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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Oct 2014 14:32:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/11/t1413034370z1vwaxniyovudi6.htm/, Retrieved Tue, 14 May 2024 13:09:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240451, Retrieved Tue, 14 May 2024 13:09:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-11 13:32:36] [9458cab04bab2efa06ad058ca673aa95] [Current]
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Dataseries X:
18,3
18,6
18,7
20,1
18,9
20,1
19,8
15,9
19,9
19,6
15,6
14,2
13,6
13,9
15
14,1
13,5
15,3
14,7
12,5
16,1
15,9
15,9
15,7
14,7
15,3
18,4
16,8
16,5
19,3
17,1
15,7
19,1
18,6
18,4
17,1
18,3
19,4
22,3
19,4
21,3
20,3
19,3
17,5
19,9
19,6
19,7
18,1
19,1
20,7
22,5
20
20,2
20,4
19,6
18,1
19,3
21
19,9
17,7
19,4
19,3
21,5
20,9
20,8
20,3
21,4
17,4
21,1
22
20,4
19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240451&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240451&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.33333333333330.28232352500270564.9373208738367
Geometric Mean18.168915461197
Harmonic Mean17.9942795341207
Quadratic Mean18.4870299880153
Winsorized Mean ( 1 / 24 )18.34444444444440.27802883803044765.9803658296609
Winsorized Mean ( 2 / 24 )18.33888888888890.27573742042337266.5085241630644
Winsorized Mean ( 3 / 24 )18.33055555555560.2690957361511868.1190858604216
Winsorized Mean ( 4 / 24 )18.33611111111110.26564730017266969.024270524085
Winsorized Mean ( 5 / 24 )18.33611111111110.26298296025560869.7235710377935
Winsorized Mean ( 6 / 24 )18.36111111111110.25148662492829173.0102887831374
Winsorized Mean ( 7 / 24 )18.35138888888890.25001559462750873.4009769119808
Winsorized Mean ( 8 / 24 )18.37361111111110.24166053946867276.0306633077472
Winsorized Mean ( 9 / 24 )18.39861111111110.23262377908560979.0917041388969
Winsorized Mean ( 10 / 24 )18.38472222222220.23063208140391179.71450506933
Winsorized Mean ( 11 / 24 )18.38472222222220.21588573350373885.1595050948742
Winsorized Mean ( 12 / 24 )18.40138888888890.21288219845913986.4393031548895
Winsorized Mean ( 13 / 24 )18.38333333333330.21053066567452487.3190291515705
Winsorized Mean ( 14 / 24 )18.42222222222220.20364655147415890.4617440799625
Winsorized Mean ( 15 / 24 )18.40138888888890.20098050979902291.5580764885611
Winsorized Mean ( 16 / 24 )18.37916666666670.19822113349017192.7205204765817
Winsorized Mean ( 17 / 24 )18.42638888888890.18998798511920296.9871272508515
Winsorized Mean ( 18 / 24 )18.50138888888890.169949972565752108.863735660392
Winsorized Mean ( 19 / 24 )18.55416666666670.153747367879552120.679572746912
Winsorized Mean ( 20 / 24 )18.63750.14062288078737132.535330634998
Winsorized Mean ( 21 / 24 )18.63750.14062288078737132.535330634998
Winsorized Mean ( 22 / 24 )18.69861111111110.122865071220265152.188176227802
Winsorized Mean ( 23 / 24 )18.69861111111110.11413231647243163.832748594286
Winsorized Mean ( 24 / 24 )18.73194444444440.100270104484053186.814849159986
Trimmed Mean ( 1 / 24 )18.35714285714290.27150048083086967.6136661009393
Trimmed Mean ( 2 / 24 )18.37058823529410.26372807402781269.6573101025143
Trimmed Mean ( 3 / 24 )18.38787878787880.25590021321070271.8556602871552
Trimmed Mean ( 4 / 24 )18.4093750.24954043822102273.7731132125949
Trimmed Mean ( 5 / 24 )18.43064516129030.24311338502476475.8109026346409
Trimmed Mean ( 6 / 24 )18.45333333333330.23612295306517478.1513745012323
Trimmed Mean ( 7 / 24 )18.47241379310340.23089810062065480.0024501866825
Trimmed Mean ( 8 / 24 )18.49464285714290.22477145164165882.2819923173692
Trimmed Mean ( 9 / 24 )18.51481481481480.2192581260476584.4430039997289
Trimmed Mean ( 10 / 24 )18.53269230769230.21449581617647286.4011831934518
Trimmed Mean ( 11 / 24 )18.5540.20882978128375488.8474808810397
Trimmed Mean ( 12 / 24 )18.57708333333330.20486632000429990.6790502848075
Trimmed Mean ( 13 / 24 )18.60.20031376354293492.8543284845898
Trimmed Mean ( 14 / 24 )18.62727272727270.19470701240678795.6682170663486
Trimmed Mean ( 15 / 24 )18.6523809523810.18892808749454198.7274110469145
Trimmed Mean ( 16 / 24 )18.68250.181619759881702102.866009800744
Trimmed Mean ( 17 / 24 )18.71842105263160.172128143040912108.747010930006
Trimmed Mean ( 18 / 24 )18.75277777777780.16146581097209116.140857713954
Trimmed Mean ( 19 / 24 )18.78235294117650.152779978123523122.937266858298
Trimmed Mean ( 20 / 24 )18.8093750.145452531817417129.316243347424
Trimmed Mean ( 21 / 24 )18.830.139221976069476135.25163578057
Trimmed Mean ( 22 / 24 )18.85357142857140.129659927892092145.407850637261
Trimmed Mean ( 23 / 24 )18.87307692307690.122104330208315154.565173003108
Trimmed Mean ( 24 / 24 )18.89583333333330.113488677636541166.499722499623
Median19.05
Midrange17.5
Midmean - Weighted Average at Xnp18.6810810810811
Midmean - Weighted Average at X(n+1)p18.7527777777778
Midmean - Empirical Distribution Function18.6810810810811
Midmean - Empirical Distribution Function - Averaging18.7527777777778
Midmean - Empirical Distribution Function - Interpolation18.7527777777778
Midmean - Closest Observation18.6810810810811
Midmean - True Basic - Statistics Graphics Toolkit18.7527777777778
Midmean - MS Excel (old versions)18.7538461538462
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.3333333333333 & 0.282323525002705 & 64.9373208738367 \tabularnewline
Geometric Mean & 18.168915461197 &  &  \tabularnewline
Harmonic Mean & 17.9942795341207 &  &  \tabularnewline
Quadratic Mean & 18.4870299880153 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 18.3444444444444 & 0.278028838030447 & 65.9803658296609 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 18.3388888888889 & 0.275737420423372 & 66.5085241630644 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 18.3305555555556 & 0.26909573615118 & 68.1190858604216 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 18.3361111111111 & 0.265647300172669 & 69.024270524085 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 18.3361111111111 & 0.262982960255608 & 69.7235710377935 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 18.3611111111111 & 0.251486624928291 & 73.0102887831374 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 18.3513888888889 & 0.250015594627508 & 73.4009769119808 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 18.3736111111111 & 0.241660539468672 & 76.0306633077472 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 18.3986111111111 & 0.232623779085609 & 79.0917041388969 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 18.3847222222222 & 0.230632081403911 & 79.71450506933 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 18.3847222222222 & 0.215885733503738 & 85.1595050948742 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 18.4013888888889 & 0.212882198459139 & 86.4393031548895 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 18.3833333333333 & 0.210530665674524 & 87.3190291515705 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 18.4222222222222 & 0.203646551474158 & 90.4617440799625 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 18.4013888888889 & 0.200980509799022 & 91.5580764885611 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 18.3791666666667 & 0.198221133490171 & 92.7205204765817 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 18.4263888888889 & 0.189987985119202 & 96.9871272508515 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 18.5013888888889 & 0.169949972565752 & 108.863735660392 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 18.5541666666667 & 0.153747367879552 & 120.679572746912 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 18.6375 & 0.14062288078737 & 132.535330634998 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 18.6375 & 0.14062288078737 & 132.535330634998 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 18.6986111111111 & 0.122865071220265 & 152.188176227802 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 18.6986111111111 & 0.11413231647243 & 163.832748594286 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 18.7319444444444 & 0.100270104484053 & 186.814849159986 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 18.3571428571429 & 0.271500480830869 & 67.6136661009393 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 18.3705882352941 & 0.263728074027812 & 69.6573101025143 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 18.3878787878788 & 0.255900213210702 & 71.8556602871552 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 18.409375 & 0.249540438221022 & 73.7731132125949 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 18.4306451612903 & 0.243113385024764 & 75.8109026346409 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 18.4533333333333 & 0.236122953065174 & 78.1513745012323 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 18.4724137931034 & 0.230898100620654 & 80.0024501866825 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 18.4946428571429 & 0.224771451641658 & 82.2819923173692 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 18.5148148148148 & 0.21925812604765 & 84.4430039997289 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 18.5326923076923 & 0.214495816176472 & 86.4011831934518 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 18.554 & 0.208829781283754 & 88.8474808810397 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 18.5770833333333 & 0.204866320004299 & 90.6790502848075 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 18.6 & 0.200313763542934 & 92.8543284845898 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 18.6272727272727 & 0.194707012406787 & 95.6682170663486 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 18.652380952381 & 0.188928087494541 & 98.7274110469145 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 18.6825 & 0.181619759881702 & 102.866009800744 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 18.7184210526316 & 0.172128143040912 & 108.747010930006 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 18.7527777777778 & 0.16146581097209 & 116.140857713954 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 18.7823529411765 & 0.152779978123523 & 122.937266858298 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 18.809375 & 0.145452531817417 & 129.316243347424 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 18.83 & 0.139221976069476 & 135.25163578057 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 18.8535714285714 & 0.129659927892092 & 145.407850637261 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 18.8730769230769 & 0.122104330208315 & 154.565173003108 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 18.8958333333333 & 0.113488677636541 & 166.499722499623 \tabularnewline
Median & 19.05 &  &  \tabularnewline
Midrange & 17.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.6810810810811 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.7527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.6810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.7527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.7527777777778 &  &  \tabularnewline
Midmean - Closest Observation & 18.6810810810811 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.7527777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.7538461538462 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240451&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]18.3333333333333[/C][C]0.282323525002705[/C][C]64.9373208738367[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.168915461197[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.9942795341207[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.4870299880153[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]18.3444444444444[/C][C]0.278028838030447[/C][C]65.9803658296609[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]18.3388888888889[/C][C]0.275737420423372[/C][C]66.5085241630644[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]18.3305555555556[/C][C]0.26909573615118[/C][C]68.1190858604216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]18.3361111111111[/C][C]0.265647300172669[/C][C]69.024270524085[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]18.3361111111111[/C][C]0.262982960255608[/C][C]69.7235710377935[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]18.3611111111111[/C][C]0.251486624928291[/C][C]73.0102887831374[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]18.3513888888889[/C][C]0.250015594627508[/C][C]73.4009769119808[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]18.3736111111111[/C][C]0.241660539468672[/C][C]76.0306633077472[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]18.3986111111111[/C][C]0.232623779085609[/C][C]79.0917041388969[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]18.3847222222222[/C][C]0.230632081403911[/C][C]79.71450506933[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]18.3847222222222[/C][C]0.215885733503738[/C][C]85.1595050948742[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]18.4013888888889[/C][C]0.212882198459139[/C][C]86.4393031548895[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]18.3833333333333[/C][C]0.210530665674524[/C][C]87.3190291515705[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]18.4222222222222[/C][C]0.203646551474158[/C][C]90.4617440799625[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]18.4013888888889[/C][C]0.200980509799022[/C][C]91.5580764885611[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]18.3791666666667[/C][C]0.198221133490171[/C][C]92.7205204765817[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]18.4263888888889[/C][C]0.189987985119202[/C][C]96.9871272508515[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]18.5013888888889[/C][C]0.169949972565752[/C][C]108.863735660392[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]18.5541666666667[/C][C]0.153747367879552[/C][C]120.679572746912[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]18.6375[/C][C]0.14062288078737[/C][C]132.535330634998[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]18.6375[/C][C]0.14062288078737[/C][C]132.535330634998[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]18.6986111111111[/C][C]0.122865071220265[/C][C]152.188176227802[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]18.6986111111111[/C][C]0.11413231647243[/C][C]163.832748594286[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]18.7319444444444[/C][C]0.100270104484053[/C][C]186.814849159986[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]18.3571428571429[/C][C]0.271500480830869[/C][C]67.6136661009393[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]18.3705882352941[/C][C]0.263728074027812[/C][C]69.6573101025143[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]18.3878787878788[/C][C]0.255900213210702[/C][C]71.8556602871552[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]18.409375[/C][C]0.249540438221022[/C][C]73.7731132125949[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]18.4306451612903[/C][C]0.243113385024764[/C][C]75.8109026346409[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]18.4533333333333[/C][C]0.236122953065174[/C][C]78.1513745012323[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]18.4724137931034[/C][C]0.230898100620654[/C][C]80.0024501866825[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]18.4946428571429[/C][C]0.224771451641658[/C][C]82.2819923173692[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]18.5148148148148[/C][C]0.21925812604765[/C][C]84.4430039997289[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]18.5326923076923[/C][C]0.214495816176472[/C][C]86.4011831934518[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]18.554[/C][C]0.208829781283754[/C][C]88.8474808810397[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]18.5770833333333[/C][C]0.204866320004299[/C][C]90.6790502848075[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]18.6[/C][C]0.200313763542934[/C][C]92.8543284845898[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]18.6272727272727[/C][C]0.194707012406787[/C][C]95.6682170663486[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]18.652380952381[/C][C]0.188928087494541[/C][C]98.7274110469145[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]18.6825[/C][C]0.181619759881702[/C][C]102.866009800744[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]18.7184210526316[/C][C]0.172128143040912[/C][C]108.747010930006[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]18.7527777777778[/C][C]0.16146581097209[/C][C]116.140857713954[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]18.7823529411765[/C][C]0.152779978123523[/C][C]122.937266858298[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]18.809375[/C][C]0.145452531817417[/C][C]129.316243347424[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]18.83[/C][C]0.139221976069476[/C][C]135.25163578057[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]18.8535714285714[/C][C]0.129659927892092[/C][C]145.407850637261[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]18.8730769230769[/C][C]0.122104330208315[/C][C]154.565173003108[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]18.8958333333333[/C][C]0.113488677636541[/C][C]166.499722499623[/C][/ROW]
[ROW][C]Median[/C][C]19.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.6810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.7527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.6810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.7527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.7527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.6810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.7527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.7538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240451&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 Mean18.33333333333330.28232352500270564.9373208738367
Geometric Mean18.168915461197
Harmonic Mean17.9942795341207
Quadratic Mean18.4870299880153
Winsorized Mean ( 1 / 24 )18.34444444444440.27802883803044765.9803658296609
Winsorized Mean ( 2 / 24 )18.33888888888890.27573742042337266.5085241630644
Winsorized Mean ( 3 / 24 )18.33055555555560.2690957361511868.1190858604216
Winsorized Mean ( 4 / 24 )18.33611111111110.26564730017266969.024270524085
Winsorized Mean ( 5 / 24 )18.33611111111110.26298296025560869.7235710377935
Winsorized Mean ( 6 / 24 )18.36111111111110.25148662492829173.0102887831374
Winsorized Mean ( 7 / 24 )18.35138888888890.25001559462750873.4009769119808
Winsorized Mean ( 8 / 24 )18.37361111111110.24166053946867276.0306633077472
Winsorized Mean ( 9 / 24 )18.39861111111110.23262377908560979.0917041388969
Winsorized Mean ( 10 / 24 )18.38472222222220.23063208140391179.71450506933
Winsorized Mean ( 11 / 24 )18.38472222222220.21588573350373885.1595050948742
Winsorized Mean ( 12 / 24 )18.40138888888890.21288219845913986.4393031548895
Winsorized Mean ( 13 / 24 )18.38333333333330.21053066567452487.3190291515705
Winsorized Mean ( 14 / 24 )18.42222222222220.20364655147415890.4617440799625
Winsorized Mean ( 15 / 24 )18.40138888888890.20098050979902291.5580764885611
Winsorized Mean ( 16 / 24 )18.37916666666670.19822113349017192.7205204765817
Winsorized Mean ( 17 / 24 )18.42638888888890.18998798511920296.9871272508515
Winsorized Mean ( 18 / 24 )18.50138888888890.169949972565752108.863735660392
Winsorized Mean ( 19 / 24 )18.55416666666670.153747367879552120.679572746912
Winsorized Mean ( 20 / 24 )18.63750.14062288078737132.535330634998
Winsorized Mean ( 21 / 24 )18.63750.14062288078737132.535330634998
Winsorized Mean ( 22 / 24 )18.69861111111110.122865071220265152.188176227802
Winsorized Mean ( 23 / 24 )18.69861111111110.11413231647243163.832748594286
Winsorized Mean ( 24 / 24 )18.73194444444440.100270104484053186.814849159986
Trimmed Mean ( 1 / 24 )18.35714285714290.27150048083086967.6136661009393
Trimmed Mean ( 2 / 24 )18.37058823529410.26372807402781269.6573101025143
Trimmed Mean ( 3 / 24 )18.38787878787880.25590021321070271.8556602871552
Trimmed Mean ( 4 / 24 )18.4093750.24954043822102273.7731132125949
Trimmed Mean ( 5 / 24 )18.43064516129030.24311338502476475.8109026346409
Trimmed Mean ( 6 / 24 )18.45333333333330.23612295306517478.1513745012323
Trimmed Mean ( 7 / 24 )18.47241379310340.23089810062065480.0024501866825
Trimmed Mean ( 8 / 24 )18.49464285714290.22477145164165882.2819923173692
Trimmed Mean ( 9 / 24 )18.51481481481480.2192581260476584.4430039997289
Trimmed Mean ( 10 / 24 )18.53269230769230.21449581617647286.4011831934518
Trimmed Mean ( 11 / 24 )18.5540.20882978128375488.8474808810397
Trimmed Mean ( 12 / 24 )18.57708333333330.20486632000429990.6790502848075
Trimmed Mean ( 13 / 24 )18.60.20031376354293492.8543284845898
Trimmed Mean ( 14 / 24 )18.62727272727270.19470701240678795.6682170663486
Trimmed Mean ( 15 / 24 )18.6523809523810.18892808749454198.7274110469145
Trimmed Mean ( 16 / 24 )18.68250.181619759881702102.866009800744
Trimmed Mean ( 17 / 24 )18.71842105263160.172128143040912108.747010930006
Trimmed Mean ( 18 / 24 )18.75277777777780.16146581097209116.140857713954
Trimmed Mean ( 19 / 24 )18.78235294117650.152779978123523122.937266858298
Trimmed Mean ( 20 / 24 )18.8093750.145452531817417129.316243347424
Trimmed Mean ( 21 / 24 )18.830.139221976069476135.25163578057
Trimmed Mean ( 22 / 24 )18.85357142857140.129659927892092145.407850637261
Trimmed Mean ( 23 / 24 )18.87307692307690.122104330208315154.565173003108
Trimmed Mean ( 24 / 24 )18.89583333333330.113488677636541166.499722499623
Median19.05
Midrange17.5
Midmean - Weighted Average at Xnp18.6810810810811
Midmean - Weighted Average at X(n+1)p18.7527777777778
Midmean - Empirical Distribution Function18.6810810810811
Midmean - Empirical Distribution Function - Averaging18.7527777777778
Midmean - Empirical Distribution Function - Interpolation18.7527777777778
Midmean - Closest Observation18.6810810810811
Midmean - True Basic - Statistics Graphics Toolkit18.7527777777778
Midmean - MS Excel (old versions)18.7538461538462
Number of observations72



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')