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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Apr 2008 14:59:27 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/21/t1208811681boqkvgjwvmuz1wu.htm/, Retrieved Thu, 16 May 2024 19:16:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10609, Retrieved Thu, 16 May 2024 19:16:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-04-21 20:59:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
110.84 
110.84 
111.01 
112.66 
114.04 
114.16 
114.2 
114.2 
114.23 
114.23 
114.23 
114.23 
114.23 
114.23 
115.97 
116.96 
117.08 
117.08 
117.08 
117.63 
119.12 
119.47 
119.5 
119.52 
119.49 
119.49 
119.5 
119.5 
119.56 
122.35 
122.92 
122.92 
123.04 
123.04 
123.04 
123.06 
123.33 
128.21 
129.57 
129.79 
131.66 
135.01 
136.01 
136.31 
136.37 
136.4 
136.4 
136.4 
137.34 
142.18 
143.79 
144.08 
144.08 
144.09 
144.09 
144.11 
144.11 
144.15 
144.15 
144.16 
144.2 
144.38 
144.38 
144.28 
144.46 
144.53 
144.53 
145.34 
147.98 
150.42




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=10609&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=10609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10609&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 Mean128.4991428571431.5114376185117585.01782758568
Geometric Mean127.891263669177
Harmonic Mean127.291883485393
Quadratic Mean129.111023265140
Winsorized Mean ( 1 / 23 )128.4642857142861.5044968972818885.3868731443567
Winsorized Mean ( 2 / 23 )128.3937142857141.4903648888518986.149180812105
Winsorized Mean ( 3 / 23 )128.4297142857141.4732903552479487.1720321987044
Winsorized Mean ( 4 / 23 )128.5085714285711.4615151145473387.9283218828526
Winsorized Mean ( 5 / 23 )128.5121428571431.4594963522354988.0523905800125
Winsorized Mean ( 6 / 23 )128.5087142857141.4579243153798988.144983199782
Winsorized Mean ( 7 / 23 )128.5087142857141.4579243153798988.144983199782
Winsorized Mean ( 8 / 23 )128.5007142857141.455637620726788.2779563100071
Winsorized Mean ( 9 / 23 )128.4904285714291.4540243779758388.3688269039217
Winsorized Mean ( 10 / 23 )128.4847142857141.4531303216629288.4192645148856
Winsorized Mean ( 11 / 23 )128.4831428571431.4528846945033388.4331312341789
Winsorized Mean ( 12 / 23 )128.4831428571431.4528846945033388.4331312341789
Winsorized Mean ( 13 / 23 )128.4757142857141.4517245056224688.498688138234
Winsorized Mean ( 14 / 23 )128.8237142857141.4038620521058391.763798367849
Winsorized Mean ( 15 / 23 )129.0315714285711.3756126831586293.7993470169927
Winsorized Mean ( 16 / 23 )129.0591.372133294715994.0571885377373
Winsorized Mean ( 17 / 23 )129.0565714285711.3717477764302794.0818521057993
Winsorized Mean ( 18 / 23 )129.0565714285711.3717477764302794.0818521057994
Winsorized Mean ( 19 / 23 )129.1271428571431.3405369917332696.3249381803232
Winsorized Mean ( 20 / 23 )129.0928571428571.21637757947658106.128935061765
Winsorized Mean ( 21 / 23 )127.7458571428570.987173485456057129.405680992172
Winsorized Mean ( 22 / 23 )127.4567142857140.945337227097823134.826716469217
Winsorized Mean ( 23 / 23 )127.4567142857140.945337227097823134.826716469217
Trimmed Mean ( 1 / 23 )128.4364705882351.4992847689709385.6651606461598
Trimmed Mean ( 2 / 23 )128.4069696969701.4919819732079586.06469247137
Trimmed Mean ( 3 / 23 )128.414218751.4907284859703086.1419231996606
Trimmed Mean ( 4 / 23 )128.4083870967741.4949485221041385.8948553733745
Trimmed Mean ( 5 / 23 )128.3791666666671.5019642749230185.4741812505808
Trimmed Mean ( 6 / 23 )128.3470689655171.5086999770021285.0713004056316
Trimmed Mean ( 7 / 23 )128.3133928571431.5148377238705884.7043817533719
Trimmed Mean ( 8 / 23 )128.2772222222221.5197723499176484.4055507584236
Trimmed Mean ( 9 / 23 )128.2396153846151.5236815125048084.1643180232599
Trimmed Mean ( 10 / 23 )128.20061.5260751421839784.0067415137445
Trimmed Mean ( 11 / 23 )128.1591666666671.5263430846880283.9648490253172
Trimmed Mean ( 12 / 23 )128.1143478260871.5237309173284584.0793780378948
Trimmed Mean ( 13 / 23 )128.0654545454551.5173437572440684.4010817812696
Trimmed Mean ( 14 / 23 )128.0128571428571.5062874145873684.9856779676575
Trimmed Mean ( 15 / 23 )127.91151.4983943350578185.3657124878713
Trimmed Mean ( 16 / 23 )127.7739473684211.4896731547669285.7731422222028
Trimmed Mean ( 17 / 23 )127.6177777777781.4742873506341586.5623500892715
Trimmed Mean ( 18 / 23 )127.4435294117651.4489400442241687.9563857178125
Trimmed Mean ( 19 / 23 )127.24751.4092697147928390.2932197182044
Trimmed Mean ( 20 / 23 )127.0166666666671.3571452741026593.5910613921937
Trimmed Mean ( 21 / 23 )126.7571428571431.3154725202850596.3586398822501
Trimmed Mean ( 22 / 23 )126.6303846153851.3259056099099095.504826036591
Trimmed Mean ( 23 / 23 )126.5208333333331.3432589232996694.1894605267467
Median123.05
Midrange130.63
Midmean - Weighted Average at Xnp127.332972972973
Midmean - Weighted Average at X(n+1)p127.332972972973
Midmean - Empirical Distribution Function127.332972972973
Midmean - Empirical Distribution Function - Averaging127.332972972973
Midmean - Empirical Distribution Function - Interpolation127.332972972973
Midmean - Closest Observation127.332972972973
Midmean - True Basic - Statistics Graphics Toolkit127.332972972973
Midmean - MS Excel (old versions)127.332972972973
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 128.499142857143 & 1.51143761851175 & 85.01782758568 \tabularnewline
Geometric Mean & 127.891263669177 &  &  \tabularnewline
Harmonic Mean & 127.291883485393 &  &  \tabularnewline
Quadratic Mean & 129.111023265140 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 128.464285714286 & 1.50449689728188 & 85.3868731443567 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 128.393714285714 & 1.49036488885189 & 86.149180812105 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 128.429714285714 & 1.47329035524794 & 87.1720321987044 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 128.508571428571 & 1.46151511454733 & 87.9283218828526 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 128.512142857143 & 1.45949635223549 & 88.0523905800125 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 128.508714285714 & 1.45792431537989 & 88.144983199782 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 128.508714285714 & 1.45792431537989 & 88.144983199782 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 128.500714285714 & 1.4556376207267 & 88.2779563100071 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 128.490428571429 & 1.45402437797583 & 88.3688269039217 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 128.484714285714 & 1.45313032166292 & 88.4192645148856 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 128.483142857143 & 1.45288469450333 & 88.4331312341789 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 128.483142857143 & 1.45288469450333 & 88.4331312341789 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 128.475714285714 & 1.45172450562246 & 88.498688138234 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 128.823714285714 & 1.40386205210583 & 91.763798367849 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 129.031571428571 & 1.37561268315862 & 93.7993470169927 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 129.059 & 1.3721332947159 & 94.0571885377373 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 129.056571428571 & 1.37174777643027 & 94.0818521057993 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 129.056571428571 & 1.37174777643027 & 94.0818521057994 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 129.127142857143 & 1.34053699173326 & 96.3249381803232 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 129.092857142857 & 1.21637757947658 & 106.128935061765 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 127.745857142857 & 0.987173485456057 & 129.405680992172 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 127.456714285714 & 0.945337227097823 & 134.826716469217 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 127.456714285714 & 0.945337227097823 & 134.826716469217 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 128.436470588235 & 1.49928476897093 & 85.6651606461598 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 128.406969696970 & 1.49198197320795 & 86.06469247137 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 128.41421875 & 1.49072848597030 & 86.1419231996606 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 128.408387096774 & 1.49494852210413 & 85.8948553733745 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 128.379166666667 & 1.50196427492301 & 85.4741812505808 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 128.347068965517 & 1.50869997700212 & 85.0713004056316 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 128.313392857143 & 1.51483772387058 & 84.7043817533719 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 128.277222222222 & 1.51977234991764 & 84.4055507584236 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 128.239615384615 & 1.52368151250480 & 84.1643180232599 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 128.2006 & 1.52607514218397 & 84.0067415137445 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 128.159166666667 & 1.52634308468802 & 83.9648490253172 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 128.114347826087 & 1.52373091732845 & 84.0793780378948 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 128.065454545455 & 1.51734375724406 & 84.4010817812696 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 128.012857142857 & 1.50628741458736 & 84.9856779676575 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 127.9115 & 1.49839433505781 & 85.3657124878713 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 127.773947368421 & 1.48967315476692 & 85.7731422222028 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 127.617777777778 & 1.47428735063415 & 86.5623500892715 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 127.443529411765 & 1.44894004422416 & 87.9563857178125 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 127.2475 & 1.40926971479283 & 90.2932197182044 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 127.016666666667 & 1.35714527410265 & 93.5910613921937 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 126.757142857143 & 1.31547252028505 & 96.3586398822501 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 126.630384615385 & 1.32590560990990 & 95.504826036591 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 126.520833333333 & 1.34325892329966 & 94.1894605267467 \tabularnewline
Median & 123.05 &  &  \tabularnewline
Midrange & 130.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 127.332972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 127.332972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 127.332972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 127.332972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 127.332972972973 &  &  \tabularnewline
Midmean - Closest Observation & 127.332972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 127.332972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 127.332972972973 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10609&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]128.499142857143[/C][C]1.51143761851175[/C][C]85.01782758568[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]127.891263669177[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]127.291883485393[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]129.111023265140[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]128.464285714286[/C][C]1.50449689728188[/C][C]85.3868731443567[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]128.393714285714[/C][C]1.49036488885189[/C][C]86.149180812105[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]128.429714285714[/C][C]1.47329035524794[/C][C]87.1720321987044[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]128.508571428571[/C][C]1.46151511454733[/C][C]87.9283218828526[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]128.512142857143[/C][C]1.45949635223549[/C][C]88.0523905800125[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]128.508714285714[/C][C]1.45792431537989[/C][C]88.144983199782[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]128.508714285714[/C][C]1.45792431537989[/C][C]88.144983199782[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]128.500714285714[/C][C]1.4556376207267[/C][C]88.2779563100071[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]128.490428571429[/C][C]1.45402437797583[/C][C]88.3688269039217[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]128.484714285714[/C][C]1.45313032166292[/C][C]88.4192645148856[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]128.483142857143[/C][C]1.45288469450333[/C][C]88.4331312341789[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]128.483142857143[/C][C]1.45288469450333[/C][C]88.4331312341789[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]128.475714285714[/C][C]1.45172450562246[/C][C]88.498688138234[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]128.823714285714[/C][C]1.40386205210583[/C][C]91.763798367849[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]129.031571428571[/C][C]1.37561268315862[/C][C]93.7993470169927[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]129.059[/C][C]1.3721332947159[/C][C]94.0571885377373[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]129.056571428571[/C][C]1.37174777643027[/C][C]94.0818521057993[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]129.056571428571[/C][C]1.37174777643027[/C][C]94.0818521057994[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]129.127142857143[/C][C]1.34053699173326[/C][C]96.3249381803232[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]129.092857142857[/C][C]1.21637757947658[/C][C]106.128935061765[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]127.745857142857[/C][C]0.987173485456057[/C][C]129.405680992172[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]127.456714285714[/C][C]0.945337227097823[/C][C]134.826716469217[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]127.456714285714[/C][C]0.945337227097823[/C][C]134.826716469217[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]128.436470588235[/C][C]1.49928476897093[/C][C]85.6651606461598[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]128.406969696970[/C][C]1.49198197320795[/C][C]86.06469247137[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]128.41421875[/C][C]1.49072848597030[/C][C]86.1419231996606[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]128.408387096774[/C][C]1.49494852210413[/C][C]85.8948553733745[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]128.379166666667[/C][C]1.50196427492301[/C][C]85.4741812505808[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]128.347068965517[/C][C]1.50869997700212[/C][C]85.0713004056316[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]128.313392857143[/C][C]1.51483772387058[/C][C]84.7043817533719[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]128.277222222222[/C][C]1.51977234991764[/C][C]84.4055507584236[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]128.239615384615[/C][C]1.52368151250480[/C][C]84.1643180232599[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]128.2006[/C][C]1.52607514218397[/C][C]84.0067415137445[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]128.159166666667[/C][C]1.52634308468802[/C][C]83.9648490253172[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]128.114347826087[/C][C]1.52373091732845[/C][C]84.0793780378948[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]128.065454545455[/C][C]1.51734375724406[/C][C]84.4010817812696[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]128.012857142857[/C][C]1.50628741458736[/C][C]84.9856779676575[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]127.9115[/C][C]1.49839433505781[/C][C]85.3657124878713[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]127.773947368421[/C][C]1.48967315476692[/C][C]85.7731422222028[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]127.617777777778[/C][C]1.47428735063415[/C][C]86.5623500892715[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]127.443529411765[/C][C]1.44894004422416[/C][C]87.9563857178125[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]127.2475[/C][C]1.40926971479283[/C][C]90.2932197182044[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]127.016666666667[/C][C]1.35714527410265[/C][C]93.5910613921937[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]126.757142857143[/C][C]1.31547252028505[/C][C]96.3586398822501[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]126.630384615385[/C][C]1.32590560990990[/C][C]95.504826036591[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]126.520833333333[/C][C]1.34325892329966[/C][C]94.1894605267467[/C][/ROW]
[ROW][C]Median[/C][C]123.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]130.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]127.332972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10609&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 Mean128.4991428571431.5114376185117585.01782758568
Geometric Mean127.891263669177
Harmonic Mean127.291883485393
Quadratic Mean129.111023265140
Winsorized Mean ( 1 / 23 )128.4642857142861.5044968972818885.3868731443567
Winsorized Mean ( 2 / 23 )128.3937142857141.4903648888518986.149180812105
Winsorized Mean ( 3 / 23 )128.4297142857141.4732903552479487.1720321987044
Winsorized Mean ( 4 / 23 )128.5085714285711.4615151145473387.9283218828526
Winsorized Mean ( 5 / 23 )128.5121428571431.4594963522354988.0523905800125
Winsorized Mean ( 6 / 23 )128.5087142857141.4579243153798988.144983199782
Winsorized Mean ( 7 / 23 )128.5087142857141.4579243153798988.144983199782
Winsorized Mean ( 8 / 23 )128.5007142857141.455637620726788.2779563100071
Winsorized Mean ( 9 / 23 )128.4904285714291.4540243779758388.3688269039217
Winsorized Mean ( 10 / 23 )128.4847142857141.4531303216629288.4192645148856
Winsorized Mean ( 11 / 23 )128.4831428571431.4528846945033388.4331312341789
Winsorized Mean ( 12 / 23 )128.4831428571431.4528846945033388.4331312341789
Winsorized Mean ( 13 / 23 )128.4757142857141.4517245056224688.498688138234
Winsorized Mean ( 14 / 23 )128.8237142857141.4038620521058391.763798367849
Winsorized Mean ( 15 / 23 )129.0315714285711.3756126831586293.7993470169927
Winsorized Mean ( 16 / 23 )129.0591.372133294715994.0571885377373
Winsorized Mean ( 17 / 23 )129.0565714285711.3717477764302794.0818521057993
Winsorized Mean ( 18 / 23 )129.0565714285711.3717477764302794.0818521057994
Winsorized Mean ( 19 / 23 )129.1271428571431.3405369917332696.3249381803232
Winsorized Mean ( 20 / 23 )129.0928571428571.21637757947658106.128935061765
Winsorized Mean ( 21 / 23 )127.7458571428570.987173485456057129.405680992172
Winsorized Mean ( 22 / 23 )127.4567142857140.945337227097823134.826716469217
Winsorized Mean ( 23 / 23 )127.4567142857140.945337227097823134.826716469217
Trimmed Mean ( 1 / 23 )128.4364705882351.4992847689709385.6651606461598
Trimmed Mean ( 2 / 23 )128.4069696969701.4919819732079586.06469247137
Trimmed Mean ( 3 / 23 )128.414218751.4907284859703086.1419231996606
Trimmed Mean ( 4 / 23 )128.4083870967741.4949485221041385.8948553733745
Trimmed Mean ( 5 / 23 )128.3791666666671.5019642749230185.4741812505808
Trimmed Mean ( 6 / 23 )128.3470689655171.5086999770021285.0713004056316
Trimmed Mean ( 7 / 23 )128.3133928571431.5148377238705884.7043817533719
Trimmed Mean ( 8 / 23 )128.2772222222221.5197723499176484.4055507584236
Trimmed Mean ( 9 / 23 )128.2396153846151.5236815125048084.1643180232599
Trimmed Mean ( 10 / 23 )128.20061.5260751421839784.0067415137445
Trimmed Mean ( 11 / 23 )128.1591666666671.5263430846880283.9648490253172
Trimmed Mean ( 12 / 23 )128.1143478260871.5237309173284584.0793780378948
Trimmed Mean ( 13 / 23 )128.0654545454551.5173437572440684.4010817812696
Trimmed Mean ( 14 / 23 )128.0128571428571.5062874145873684.9856779676575
Trimmed Mean ( 15 / 23 )127.91151.4983943350578185.3657124878713
Trimmed Mean ( 16 / 23 )127.7739473684211.4896731547669285.7731422222028
Trimmed Mean ( 17 / 23 )127.6177777777781.4742873506341586.5623500892715
Trimmed Mean ( 18 / 23 )127.4435294117651.4489400442241687.9563857178125
Trimmed Mean ( 19 / 23 )127.24751.4092697147928390.2932197182044
Trimmed Mean ( 20 / 23 )127.0166666666671.3571452741026593.5910613921937
Trimmed Mean ( 21 / 23 )126.7571428571431.3154725202850596.3586398822501
Trimmed Mean ( 22 / 23 )126.6303846153851.3259056099099095.504826036591
Trimmed Mean ( 23 / 23 )126.5208333333331.3432589232996694.1894605267467
Median123.05
Midrange130.63
Midmean - Weighted Average at Xnp127.332972972973
Midmean - Weighted Average at X(n+1)p127.332972972973
Midmean - Empirical Distribution Function127.332972972973
Midmean - Empirical Distribution Function - Averaging127.332972972973
Midmean - Empirical Distribution Function - Interpolation127.332972972973
Midmean - Closest Observation127.332972972973
Midmean - True Basic - Statistics Graphics Toolkit127.332972972973
Midmean - MS Excel (old versions)127.332972972973
Number of observations70



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')