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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 12:48:53 -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/t1197660896t474vp4yy50ieii.htm/, Retrieved Thu, 02 May 2024 21:51:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3951, Retrieved Thu, 02 May 2024 21:51:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-14 19:48:53] [ba3202e2798d2e4685d19d988e9c69df] [Current]
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Dataseries X:
92.80902569
59.03937784
72.80793034
91.80951859
68.07327893
49.15931869
124.6070431
109.8882743
110.5126239
114.7735363
92.36540884
103.6256093
90.43485404
65.85793307
83.326031
94.49312668
68.97694288
55.46032094
132.8851525
121.7098417
127.0058601
134.0434854
106.4762583
117.5529876
101.6129032
82.66060573
89.27652117
109.2392793
88.15926392
59.22832576
164.2149077
125.1273345
152.6808697
132.9590887
112.415795
136.4313489
107.319678
87.61158881
97.85585191
106.6049619
92.1682458
65.30751958
161.4874856
162.2460157
175.1328112
147.2835314
144.4766964
122.6655348
102.2728517
88.64121803
89.59143436
112.2022017
91.98477463
57.84544608
160.4907169
128.3339723
140.6922614
126.6087957
129.2677584
124.2729613
112.8950107
92.54340325
85.69746426
116.7232598
92.0778794
58.97913358
154.5018895
145.5501397
146.6016759
143.5127882
113.5166219
104.8003724
96.68108878




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=3951&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=3951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3951&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 Mean108.6047263641103.4997390428990231.0322355560963
Geometric Mean104.293337769075
Harmonic Mean99.722581309224
Quadratic Mean112.591540850755
Winsorized Mean ( 1 / 24 )108.5414811415073.4437528851761531.5183710215476
Winsorized Mean ( 2 / 24 )108.5528847891783.4180842722547231.7583991917120
Winsorized Mean ( 3 / 24 )108.5683022165753.4017998276540931.9149590560844
Winsorized Mean ( 4 / 24 )108.5169858089043.3894145247165532.0164397177059
Winsorized Mean ( 5 / 24 )108.1197337897263.3030444750266732.7333569399949
Winsorized Mean ( 6 / 24 )108.4697206954793.1753664662578234.1597487559637
Winsorized Mean ( 7 / 24 )108.0049470835623.0692462656024135.1894040872485
Winsorized Mean ( 8 / 24 )108.1730008216443.0103649044507535.9335177810878
Winsorized Mean ( 9 / 24 )108.1547699963012.9670015576706536.4525491119770
Winsorized Mean ( 10 / 24 )108.5325157716442.8473439466356238.1171076644549
Winsorized Mean ( 11 / 24 )109.8719190468492.5824883526022542.544981446339
Winsorized Mean ( 12 / 24 )109.5176557816442.4840956844535944.0875351408751
Winsorized Mean ( 13 / 24 )109.1811731772602.2942620845649747.5887972484899
Winsorized Mean ( 14 / 24 )109.0903191320552.1684936857383750.3069572438758
Winsorized Mean ( 15 / 24 )108.9800338738362.1177389552261951.4605606157892
Winsorized Mean ( 16 / 24 )109.0694624568492.1008434284845351.9169877098018
Winsorized Mean ( 17 / 24 )108.3750029182191.9517247741436555.5278102496652
Winsorized Mean ( 18 / 24 )108.2224041184931.9072000132538256.744129281888
Winsorized Mean ( 19 / 24 )108.0962512708221.8274077723367559.1527807351922
Winsorized Mean ( 20 / 24 )108.3640869283561.7619036607775161.5039796673878
Winsorized Mean ( 21 / 24 )107.9883292795891.6947175266719063.7205478671466
Winsorized Mean ( 22 / 24 )107.8595881034251.6690965448418364.6215393811422
Winsorized Mean ( 23 / 24 )107.7828010595891.6507201599471565.2944112968486
Winsorized Mean ( 24 / 24 )107.3191527987671.5696118717299368.3730511546694
Trimmed Mean ( 1 / 24 )108.5049703477463.369168712114532.2052647460472
Trimmed Mean ( 2 / 24 )108.4663429862323.2806530450937733.0624243086125
Trimmed Mean ( 3 / 24 )108.4191970786573.1915919435581833.9702565352964
Trimmed Mean ( 4 / 24 )108.3633782321543.0924408552074235.0413745341899
Trimmed Mean ( 5 / 24 )108.3188807992062.9776703991812836.3770553077295
Trimmed Mean ( 6 / 24 )108.3665454932792.8672705350773337.7943218707669
Trimmed Mean ( 7 / 24 )108.3452692510172.7708021900879139.1024915595217
Trimmed Mean ( 8 / 24 )108.4075337077192.6814064858380340.4293546242535
Trimmed Mean ( 9 / 24 )108.4464448456362.5861950893226941.9328167829899
Trimmed Mean ( 10 / 24 )108.4910827156602.4784947037981343.7729733896163
Trimmed Mean ( 11 / 24 )108.4851521017652.3731899651762245.7127974134634
Trimmed Mean ( 12 / 24 )108.2973339440822.3022197090099147.0403991071105
Trimmed Mean ( 13 / 24 )108.1393844863832.2341990362512648.4018579955297
Trimmed Mean ( 14 / 24 )108.0093835044442.1889416364595249.3431993368005
Trimmed Mean ( 15 / 24 )107.8783065927912.1556948177850050.0434039655191
Trimmed Mean ( 16 / 24 )107.7475324602442.1204479126437250.8135718957166
Trimmed Mean ( 17 / 24 )107.5928835984622.0742048876545451.8718687044099
Trimmed Mean ( 18 / 24 )107.5021129937842.0449991782114552.5682915373125
Trimmed Mean ( 19 / 24 )107.4186506888572.0116154809169053.3991966694826
Trimmed Mean ( 20 / 24 )107.3397593930301.9807637261759354.1910970877181
Trimmed Mean ( 21 / 24 )107.2191530864521.9483110065035555.0318469323168
Trimmed Mean ( 22 / 24 )107.1269529844831.9148003729434755.9467997281645
Trimmed Mean ( 23 / 24 )107.0369153351851.8662235627118257.3548193656119
Trimmed Mean ( 24 / 24 )106.9422202781.7918966013196159.6810218844347
Median107.319678
Midrange112.146064945
Midmean - Weighted Average at Xnp106.923450235278
Midmean - Weighted Average at X(n+1)p107.502112993784
Midmean - Empirical Distribution Function107.502112993784
Midmean - Empirical Distribution Function - Averaging107.502112993784
Midmean - Empirical Distribution Function - Interpolation107.502112993784
Midmean - Closest Observation107.022492156316
Midmean - True Basic - Statistics Graphics Toolkit107.502112993784
Midmean - MS Excel (old versions)107.502112993784
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.604726364110 & 3.49973904289902 & 31.0322355560963 \tabularnewline
Geometric Mean & 104.293337769075 &  &  \tabularnewline
Harmonic Mean & 99.722581309224 &  &  \tabularnewline
Quadratic Mean & 112.591540850755 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.541481141507 & 3.44375288517615 & 31.5183710215476 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.552884789178 & 3.41808427225472 & 31.7583991917120 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.568302216575 & 3.40179982765409 & 31.9149590560844 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.516985808904 & 3.38941452471655 & 32.0164397177059 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.119733789726 & 3.30304447502667 & 32.7333569399949 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.469720695479 & 3.17536646625782 & 34.1597487559637 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.004947083562 & 3.06924626560241 & 35.1894040872485 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.173000821644 & 3.01036490445075 & 35.9335177810878 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.154769996301 & 2.96700155767065 & 36.4525491119770 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.532515771644 & 2.84734394663562 & 38.1171076644549 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 109.871919046849 & 2.58248835260225 & 42.544981446339 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 109.517655781644 & 2.48409568445359 & 44.0875351408751 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 109.181173177260 & 2.29426208456497 & 47.5887972484899 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 109.090319132055 & 2.16849368573837 & 50.3069572438758 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.980033873836 & 2.11773895522619 & 51.4605606157892 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 109.069462456849 & 2.10084342848453 & 51.9169877098018 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.375002918219 & 1.95172477414365 & 55.5278102496652 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.222404118493 & 1.90720001325382 & 56.744129281888 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.096251270822 & 1.82740777233675 & 59.1527807351922 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.364086928356 & 1.76190366077751 & 61.5039796673878 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 107.988329279589 & 1.69471752667190 & 63.7205478671466 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 107.859588103425 & 1.66909654484183 & 64.6215393811422 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 107.782801059589 & 1.65072015994715 & 65.2944112968486 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 107.319152798767 & 1.56961187172993 & 68.3730511546694 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.504970347746 & 3.3691687121145 & 32.2052647460472 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.466342986232 & 3.28065304509377 & 33.0624243086125 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.419197078657 & 3.19159194355818 & 33.9702565352964 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.363378232154 & 3.09244085520742 & 35.0413745341899 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.318880799206 & 2.97767039918128 & 36.3770553077295 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.366545493279 & 2.86727053507733 & 37.7943218707669 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.345269251017 & 2.77080219008791 & 39.1024915595217 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.407533707719 & 2.68140648583803 & 40.4293546242535 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.446444845636 & 2.58619508932269 & 41.9328167829899 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.491082715660 & 2.47849470379813 & 43.7729733896163 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.485152101765 & 2.37318996517622 & 45.7127974134634 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.297333944082 & 2.30221970900991 & 47.0403991071105 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.139384486383 & 2.23419903625126 & 48.4018579955297 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.009383504444 & 2.18894163645952 & 49.3431993368005 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 107.878306592791 & 2.15569481778500 & 50.0434039655191 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 107.747532460244 & 2.12044791264372 & 50.8135718957166 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 107.592883598462 & 2.07420488765454 & 51.8718687044099 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 107.502112993784 & 2.04499917821145 & 52.5682915373125 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 107.418650688857 & 2.01161548091690 & 53.3991966694826 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 107.339759393030 & 1.98076372617593 & 54.1910970877181 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 107.219153086452 & 1.94831100650355 & 55.0318469323168 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 107.126952984483 & 1.91480037294347 & 55.9467997281645 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 107.036915335185 & 1.86622356271182 & 57.3548193656119 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 106.942220278 & 1.79189660131961 & 59.6810218844347 \tabularnewline
Median & 107.319678 &  &  \tabularnewline
Midrange & 112.146064945 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.923450235278 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.502112993784 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.502112993784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.502112993784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.502112993784 &  &  \tabularnewline
Midmean - Closest Observation & 107.022492156316 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.502112993784 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.502112993784 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3951&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]108.604726364110[/C][C]3.49973904289902[/C][C]31.0322355560963[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.293337769075[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.722581309224[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.591540850755[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.541481141507[/C][C]3.44375288517615[/C][C]31.5183710215476[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.552884789178[/C][C]3.41808427225472[/C][C]31.7583991917120[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.568302216575[/C][C]3.40179982765409[/C][C]31.9149590560844[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.516985808904[/C][C]3.38941452471655[/C][C]32.0164397177059[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.119733789726[/C][C]3.30304447502667[/C][C]32.7333569399949[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.469720695479[/C][C]3.17536646625782[/C][C]34.1597487559637[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.004947083562[/C][C]3.06924626560241[/C][C]35.1894040872485[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.173000821644[/C][C]3.01036490445075[/C][C]35.9335177810878[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.154769996301[/C][C]2.96700155767065[/C][C]36.4525491119770[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.532515771644[/C][C]2.84734394663562[/C][C]38.1171076644549[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]109.871919046849[/C][C]2.58248835260225[/C][C]42.544981446339[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]109.517655781644[/C][C]2.48409568445359[/C][C]44.0875351408751[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]109.181173177260[/C][C]2.29426208456497[/C][C]47.5887972484899[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]109.090319132055[/C][C]2.16849368573837[/C][C]50.3069572438758[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.980033873836[/C][C]2.11773895522619[/C][C]51.4605606157892[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]109.069462456849[/C][C]2.10084342848453[/C][C]51.9169877098018[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.375002918219[/C][C]1.95172477414365[/C][C]55.5278102496652[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.222404118493[/C][C]1.90720001325382[/C][C]56.744129281888[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.096251270822[/C][C]1.82740777233675[/C][C]59.1527807351922[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.364086928356[/C][C]1.76190366077751[/C][C]61.5039796673878[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]107.988329279589[/C][C]1.69471752667190[/C][C]63.7205478671466[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]107.859588103425[/C][C]1.66909654484183[/C][C]64.6215393811422[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]107.782801059589[/C][C]1.65072015994715[/C][C]65.2944112968486[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]107.319152798767[/C][C]1.56961187172993[/C][C]68.3730511546694[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.504970347746[/C][C]3.3691687121145[/C][C]32.2052647460472[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.466342986232[/C][C]3.28065304509377[/C][C]33.0624243086125[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.419197078657[/C][C]3.19159194355818[/C][C]33.9702565352964[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.363378232154[/C][C]3.09244085520742[/C][C]35.0413745341899[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.318880799206[/C][C]2.97767039918128[/C][C]36.3770553077295[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.366545493279[/C][C]2.86727053507733[/C][C]37.7943218707669[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.345269251017[/C][C]2.77080219008791[/C][C]39.1024915595217[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.407533707719[/C][C]2.68140648583803[/C][C]40.4293546242535[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.446444845636[/C][C]2.58619508932269[/C][C]41.9328167829899[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.491082715660[/C][C]2.47849470379813[/C][C]43.7729733896163[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.485152101765[/C][C]2.37318996517622[/C][C]45.7127974134634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.297333944082[/C][C]2.30221970900991[/C][C]47.0403991071105[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.139384486383[/C][C]2.23419903625126[/C][C]48.4018579955297[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.009383504444[/C][C]2.18894163645952[/C][C]49.3431993368005[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]107.878306592791[/C][C]2.15569481778500[/C][C]50.0434039655191[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]107.747532460244[/C][C]2.12044791264372[/C][C]50.8135718957166[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]107.592883598462[/C][C]2.07420488765454[/C][C]51.8718687044099[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]107.502112993784[/C][C]2.04499917821145[/C][C]52.5682915373125[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]107.418650688857[/C][C]2.01161548091690[/C][C]53.3991966694826[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]107.339759393030[/C][C]1.98076372617593[/C][C]54.1910970877181[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]107.219153086452[/C][C]1.94831100650355[/C][C]55.0318469323168[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]107.126952984483[/C][C]1.91480037294347[/C][C]55.9467997281645[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]107.036915335185[/C][C]1.86622356271182[/C][C]57.3548193656119[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]106.942220278[/C][C]1.79189660131961[/C][C]59.6810218844347[/C][/ROW]
[ROW][C]Median[/C][C]107.319678[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.146064945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.923450235278[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.502112993784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.502112993784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.502112993784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.502112993784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.022492156316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.502112993784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.502112993784[/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=3951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3951&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 Mean108.6047263641103.4997390428990231.0322355560963
Geometric Mean104.293337769075
Harmonic Mean99.722581309224
Quadratic Mean112.591540850755
Winsorized Mean ( 1 / 24 )108.5414811415073.4437528851761531.5183710215476
Winsorized Mean ( 2 / 24 )108.5528847891783.4180842722547231.7583991917120
Winsorized Mean ( 3 / 24 )108.5683022165753.4017998276540931.9149590560844
Winsorized Mean ( 4 / 24 )108.5169858089043.3894145247165532.0164397177059
Winsorized Mean ( 5 / 24 )108.1197337897263.3030444750266732.7333569399949
Winsorized Mean ( 6 / 24 )108.4697206954793.1753664662578234.1597487559637
Winsorized Mean ( 7 / 24 )108.0049470835623.0692462656024135.1894040872485
Winsorized Mean ( 8 / 24 )108.1730008216443.0103649044507535.9335177810878
Winsorized Mean ( 9 / 24 )108.1547699963012.9670015576706536.4525491119770
Winsorized Mean ( 10 / 24 )108.5325157716442.8473439466356238.1171076644549
Winsorized Mean ( 11 / 24 )109.8719190468492.5824883526022542.544981446339
Winsorized Mean ( 12 / 24 )109.5176557816442.4840956844535944.0875351408751
Winsorized Mean ( 13 / 24 )109.1811731772602.2942620845649747.5887972484899
Winsorized Mean ( 14 / 24 )109.0903191320552.1684936857383750.3069572438758
Winsorized Mean ( 15 / 24 )108.9800338738362.1177389552261951.4605606157892
Winsorized Mean ( 16 / 24 )109.0694624568492.1008434284845351.9169877098018
Winsorized Mean ( 17 / 24 )108.3750029182191.9517247741436555.5278102496652
Winsorized Mean ( 18 / 24 )108.2224041184931.9072000132538256.744129281888
Winsorized Mean ( 19 / 24 )108.0962512708221.8274077723367559.1527807351922
Winsorized Mean ( 20 / 24 )108.3640869283561.7619036607775161.5039796673878
Winsorized Mean ( 21 / 24 )107.9883292795891.6947175266719063.7205478671466
Winsorized Mean ( 22 / 24 )107.8595881034251.6690965448418364.6215393811422
Winsorized Mean ( 23 / 24 )107.7828010595891.6507201599471565.2944112968486
Winsorized Mean ( 24 / 24 )107.3191527987671.5696118717299368.3730511546694
Trimmed Mean ( 1 / 24 )108.5049703477463.369168712114532.2052647460472
Trimmed Mean ( 2 / 24 )108.4663429862323.2806530450937733.0624243086125
Trimmed Mean ( 3 / 24 )108.4191970786573.1915919435581833.9702565352964
Trimmed Mean ( 4 / 24 )108.3633782321543.0924408552074235.0413745341899
Trimmed Mean ( 5 / 24 )108.3188807992062.9776703991812836.3770553077295
Trimmed Mean ( 6 / 24 )108.3665454932792.8672705350773337.7943218707669
Trimmed Mean ( 7 / 24 )108.3452692510172.7708021900879139.1024915595217
Trimmed Mean ( 8 / 24 )108.4075337077192.6814064858380340.4293546242535
Trimmed Mean ( 9 / 24 )108.4464448456362.5861950893226941.9328167829899
Trimmed Mean ( 10 / 24 )108.4910827156602.4784947037981343.7729733896163
Trimmed Mean ( 11 / 24 )108.4851521017652.3731899651762245.7127974134634
Trimmed Mean ( 12 / 24 )108.2973339440822.3022197090099147.0403991071105
Trimmed Mean ( 13 / 24 )108.1393844863832.2341990362512648.4018579955297
Trimmed Mean ( 14 / 24 )108.0093835044442.1889416364595249.3431993368005
Trimmed Mean ( 15 / 24 )107.8783065927912.1556948177850050.0434039655191
Trimmed Mean ( 16 / 24 )107.7475324602442.1204479126437250.8135718957166
Trimmed Mean ( 17 / 24 )107.5928835984622.0742048876545451.8718687044099
Trimmed Mean ( 18 / 24 )107.5021129937842.0449991782114552.5682915373125
Trimmed Mean ( 19 / 24 )107.4186506888572.0116154809169053.3991966694826
Trimmed Mean ( 20 / 24 )107.3397593930301.9807637261759354.1910970877181
Trimmed Mean ( 21 / 24 )107.2191530864521.9483110065035555.0318469323168
Trimmed Mean ( 22 / 24 )107.1269529844831.9148003729434755.9467997281645
Trimmed Mean ( 23 / 24 )107.0369153351851.8662235627118257.3548193656119
Trimmed Mean ( 24 / 24 )106.9422202781.7918966013196159.6810218844347
Median107.319678
Midrange112.146064945
Midmean - Weighted Average at Xnp106.923450235278
Midmean - Weighted Average at X(n+1)p107.502112993784
Midmean - Empirical Distribution Function107.502112993784
Midmean - Empirical Distribution Function - Averaging107.502112993784
Midmean - Empirical Distribution Function - Interpolation107.502112993784
Midmean - Closest Observation107.022492156316
Midmean - True Basic - Statistics Graphics Toolkit107.502112993784
Midmean - MS Excel (old versions)107.502112993784
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')