3021613941341[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.4631351260997[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]93.3383561643836[/C][C]2.8640695401492[/C][C]32.5894168615477[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]93.341095890411[/C][C]2.83527252710467[/C][C]32.9213840990902[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]93.0904109589041[/C][C]2.71825888600084[/C][C]34.2463374030796[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]93.172602739726[/C][C]2.69180662533478[/C][C]34.6134086538025[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]92.9397260273973[/C][C]2.60765012842221[/C][C]35.6411793953476[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]92.7342465753425[/C][C]2.57131481742854[/C][C]36.0649135402572[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]92.772602739726[/C][C]2.55431578875504[/C][C]36.3199425647143[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]92.7397260273973[/C][C]2.52690826344461[/C][C]36.7008677635876[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]92.7890410958904[/C][C]2.51790283955744[/C][C]36.8517162926745[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]92.8164383561644[/C][C]2.44926293831728[/C][C]37.8956611411972[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]92.8616438356164[/C][C]2.42644740195063[/C][C]38.2706189142878[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]92.3520547945205[/C][C]2.33200966172166[/C][C]39.6019177409151[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]92.3520547945206[/C][C]2.25945932231188[/C][C]40.8735195551235[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.0232876712329[/C][C]2.12665596731175[/C][C]43.7415779049684[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.5986301369863[/C][C]2.02674797544656[/C][C]46.1816818227552[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]93.927397260274[/C][C]1.97514450492868[/C][C]47.5546963910195[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]94.1835616438356[/C][C]1.91542744701785[/C][C]49.1710410595145[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]95.1698630136986[/C][C]1.76444536511248[/C][C]53.9375516496265[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]95.9506849315068[/C][C]1.63737283922785[/C][C]58.6003887646966[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]95.8958904109589[/C][C]1.62941641787693[/C][C]58.8529054690068[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]95.6082191780822[/C][C]1.52565672341092[/C][C]62.666927435898[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]95.9698630136986[/C][C]1.47187701136116[/C][C]65.2023656004707[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]95.7493150684932[/C][C]1.40745882617062[/C][C]68.0299226436384[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]95.6506849315069[/C][C]1.37644226736979[/C][C]69.4912436206156[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.2859154929577[/C][C]2.78940456911503[/C][C]33.4429492680418[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.2304347826087[/C][C]2.70084551848058[/C][C]34.5189808690197[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.1701492537313[/C][C]2.61387334297637[/C][C]35.6444773822286[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.2[/C][C]2.56351152643280[/C][C]36.3563803162182[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.2079365079365[/C][C]2.51219483639154[/C][C]37.1021925360766[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.272131147541[/C][C]2.47568517992411[/C][C]37.6752795161137[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.3830508474576[/C][C]2.44009723836671[/C][C]38.2702170139597[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.4947368421053[/C][C]2.39974077162648[/C][C]38.9603485291192[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.62[/C][C]2.35548703921698[/C][C]39.7454957048379[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.7471698113208[/C][C]2.30167889089452[/C][C]40.7299081475639[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.8803921568627[/C][C]2.24921253253936[/C][C]41.7392268621552[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]94.0183673469388[/C][C]2.18724400536964[/C][C]42.9848554235951[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]94.2340425531915[/C][C]2.12781733920180[/C][C]44.2867161654681[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]94.4688888888889[/C][C]2.06647560754733[/C][C]45.7149789447613[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]94.6441860465116[/C][C]2.01723279623712[/C][C]46.9178303183737[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]94.7682926829268[/C][C]1.97448183701134[/C][C]47.9965380823011[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]94.8666666666667[/C][C]1.92787049885849[/C][C]49.2080078629961[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]94.945945945946[/C][C]1.87755269514386[/C][C]50.5689913212642[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]94.92[/C][C]1.84416773148451[/C][C]51.4703724501195[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]94.8[/C][C]1.82416959106595[/C][C]51.9688522735455[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]94.6709677419355[/C][C]1.79215850842501[/C][C]52.8251085475327[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]94.5586206896552[/C][C]1.76976882825207[/C][C]53.4299277850018[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]94.3851851851852[/C][C]1.74346728337434[/C][C]54.1364819892178[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]94.212[/C][C]1.71623929955392[/C][C]54.8944427647632[/C][/ROW]
[ROW][C]Median[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]94.4333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]94.3763157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]94.945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3957&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 Mean93.33698630136992.8706934570037532.5137419579411
Geometric Mean89.9201005053115
Harmonic Mean86.3021613941341
Quadratic Mean96.4631351260997
Winsorized Mean ( 1 / 24 )93.33835616438362.864069540149232.5894168615477
Winsorized Mean ( 2 / 24 )93.3410958904112.8352725271046732.9213840990902
Winsorized Mean ( 3 / 24 )93.09041095890412.7182588860008434.2463374030796
Winsorized Mean ( 4 / 24 )93.1726027397262.6918066253347834.6134086538025
Winsorized Mean ( 5 / 24 )92.93972602739732.6076501284222135.6411793953476
Winsorized Mean ( 6 / 24 )92.73424657534252.5713148174285436.0649135402572
Winsorized Mean ( 7 / 24 )92.7726027397262.5543157887550436.3199425647143
Winsorized Mean ( 8 / 24 )92.73972602739732.5269082634446136.7008677635876
Winsorized Mean ( 9 / 24 )92.78904109589042.5179028395574436.8517162926745
Winsorized Mean ( 10 / 24 )92.81643835616442.4492629383172837.8956611411972
Winsorized Mean ( 11 / 24 )92.86164383561642.4264474019506338.2706189142878
Winsorized Mean ( 12 / 24 )92.35205479452052.3320096617216639.6019177409151
Winsorized Mean ( 13 / 24 )92.35205479452062.2594593223118840.8735195551235
Winsorized Mean ( 14 / 24 )93.02328767123292.1266559673117543.7415779049684
Winsorized Mean ( 15 / 24 )93.59863013698632.0267479754465646.1816818227552
Winsorized Mean ( 16 / 24 )93.9273972602741.9751445049286847.5546963910195
Winsorized Mean ( 17 / 24 )94.18356164383561.9154274470178549.1710410595145
Winsorized Mean ( 18 / 24 )95.16986301369861.7644453651124853.9375516496265
Winsorized Mean ( 19 / 24 )95.95068493150681.6373728392278558.6003887646966
Winsorized Mean ( 20 / 24 )95.89589041095891.6294164178769358.8529054690068
Winsorized Mean ( 21 / 24 )95.60821917808221.5256567234109262.666927435898
Winsorized Mean ( 22 / 24 )95.96986301369861.4718770113611665.2023656004707
Winsorized Mean ( 23 / 24 )95.74931506849321.4074588261706268.0299226436384
Winsorized Mean ( 24 / 24 )95.65068493150691.3764422673697969.4912436206156
Trimmed Mean ( 1 / 24 )93.28591549295772.7894045691150333.4429492680418
Trimmed Mean ( 2 / 24 )93.23043478260872.7008455184805834.5189808690197
Trimmed Mean ( 3 / 24 )93.17014925373132.6138733429763735.6444773822286
Trimmed Mean ( 4 / 24 )93.22.5635115264328036.3563803162182
Trimmed Mean ( 5 / 24 )93.20793650793652.5121948363915437.1021925360766
Trimmed Mean ( 6 / 24 )93.2721311475412.4756851799241137.6752795161137
Trimmed Mean ( 7 / 24 )93.38305084745762.4400972383667138.2702170139597
Trimmed Mean ( 8 / 24 )93.49473684210532.3997407716264838.9603485291192
Trimmed Mean ( 9 / 24 )93.622.3554870392169839.7454957048379
Trimmed Mean ( 10 / 24 )93.74716981132082.3016788908945240.7299081475639
Trimmed Mean ( 11 / 24 )93.88039215686272.2492125325393641.7392268621552
Trimmed Mean ( 12 / 24 )94.01836734693882.1872440053696442.9848554235951
Trimmed Mean ( 13 / 24 )94.23404255319152.1278173392018044.2867161654681
Trimmed Mean ( 14 / 24 )94.46888888888892.0664756075473345.7149789447613
Trimmed Mean ( 15 / 24 )94.64418604651162.0172327962371246.9178303183737
Trimmed Mean ( 16 / 24 )94.76829268292681.9744818370113447.9965380823011
Trimmed Mean ( 17 / 24 )94.86666666666671.9278704988584949.2080078629961
Trimmed Mean ( 18 / 24 )94.9459459459461.8775526951438650.5689913212642
Trimmed Mean ( 19 / 24 )94.921.8441677314845151.4703724501195
Trimmed Mean ( 20 / 24 )94.81.8241695910659551.9688522735455
Trimmed Mean ( 21 / 24 )94.67096774193551.7921585084250152.8251085475327
Trimmed Mean ( 22 / 24 )94.55862068965521.7697688282520753.4299277850018
Trimmed Mean ( 23 / 24 )94.38518518518521.7434672833743454.1364819892178
Trimmed Mean ( 24 / 24 )94.2121.7162392995539254.8944427647632
Median91.2
Midrange95.15
Midmean - Weighted Average at Xnp94.4333333333333
Midmean - Weighted Average at X(n+1)p94.945945945946
Midmean - Empirical Distribution Function94.945945945946
Midmean - Empirical Distribution Function - Averaging94.945945945946
Midmean - Empirical Distribution Function - Interpolation94.945945945946
Midmean - Closest Observation94.3763157894737
Midmean - True Basic - Statistics Graphics Toolkit94.945945945946
Midmean - MS Excel (old versions)94.945945945946
Number of observations73



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