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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 computationMon, 04 Apr 2011 20:15:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/04/t1301947967sx3yv8ey4w19onq.htm/, Retrieved Thu, 09 May 2024 01:30:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120248, Retrieved Thu, 09 May 2024 01:30:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-04-04 20:15:43] [764118764852521a1756ded753a212d7] [Current]
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Dataseries X:
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120248&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120248&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'Herman Ole Andreas Wold' @ www.yougetit.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.7534246575341.8783170377188362.690920804585
Geometric Mean116.697142490666
Harmonic Mean115.659910754145
Quadratic Mean118.827145093025
Winsorized Mean ( 1 / 24 )117.7945205479451.8684840003882463.0428307245175
Winsorized Mean ( 2 / 24 )117.7671232876711.7815988821403366.101929266026
Winsorized Mean ( 3 / 24 )117.726027397261.7713967300353266.4594358796816
Winsorized Mean ( 4 / 24 )117.8356164383561.750843860320867.3021844545097
Winsorized Mean ( 5 / 24 )117.6986301369861.7176765805671368.5219973704977
Winsorized Mean ( 6 / 24 )117.7808219178081.6033933023252873.4572245917451
Winsorized Mean ( 7 / 24 )117.2054794520551.4470563865082380.9957929385695
Winsorized Mean ( 8 / 24 )117.3150684931511.4293185665949682.0776216268065
Winsorized Mean ( 9 / 24 )117.3150684931511.3867546831052984.596843206942
Winsorized Mean ( 10 / 24 )117.1780821917811.3614812063516186.066617478904
Winsorized Mean ( 11 / 24 )117.1780821917811.3113690990370489.3555310078807
Winsorized Mean ( 12 / 24 )117.3424657534251.234680736603795.0387110405599
Winsorized Mean ( 13 / 24 )117.1643835616441.2037507495568497.332760627379
Winsorized Mean ( 14 / 24 )116.9726027397261.1713819588777999.858634370456
Winsorized Mean ( 15 / 24 )116.7671232876711.13768981187586102.635289574354
Winsorized Mean ( 16 / 24 )116.9863013698631.1068303832189105.694877140653
Winsorized Mean ( 17 / 24 )117.2191780821921.0754006324611109.000473445817
Winsorized Mean ( 18 / 24 )116.4794520547950.957647578558435121.630811441233
Winsorized Mean ( 19 / 24 )115.9589041095890.880716455477241131.66428694324
Winsorized Mean ( 20 / 24 )115.9589041095890.80391885389922144.242050733302
Winsorized Mean ( 21 / 24 )116.2465753424660.765201305056023151.916331786647
Winsorized Mean ( 22 / 24 )116.2465753424660.765201305056023151.916331786647
Winsorized Mean ( 23 / 24 )115.9315068493150.72157677820906160.664132148286
Winsorized Mean ( 24 / 24 )115.9315068493150.72157677820906160.664132148286
Trimmed Mean ( 1 / 24 )117.6760563380281.7865780210521965.866732351674
Trimmed Mean ( 2 / 24 )117.5507246376811.6883756112175369.623562349916
Trimmed Mean ( 3 / 24 )117.4328358208961.6278923229177372.1379627925369
Trimmed Mean ( 4 / 24 )117.3230769230771.5600338526140375.2054686034457
Trimmed Mean ( 5 / 24 )117.1746031746031.4856438248332278.871261883889
Trimmed Mean ( 6 / 24 )117.0491803278691.4063529218211483.228881251441
Trimmed Mean ( 7 / 24 )116.8983050847461.3444465325240986.949017500368
Trimmed Mean ( 8 / 24 )116.8421052631581.312125223657889.0479834976712
Trimmed Mean ( 9 / 24 )116.7636363636361.2762961026576191.4863221163968
Trimmed Mean ( 10 / 24 )116.6792452830191.2417430001619293.964085376607
Trimmed Mean ( 11 / 24 )116.6078431372551.2042664128976596.8289424070863
Trimmed Mean ( 12 / 24 )116.5306122448981.1682819384758999.7452827156779
Trimmed Mean ( 13 / 24 )116.4255319148941.13913833773544102.204910552253
Trimmed Mean ( 14 / 24 )116.3333333333331.10827921945818104.9675310074
Trimmed Mean ( 15 / 24 )116.2558139534881.07529028415083108.115748525802
Trimmed Mean ( 16 / 24 )116.195121951221.03959391238934111.769721394543
Trimmed Mean ( 17 / 24 )116.1025641025640.998510950606756116.275704369605
Trimmed Mean ( 18 / 24 )115.9729729729730.949542711567426122.135604391649
Trimmed Mean ( 19 / 24 )115.9142857142860.916122105335721126.527113622925
Trimmed Mean ( 20 / 24 )115.9090909090910.89014345579846130.213944902982
Trimmed Mean ( 21 / 24 )115.9032258064520.87295670945354132.770874605003
Trimmed Mean ( 22 / 24 )115.8620689655170.856335614440506135.299836900065
Trimmed Mean ( 23 / 24 )115.8148148148150.828682813405542139.757713013094
Trimmed Mean ( 24 / 24 )115.80.8144.75
Median116
Midrange120.5
Midmean - Weighted Average at Xnp115.432432432432
Midmean - Weighted Average at X(n+1)p115.736842105263
Midmean - Empirical Distribution Function115.736842105263
Midmean - Empirical Distribution Function - Averaging115.736842105263
Midmean - Empirical Distribution Function - Interpolation115.736842105263
Midmean - Closest Observation115.736842105263
Midmean - True Basic - Statistics Graphics Toolkit115.736842105263
Midmean - MS Excel (old versions)115.736842105263
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.753424657534 & 1.87831703771883 & 62.690920804585 \tabularnewline
Geometric Mean & 116.697142490666 &  &  \tabularnewline
Harmonic Mean & 115.659910754145 &  &  \tabularnewline
Quadratic Mean & 118.827145093025 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 117.794520547945 & 1.86848400038824 & 63.0428307245175 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 117.767123287671 & 1.78159888214033 & 66.101929266026 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 117.72602739726 & 1.77139673003532 & 66.4594358796816 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 117.835616438356 & 1.7508438603208 & 67.3021844545097 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 117.698630136986 & 1.71767658056713 & 68.5219973704977 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 117.780821917808 & 1.60339330232528 & 73.4572245917451 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 117.205479452055 & 1.44705638650823 & 80.9957929385695 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 117.315068493151 & 1.42931856659496 & 82.0776216268065 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 117.315068493151 & 1.38675468310529 & 84.596843206942 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 117.178082191781 & 1.36148120635161 & 86.066617478904 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 117.178082191781 & 1.31136909903704 & 89.3555310078807 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 117.342465753425 & 1.2346807366037 & 95.0387110405599 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 117.164383561644 & 1.20375074955684 & 97.332760627379 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 116.972602739726 & 1.17138195887779 & 99.858634370456 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 116.767123287671 & 1.13768981187586 & 102.635289574354 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 116.986301369863 & 1.1068303832189 & 105.694877140653 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 117.219178082192 & 1.0754006324611 & 109.000473445817 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 116.479452054795 & 0.957647578558435 & 121.630811441233 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 115.958904109589 & 0.880716455477241 & 131.66428694324 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 115.958904109589 & 0.80391885389922 & 144.242050733302 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 116.246575342466 & 0.765201305056023 & 151.916331786647 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 116.246575342466 & 0.765201305056023 & 151.916331786647 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 115.931506849315 & 0.72157677820906 & 160.664132148286 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 115.931506849315 & 0.72157677820906 & 160.664132148286 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 117.676056338028 & 1.78657802105219 & 65.866732351674 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 117.550724637681 & 1.68837561121753 & 69.623562349916 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 117.432835820896 & 1.62789232291773 & 72.1379627925369 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 117.323076923077 & 1.56003385261403 & 75.2054686034457 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 117.174603174603 & 1.48564382483322 & 78.871261883889 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 117.049180327869 & 1.40635292182114 & 83.228881251441 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 116.898305084746 & 1.34444653252409 & 86.949017500368 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 116.842105263158 & 1.3121252236578 & 89.0479834976712 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 116.763636363636 & 1.27629610265761 & 91.4863221163968 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 116.679245283019 & 1.24174300016192 & 93.964085376607 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 116.607843137255 & 1.20426641289765 & 96.8289424070863 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 116.530612244898 & 1.16828193847589 & 99.7452827156779 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 116.425531914894 & 1.13913833773544 & 102.204910552253 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 116.333333333333 & 1.10827921945818 & 104.9675310074 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 116.255813953488 & 1.07529028415083 & 108.115748525802 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 116.19512195122 & 1.03959391238934 & 111.769721394543 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 116.102564102564 & 0.998510950606756 & 116.275704369605 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 115.972972972973 & 0.949542711567426 & 122.135604391649 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 115.914285714286 & 0.916122105335721 & 126.527113622925 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 115.909090909091 & 0.89014345579846 & 130.213944902982 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 115.903225806452 & 0.87295670945354 & 132.770874605003 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 115.862068965517 & 0.856335614440506 & 135.299836900065 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 115.814814814815 & 0.828682813405542 & 139.757713013094 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 115.8 & 0.8 & 144.75 \tabularnewline
Median & 116 &  &  \tabularnewline
Midrange & 120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.432432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.736842105263 &  &  \tabularnewline
Midmean - Closest Observation & 115.736842105263 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.736842105263 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.736842105263 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120248&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]117.753424657534[/C][C]1.87831703771883[/C][C]62.690920804585[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.697142490666[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.659910754145[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.827145093025[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]117.794520547945[/C][C]1.86848400038824[/C][C]63.0428307245175[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]117.767123287671[/C][C]1.78159888214033[/C][C]66.101929266026[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]117.72602739726[/C][C]1.77139673003532[/C][C]66.4594358796816[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]117.835616438356[/C][C]1.7508438603208[/C][C]67.3021844545097[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]117.698630136986[/C][C]1.71767658056713[/C][C]68.5219973704977[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]117.780821917808[/C][C]1.60339330232528[/C][C]73.4572245917451[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]117.205479452055[/C][C]1.44705638650823[/C][C]80.9957929385695[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]117.315068493151[/C][C]1.42931856659496[/C][C]82.0776216268065[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]117.315068493151[/C][C]1.38675468310529[/C][C]84.596843206942[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]117.178082191781[/C][C]1.36148120635161[/C][C]86.066617478904[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]117.178082191781[/C][C]1.31136909903704[/C][C]89.3555310078807[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]117.342465753425[/C][C]1.2346807366037[/C][C]95.0387110405599[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]117.164383561644[/C][C]1.20375074955684[/C][C]97.332760627379[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]116.972602739726[/C][C]1.17138195887779[/C][C]99.858634370456[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]116.767123287671[/C][C]1.13768981187586[/C][C]102.635289574354[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]116.986301369863[/C][C]1.1068303832189[/C][C]105.694877140653[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]117.219178082192[/C][C]1.0754006324611[/C][C]109.000473445817[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]116.479452054795[/C][C]0.957647578558435[/C][C]121.630811441233[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]115.958904109589[/C][C]0.880716455477241[/C][C]131.66428694324[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]115.958904109589[/C][C]0.80391885389922[/C][C]144.242050733302[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]116.246575342466[/C][C]0.765201305056023[/C][C]151.916331786647[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]116.246575342466[/C][C]0.765201305056023[/C][C]151.916331786647[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]115.931506849315[/C][C]0.72157677820906[/C][C]160.664132148286[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]115.931506849315[/C][C]0.72157677820906[/C][C]160.664132148286[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]117.676056338028[/C][C]1.78657802105219[/C][C]65.866732351674[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]117.550724637681[/C][C]1.68837561121753[/C][C]69.623562349916[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]117.432835820896[/C][C]1.62789232291773[/C][C]72.1379627925369[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]117.323076923077[/C][C]1.56003385261403[/C][C]75.2054686034457[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]117.174603174603[/C][C]1.48564382483322[/C][C]78.871261883889[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]117.049180327869[/C][C]1.40635292182114[/C][C]83.228881251441[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]116.898305084746[/C][C]1.34444653252409[/C][C]86.949017500368[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]116.842105263158[/C][C]1.3121252236578[/C][C]89.0479834976712[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]116.763636363636[/C][C]1.27629610265761[/C][C]91.4863221163968[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]116.679245283019[/C][C]1.24174300016192[/C][C]93.964085376607[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]116.607843137255[/C][C]1.20426641289765[/C][C]96.8289424070863[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]116.530612244898[/C][C]1.16828193847589[/C][C]99.7452827156779[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]116.425531914894[/C][C]1.13913833773544[/C][C]102.204910552253[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]116.333333333333[/C][C]1.10827921945818[/C][C]104.9675310074[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]116.255813953488[/C][C]1.07529028415083[/C][C]108.115748525802[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]116.19512195122[/C][C]1.03959391238934[/C][C]111.769721394543[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]116.102564102564[/C][C]0.998510950606756[/C][C]116.275704369605[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]115.972972972973[/C][C]0.949542711567426[/C][C]122.135604391649[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]115.914285714286[/C][C]0.916122105335721[/C][C]126.527113622925[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]115.909090909091[/C][C]0.89014345579846[/C][C]130.213944902982[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]115.903225806452[/C][C]0.87295670945354[/C][C]132.770874605003[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]115.862068965517[/C][C]0.856335614440506[/C][C]135.299836900065[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]115.814814814815[/C][C]0.828682813405542[/C][C]139.757713013094[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]115.8[/C][C]0.8[/C][C]144.75[/C][/ROW]
[ROW][C]Median[/C][C]116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.736842105263[/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=120248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120248&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 Mean117.7534246575341.8783170377188362.690920804585
Geometric Mean116.697142490666
Harmonic Mean115.659910754145
Quadratic Mean118.827145093025
Winsorized Mean ( 1 / 24 )117.7945205479451.8684840003882463.0428307245175
Winsorized Mean ( 2 / 24 )117.7671232876711.7815988821403366.101929266026
Winsorized Mean ( 3 / 24 )117.726027397261.7713967300353266.4594358796816
Winsorized Mean ( 4 / 24 )117.8356164383561.750843860320867.3021844545097
Winsorized Mean ( 5 / 24 )117.6986301369861.7176765805671368.5219973704977
Winsorized Mean ( 6 / 24 )117.7808219178081.6033933023252873.4572245917451
Winsorized Mean ( 7 / 24 )117.2054794520551.4470563865082380.9957929385695
Winsorized Mean ( 8 / 24 )117.3150684931511.4293185665949682.0776216268065
Winsorized Mean ( 9 / 24 )117.3150684931511.3867546831052984.596843206942
Winsorized Mean ( 10 / 24 )117.1780821917811.3614812063516186.066617478904
Winsorized Mean ( 11 / 24 )117.1780821917811.3113690990370489.3555310078807
Winsorized Mean ( 12 / 24 )117.3424657534251.234680736603795.0387110405599
Winsorized Mean ( 13 / 24 )117.1643835616441.2037507495568497.332760627379
Winsorized Mean ( 14 / 24 )116.9726027397261.1713819588777999.858634370456
Winsorized Mean ( 15 / 24 )116.7671232876711.13768981187586102.635289574354
Winsorized Mean ( 16 / 24 )116.9863013698631.1068303832189105.694877140653
Winsorized Mean ( 17 / 24 )117.2191780821921.0754006324611109.000473445817
Winsorized Mean ( 18 / 24 )116.4794520547950.957647578558435121.630811441233
Winsorized Mean ( 19 / 24 )115.9589041095890.880716455477241131.66428694324
Winsorized Mean ( 20 / 24 )115.9589041095890.80391885389922144.242050733302
Winsorized Mean ( 21 / 24 )116.2465753424660.765201305056023151.916331786647
Winsorized Mean ( 22 / 24 )116.2465753424660.765201305056023151.916331786647
Winsorized Mean ( 23 / 24 )115.9315068493150.72157677820906160.664132148286
Winsorized Mean ( 24 / 24 )115.9315068493150.72157677820906160.664132148286
Trimmed Mean ( 1 / 24 )117.6760563380281.7865780210521965.866732351674
Trimmed Mean ( 2 / 24 )117.5507246376811.6883756112175369.623562349916
Trimmed Mean ( 3 / 24 )117.4328358208961.6278923229177372.1379627925369
Trimmed Mean ( 4 / 24 )117.3230769230771.5600338526140375.2054686034457
Trimmed Mean ( 5 / 24 )117.1746031746031.4856438248332278.871261883889
Trimmed Mean ( 6 / 24 )117.0491803278691.4063529218211483.228881251441
Trimmed Mean ( 7 / 24 )116.8983050847461.3444465325240986.949017500368
Trimmed Mean ( 8 / 24 )116.8421052631581.312125223657889.0479834976712
Trimmed Mean ( 9 / 24 )116.7636363636361.2762961026576191.4863221163968
Trimmed Mean ( 10 / 24 )116.6792452830191.2417430001619293.964085376607
Trimmed Mean ( 11 / 24 )116.6078431372551.2042664128976596.8289424070863
Trimmed Mean ( 12 / 24 )116.5306122448981.1682819384758999.7452827156779
Trimmed Mean ( 13 / 24 )116.4255319148941.13913833773544102.204910552253
Trimmed Mean ( 14 / 24 )116.3333333333331.10827921945818104.9675310074
Trimmed Mean ( 15 / 24 )116.2558139534881.07529028415083108.115748525802
Trimmed Mean ( 16 / 24 )116.195121951221.03959391238934111.769721394543
Trimmed Mean ( 17 / 24 )116.1025641025640.998510950606756116.275704369605
Trimmed Mean ( 18 / 24 )115.9729729729730.949542711567426122.135604391649
Trimmed Mean ( 19 / 24 )115.9142857142860.916122105335721126.527113622925
Trimmed Mean ( 20 / 24 )115.9090909090910.89014345579846130.213944902982
Trimmed Mean ( 21 / 24 )115.9032258064520.87295670945354132.770874605003
Trimmed Mean ( 22 / 24 )115.8620689655170.856335614440506135.299836900065
Trimmed Mean ( 23 / 24 )115.8148148148150.828682813405542139.757713013094
Trimmed Mean ( 24 / 24 )115.80.8144.75
Median116
Midrange120.5
Midmean - Weighted Average at Xnp115.432432432432
Midmean - Weighted Average at X(n+1)p115.736842105263
Midmean - Empirical Distribution Function115.736842105263
Midmean - Empirical Distribution Function - Averaging115.736842105263
Midmean - Empirical Distribution Function - Interpolation115.736842105263
Midmean - Closest Observation115.736842105263
Midmean - True Basic - Statistics Graphics Toolkit115.736842105263
Midmean - MS Excel (old versions)115.736842105263
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')