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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 computationTue, 11 Dec 2007 15:11:42 -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/11/t1197410230a3igjlosomhf3ug.htm/, Retrieved Mon, 29 Apr 2024 05:18:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3170, Retrieved Mon, 29 Apr 2024 05:18:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Workshop2: the se...] [2007-11-22 16:20:38] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [Tijdreeks 2: omze...] [2007-12-11 22:11:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
106,0
100,9
114,3
101,2
109,2
111,6
91,7
93,7
105,7
109,5
105,3
102,8
100,6
97,6
110,3
107,2
107,2
108,1
97,1
92,2
112,2
111,6
115,7
111,3
104,2
103,2
112,7
106,4
102,6
110,6
95,2
89,0
112,5
116,8
107,2
113,6
101,8
102,6
122,7
110,3
110,5
121,6
100,3
100,7
123,4
127,1
124,1
131,2
111,6
114,2
130,1
125,9
119,0
133,8
107,5
113,5
134,4
126,8
135,6
139,9
129,8
131,0
153,1
134,1
144,1
155,9
123,3
128,1
144,3
153,0
149,9
150,9
141,0
138,9
157,4
142,9
151,7
161,0
138,6
136,0
151,9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3170&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]2 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=3170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3170&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.5370370370372.0313282801208358.8467350190814
Geometric Mean118.206366627082
Harmonic Mean116.930717267007
Quadratic Mean120.909911877081
Winsorized Mean ( 1 / 27 )119.5259259259262.0144231305008559.3350642753035
Winsorized Mean ( 2 / 27 )119.5012345679012.0037484116019759.6388418206464
Winsorized Mean ( 3 / 27 )119.4530864197531.9716400442926960.5856463331296
Winsorized Mean ( 4 / 27 )119.5222222222221.9587891510501161.0184215887382
Winsorized Mean ( 5 / 27 )119.5716049382721.9267586439726162.0584240337119
Winsorized Mean ( 6 / 27 )119.5938271604941.9183015134592862.3436025678935
Winsorized Mean ( 7 / 27 )119.7580246913581.871983057752163.9738827738991
Winsorized Mean ( 8 / 27 )119.6888888888891.8477822876941064.774345812272
Winsorized Mean ( 9 / 27 )119.0777777777781.7256730660424169.0036717388574
Winsorized Mean ( 10 / 27 )119.0777777777781.7178933050126969.3161661613778
Winsorized Mean ( 11 / 27 )118.9555555555561.6831848119297970.67290217476
Winsorized Mean ( 12 / 27 )118.7629629629631.6223577230742573.203931089819
Winsorized Mean ( 13 / 27 )118.7148148148151.5757960080495575.3364104290088
Winsorized Mean ( 14 / 27 )118.5419753086421.5470550121072676.6242792796194
Winsorized Mean ( 15 / 27 )118.5234567901231.5331796134751377.3056566552412
Winsorized Mean ( 16 / 27 )118.0888888888891.4410183727549481.9482187885827
Winsorized Mean ( 17 / 27 )118.2148148148151.4013090342969384.3602745158394
Winsorized Mean ( 18 / 27 )118.1925925925931.3302160060572688.8521804386597
Winsorized Mean ( 19 / 27 )118.2160493827161.3082224024570590.363877854933
Winsorized Mean ( 20 / 27 )118.2160493827161.2881804288427491.769791510431
Winsorized Mean ( 21 / 27 )117.6456790123461.17621364873798100.020671532399
Winsorized Mean ( 22 / 27 )117.8086419753091.14278628194705103.088953583332
Winsorized Mean ( 23 / 27 )117.5530864197531.10622827999847106.264763381312
Winsorized Mean ( 24 / 27 )117.4641975308641.09366061700661107.404615018842
Winsorized Mean ( 25 / 27 )117.0320987654321.00979436111018115.896962067371
Winsorized Mean ( 26 / 27 )116.9037037037040.943516610327733123.902115155235
Winsorized Mean ( 27 / 27 )117.1703703703700.888009016687004131.947275498971
Trimmed Mean ( 1 / 27 )119.3987341772151.9770342369657360.3928510416004
Trimmed Mean ( 2 / 27 )119.2649350649351.9332900129597061.6901418128936
Trimmed Mean ( 3 / 27 )119.1373333333331.8886400782958563.0810151190019
Trimmed Mean ( 4 / 27 )119.0205479452051.8503321094225964.3238839876951
Trimmed Mean ( 5 / 27 )118.8774647887321.8094122317701065.6994921894816
Trimmed Mean ( 6 / 27 )118.7144927536231.7703310234220967.057793815388
Trimmed Mean ( 7 / 27 )118.5373134328361.7257132137115768.6888832344814
Trimmed Mean ( 8 / 27 )118.321.6832092173080570.2942918701627
Trimmed Mean ( 9 / 27 )118.11.6373567173860772.1284487039201
Trimmed Mean ( 10 / 27 )117.9557377049181.6095064657634173.2868989432546
Trimmed Mean ( 11 / 27 )117.8016949152541.5765532385926774.7210382951682
Trimmed Mean ( 12 / 27 )117.6526315789471.5428956462875576.2544322825969
Trimmed Mean ( 13 / 27 )117.5163636363641.5132651691949977.65748265975
Trimmed Mean ( 14 / 27 )117.3754716981131.4848824694865679.0469778653248
Trimmed Mean ( 15 / 27 )117.2431372549021.4544219386758680.6115021625999
Trimmed Mean ( 16 / 27 )117.1020408163271.4178811015005882.5894644426774
Trimmed Mean ( 17 / 27 )116.9957446808511.3900497380502484.1665887761365
Trimmed Mean ( 18 / 27 )116.8666666666671.3608709332518385.8763779952384
Trimmed Mean ( 19 / 27 )116.7279069767441.3362785532541587.3529749411041
Trimmed Mean ( 20 / 27 )116.5731707317071.3067555446752789.2080934392943
Trimmed Mean ( 21 / 27 )116.4025641025641.2701253680111391.6465154025204
Trimmed Mean ( 22 / 27 )116.2729729729731.2469641732540393.244838518136
Trimmed Mean ( 23 / 27 )116.1114285714291.2199446979377495.177616467131
Trimmed Mean ( 24 / 27 )115.9575757575761.1899041079188997.4511937439923
Trimmed Mean ( 25 / 27 )115.7935483870971.14817232496920100.850321740861
Trimmed Mean ( 26 / 27 )115.6551724137931.11264104886443103.946526628540
Trimmed Mean ( 27 / 27 )115.5111111111111.07854409271204107.099108781593
Median113.5
Midrange125
Midmean - Weighted Average at Xnp116.1425
Midmean - Weighted Average at X(n+1)p116.573170731707
Midmean - Empirical Distribution Function116.573170731707
Midmean - Empirical Distribution Function - Averaging116.573170731707
Midmean - Empirical Distribution Function - Interpolation116.573170731707
Midmean - Closest Observation116.314285714286
Midmean - True Basic - Statistics Graphics Toolkit116.573170731707
Midmean - MS Excel (old versions)116.573170731707
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.537037037037 & 2.03132828012083 & 58.8467350190814 \tabularnewline
Geometric Mean & 118.206366627082 &  &  \tabularnewline
Harmonic Mean & 116.930717267007 &  &  \tabularnewline
Quadratic Mean & 120.909911877081 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 119.525925925926 & 2.01442313050085 & 59.3350642753035 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 119.501234567901 & 2.00374841160197 & 59.6388418206464 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 119.453086419753 & 1.97164004429269 & 60.5856463331296 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 119.522222222222 & 1.95878915105011 & 61.0184215887382 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 119.571604938272 & 1.92675864397261 & 62.0584240337119 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 119.593827160494 & 1.91830151345928 & 62.3436025678935 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 119.758024691358 & 1.8719830577521 & 63.9738827738991 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 119.688888888889 & 1.84778228769410 & 64.774345812272 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 119.077777777778 & 1.72567306604241 & 69.0036717388574 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 119.077777777778 & 1.71789330501269 & 69.3161661613778 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 118.955555555556 & 1.68318481192979 & 70.67290217476 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 118.762962962963 & 1.62235772307425 & 73.203931089819 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 118.714814814815 & 1.57579600804955 & 75.3364104290088 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 118.541975308642 & 1.54705501210726 & 76.6242792796194 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 118.523456790123 & 1.53317961347513 & 77.3056566552412 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 118.088888888889 & 1.44101837275494 & 81.9482187885827 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 118.214814814815 & 1.40130903429693 & 84.3602745158394 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 118.192592592593 & 1.33021600605726 & 88.8521804386597 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 118.216049382716 & 1.30822240245705 & 90.363877854933 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 118.216049382716 & 1.28818042884274 & 91.769791510431 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 117.645679012346 & 1.17621364873798 & 100.020671532399 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 117.808641975309 & 1.14278628194705 & 103.088953583332 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 117.553086419753 & 1.10622827999847 & 106.264763381312 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 117.464197530864 & 1.09366061700661 & 107.404615018842 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 117.032098765432 & 1.00979436111018 & 115.896962067371 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 116.903703703704 & 0.943516610327733 & 123.902115155235 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 117.170370370370 & 0.888009016687004 & 131.947275498971 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 119.398734177215 & 1.97703423696573 & 60.3928510416004 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 119.264935064935 & 1.93329001295970 & 61.6901418128936 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 119.137333333333 & 1.88864007829585 & 63.0810151190019 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 119.020547945205 & 1.85033210942259 & 64.3238839876951 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 118.877464788732 & 1.80941223177010 & 65.6994921894816 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 118.714492753623 & 1.77033102342209 & 67.057793815388 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 118.537313432836 & 1.72571321371157 & 68.6888832344814 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 118.32 & 1.68320921730805 & 70.2942918701627 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 118.1 & 1.63735671738607 & 72.1284487039201 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 117.955737704918 & 1.60950646576341 & 73.2868989432546 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 117.801694915254 & 1.57655323859267 & 74.7210382951682 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 117.652631578947 & 1.54289564628755 & 76.2544322825969 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 117.516363636364 & 1.51326516919499 & 77.65748265975 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 117.375471698113 & 1.48488246948656 & 79.0469778653248 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 117.243137254902 & 1.45442193867586 & 80.6115021625999 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 117.102040816327 & 1.41788110150058 & 82.5894644426774 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 116.995744680851 & 1.39004973805024 & 84.1665887761365 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 116.866666666667 & 1.36087093325183 & 85.8763779952384 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 116.727906976744 & 1.33627855325415 & 87.3529749411041 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 116.573170731707 & 1.30675554467527 & 89.2080934392943 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 116.402564102564 & 1.27012536801113 & 91.6465154025204 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 116.272972972973 & 1.24696417325403 & 93.244838518136 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 116.111428571429 & 1.21994469793774 & 95.177616467131 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 115.957575757576 & 1.18990410791889 & 97.4511937439923 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 115.793548387097 & 1.14817232496920 & 100.850321740861 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 115.655172413793 & 1.11264104886443 & 103.946526628540 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 115.511111111111 & 1.07854409271204 & 107.099108781593 \tabularnewline
Median & 113.5 &  &  \tabularnewline
Midrange & 125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.1425 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.573170731707 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.573170731707 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.573170731707 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.573170731707 &  &  \tabularnewline
Midmean - Closest Observation & 116.314285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.573170731707 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.573170731707 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3170&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]119.537037037037[/C][C]2.03132828012083[/C][C]58.8467350190814[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]118.206366627082[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]116.930717267007[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.909911877081[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]119.525925925926[/C][C]2.01442313050085[/C][C]59.3350642753035[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]119.501234567901[/C][C]2.00374841160197[/C][C]59.6388418206464[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]119.453086419753[/C][C]1.97164004429269[/C][C]60.5856463331296[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]119.522222222222[/C][C]1.95878915105011[/C][C]61.0184215887382[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]119.571604938272[/C][C]1.92675864397261[/C][C]62.0584240337119[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]119.593827160494[/C][C]1.91830151345928[/C][C]62.3436025678935[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]119.758024691358[/C][C]1.8719830577521[/C][C]63.9738827738991[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]119.688888888889[/C][C]1.84778228769410[/C][C]64.774345812272[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]119.077777777778[/C][C]1.72567306604241[/C][C]69.0036717388574[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]119.077777777778[/C][C]1.71789330501269[/C][C]69.3161661613778[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]118.955555555556[/C][C]1.68318481192979[/C][C]70.67290217476[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]118.762962962963[/C][C]1.62235772307425[/C][C]73.203931089819[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]118.714814814815[/C][C]1.57579600804955[/C][C]75.3364104290088[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]118.541975308642[/C][C]1.54705501210726[/C][C]76.6242792796194[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]118.523456790123[/C][C]1.53317961347513[/C][C]77.3056566552412[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]118.088888888889[/C][C]1.44101837275494[/C][C]81.9482187885827[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]118.214814814815[/C][C]1.40130903429693[/C][C]84.3602745158394[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]118.192592592593[/C][C]1.33021600605726[/C][C]88.8521804386597[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]118.216049382716[/C][C]1.30822240245705[/C][C]90.363877854933[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]118.216049382716[/C][C]1.28818042884274[/C][C]91.769791510431[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]117.645679012346[/C][C]1.17621364873798[/C][C]100.020671532399[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]117.808641975309[/C][C]1.14278628194705[/C][C]103.088953583332[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]117.553086419753[/C][C]1.10622827999847[/C][C]106.264763381312[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]117.464197530864[/C][C]1.09366061700661[/C][C]107.404615018842[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]117.032098765432[/C][C]1.00979436111018[/C][C]115.896962067371[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]116.903703703704[/C][C]0.943516610327733[/C][C]123.902115155235[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]117.170370370370[/C][C]0.888009016687004[/C][C]131.947275498971[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]119.398734177215[/C][C]1.97703423696573[/C][C]60.3928510416004[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]119.264935064935[/C][C]1.93329001295970[/C][C]61.6901418128936[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]119.137333333333[/C][C]1.88864007829585[/C][C]63.0810151190019[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]119.020547945205[/C][C]1.85033210942259[/C][C]64.3238839876951[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]118.877464788732[/C][C]1.80941223177010[/C][C]65.6994921894816[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]118.714492753623[/C][C]1.77033102342209[/C][C]67.057793815388[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]118.537313432836[/C][C]1.72571321371157[/C][C]68.6888832344814[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]118.32[/C][C]1.68320921730805[/C][C]70.2942918701627[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]118.1[/C][C]1.63735671738607[/C][C]72.1284487039201[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]117.955737704918[/C][C]1.60950646576341[/C][C]73.2868989432546[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]117.801694915254[/C][C]1.57655323859267[/C][C]74.7210382951682[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]117.652631578947[/C][C]1.54289564628755[/C][C]76.2544322825969[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]117.516363636364[/C][C]1.51326516919499[/C][C]77.65748265975[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]117.375471698113[/C][C]1.48488246948656[/C][C]79.0469778653248[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]117.243137254902[/C][C]1.45442193867586[/C][C]80.6115021625999[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]117.102040816327[/C][C]1.41788110150058[/C][C]82.5894644426774[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]116.995744680851[/C][C]1.39004973805024[/C][C]84.1665887761365[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]116.866666666667[/C][C]1.36087093325183[/C][C]85.8763779952384[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]116.727906976744[/C][C]1.33627855325415[/C][C]87.3529749411041[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]116.573170731707[/C][C]1.30675554467527[/C][C]89.2080934392943[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]116.402564102564[/C][C]1.27012536801113[/C][C]91.6465154025204[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]116.272972972973[/C][C]1.24696417325403[/C][C]93.244838518136[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]116.111428571429[/C][C]1.21994469793774[/C][C]95.177616467131[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]115.957575757576[/C][C]1.18990410791889[/C][C]97.4511937439923[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]115.793548387097[/C][C]1.14817232496920[/C][C]100.850321740861[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]115.655172413793[/C][C]1.11264104886443[/C][C]103.946526628540[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]115.511111111111[/C][C]1.07854409271204[/C][C]107.099108781593[/C][/ROW]
[ROW][C]Median[/C][C]113.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.1425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.314285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3170&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 Mean119.5370370370372.0313282801208358.8467350190814
Geometric Mean118.206366627082
Harmonic Mean116.930717267007
Quadratic Mean120.909911877081
Winsorized Mean ( 1 / 27 )119.5259259259262.0144231305008559.3350642753035
Winsorized Mean ( 2 / 27 )119.5012345679012.0037484116019759.6388418206464
Winsorized Mean ( 3 / 27 )119.4530864197531.9716400442926960.5856463331296
Winsorized Mean ( 4 / 27 )119.5222222222221.9587891510501161.0184215887382
Winsorized Mean ( 5 / 27 )119.5716049382721.9267586439726162.0584240337119
Winsorized Mean ( 6 / 27 )119.5938271604941.9183015134592862.3436025678935
Winsorized Mean ( 7 / 27 )119.7580246913581.871983057752163.9738827738991
Winsorized Mean ( 8 / 27 )119.6888888888891.8477822876941064.774345812272
Winsorized Mean ( 9 / 27 )119.0777777777781.7256730660424169.0036717388574
Winsorized Mean ( 10 / 27 )119.0777777777781.7178933050126969.3161661613778
Winsorized Mean ( 11 / 27 )118.9555555555561.6831848119297970.67290217476
Winsorized Mean ( 12 / 27 )118.7629629629631.6223577230742573.203931089819
Winsorized Mean ( 13 / 27 )118.7148148148151.5757960080495575.3364104290088
Winsorized Mean ( 14 / 27 )118.5419753086421.5470550121072676.6242792796194
Winsorized Mean ( 15 / 27 )118.5234567901231.5331796134751377.3056566552412
Winsorized Mean ( 16 / 27 )118.0888888888891.4410183727549481.9482187885827
Winsorized Mean ( 17 / 27 )118.2148148148151.4013090342969384.3602745158394
Winsorized Mean ( 18 / 27 )118.1925925925931.3302160060572688.8521804386597
Winsorized Mean ( 19 / 27 )118.2160493827161.3082224024570590.363877854933
Winsorized Mean ( 20 / 27 )118.2160493827161.2881804288427491.769791510431
Winsorized Mean ( 21 / 27 )117.6456790123461.17621364873798100.020671532399
Winsorized Mean ( 22 / 27 )117.8086419753091.14278628194705103.088953583332
Winsorized Mean ( 23 / 27 )117.5530864197531.10622827999847106.264763381312
Winsorized Mean ( 24 / 27 )117.4641975308641.09366061700661107.404615018842
Winsorized Mean ( 25 / 27 )117.0320987654321.00979436111018115.896962067371
Winsorized Mean ( 26 / 27 )116.9037037037040.943516610327733123.902115155235
Winsorized Mean ( 27 / 27 )117.1703703703700.888009016687004131.947275498971
Trimmed Mean ( 1 / 27 )119.3987341772151.9770342369657360.3928510416004
Trimmed Mean ( 2 / 27 )119.2649350649351.9332900129597061.6901418128936
Trimmed Mean ( 3 / 27 )119.1373333333331.8886400782958563.0810151190019
Trimmed Mean ( 4 / 27 )119.0205479452051.8503321094225964.3238839876951
Trimmed Mean ( 5 / 27 )118.8774647887321.8094122317701065.6994921894816
Trimmed Mean ( 6 / 27 )118.7144927536231.7703310234220967.057793815388
Trimmed Mean ( 7 / 27 )118.5373134328361.7257132137115768.6888832344814
Trimmed Mean ( 8 / 27 )118.321.6832092173080570.2942918701627
Trimmed Mean ( 9 / 27 )118.11.6373567173860772.1284487039201
Trimmed Mean ( 10 / 27 )117.9557377049181.6095064657634173.2868989432546
Trimmed Mean ( 11 / 27 )117.8016949152541.5765532385926774.7210382951682
Trimmed Mean ( 12 / 27 )117.6526315789471.5428956462875576.2544322825969
Trimmed Mean ( 13 / 27 )117.5163636363641.5132651691949977.65748265975
Trimmed Mean ( 14 / 27 )117.3754716981131.4848824694865679.0469778653248
Trimmed Mean ( 15 / 27 )117.2431372549021.4544219386758680.6115021625999
Trimmed Mean ( 16 / 27 )117.1020408163271.4178811015005882.5894644426774
Trimmed Mean ( 17 / 27 )116.9957446808511.3900497380502484.1665887761365
Trimmed Mean ( 18 / 27 )116.8666666666671.3608709332518385.8763779952384
Trimmed Mean ( 19 / 27 )116.7279069767441.3362785532541587.3529749411041
Trimmed Mean ( 20 / 27 )116.5731707317071.3067555446752789.2080934392943
Trimmed Mean ( 21 / 27 )116.4025641025641.2701253680111391.6465154025204
Trimmed Mean ( 22 / 27 )116.2729729729731.2469641732540393.244838518136
Trimmed Mean ( 23 / 27 )116.1114285714291.2199446979377495.177616467131
Trimmed Mean ( 24 / 27 )115.9575757575761.1899041079188997.4511937439923
Trimmed Mean ( 25 / 27 )115.7935483870971.14817232496920100.850321740861
Trimmed Mean ( 26 / 27 )115.6551724137931.11264104886443103.946526628540
Trimmed Mean ( 27 / 27 )115.5111111111111.07854409271204107.099108781593
Median113.5
Midrange125
Midmean - Weighted Average at Xnp116.1425
Midmean - Weighted Average at X(n+1)p116.573170731707
Midmean - Empirical Distribution Function116.573170731707
Midmean - Empirical Distribution Function - Averaging116.573170731707
Midmean - Empirical Distribution Function - Interpolation116.573170731707
Midmean - Closest Observation116.314285714286
Midmean - True Basic - Statistics Graphics Toolkit116.573170731707
Midmean - MS Excel (old versions)116.573170731707
Number of observations81



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')