Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Apr 2008 01:11:59 -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/t1208761998ihaqdik2p4n86lv.htm/, Retrieved Thu, 16 May 2024 19:31:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10458, Retrieved Thu, 16 May 2024 19:31:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact255
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Central Tendency ...] [-0001-11-30 00:00:00] [ae8cb49fb5e8aeb2fdfa69938caf5918]
- RM D    [Central Tendency] [Central Tendency ...] [2008-04-21 07:11:59] [e1b1b3318b3a8a01c97d416cfdcee2a5] [Current]
Feedback Forum

Post a new message
Dataseries X:
229,7
231,5
226,4
242,1
228,3
209,9
209,3
220,8
239,6
241,1
241,9
240,8
179,9
190,8
174,2
170
170,3
159,3
147,9
154,2
164,5
173,9
163,6
149,7
128,2
124,7
125,1
120,9
117,5
114
113,4
118,9
121,7
121,9
120,3
115,6
105,7
105,1
104,6
105
104,9
105,1
103,9
101,9
99
97
95,8
94,7
97,6
97,9
99,3
99,7
99,7
100
99,1
98,2
98,1
98,6
100,2
101,9
97,5
97,1
98,1
98,5
98,3
99,3
100,9
100,4
101,7
102
103,2
103,1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10458&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10458&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean136.3194444444445.7671889227569423.6370693365943
Geometric Mean129.096947736812
Harmonic Mean123.353329622673
Quadratic Mean144.722092876888
Winsorized Mean ( 1 / 24 )136.3319444444445.7649390293806323.6484624988465
Winsorized Mean ( 2 / 24 )136.3430555555565.7559701694419723.6872415147999
Winsorized Mean ( 3 / 24 )136.3347222222225.7523687574156723.7006228167250
Winsorized Mean ( 4 / 24 )136.2902777777785.7332566185643823.7718781567299
Winsorized Mean ( 5 / 24 )135.7347222222225.5933468329708824.267174247467
Winsorized Mean ( 6 / 24 )135.6097222222225.554972521734324.4123119766368
Winsorized Mean ( 7 / 24 )135.4930555555565.5207661485464324.542437029547
Winsorized Mean ( 8 / 24 )135.2819444444445.4710124310131924.7270402234110
Winsorized Mean ( 9 / 24 )134.5944444444445.3076136328948425.3587494783480
Winsorized Mean ( 10 / 24 )133.0944444444444.9680028171246126.7903319188287
Winsorized Mean ( 11 / 24 )133.0333333333334.9450568891502926.9022857199511
Winsorized Mean ( 12 / 24 )129.9666666666674.2993307518645330.2295110954892
Winsorized Mean ( 13 / 24 )128.0708333333333.9115041581150732.7420931069775
Winsorized Mean ( 14 / 24 )126.9819444444443.7064953383522934.2593023470235
Winsorized Mean ( 15 / 24 )126.9611111111113.6908843613899934.3985610709563
Winsorized Mean ( 16 / 24 )126.1611111111113.5491405843034835.5469466802962
Winsorized Mean ( 17 / 24 )126.1847222222223.5267109853941935.7797173470732
Winsorized Mean ( 18 / 24 )124.8097222222223.2894536506427637.9423866324532
Winsorized Mean ( 19 / 24 )124.6513888888893.2406739872214338.4646494465077
Winsorized Mean ( 20 / 24 )123.51253.0343269135139540.7050734876039
Winsorized Mean ( 21 / 24 )122.0833333333332.7834387542937843.8606141935063
Winsorized Mean ( 22 / 24 )120.8611111111112.5450822163712247.4880969792147
Winsorized Mean ( 23 / 24 )120.5416666666672.4254194335815449.6993076734223
Winsorized Mean ( 24 / 24 )114.0416666666671.4190710747457280.363604541162
Trimmed Mean ( 1 / 24 )135.4028571428575.7021843809184223.7457872453168
Trimmed Mean ( 2 / 24 )134.4191176470595.6233702184268123.9036578467821
Trimmed Mean ( 3 / 24 )133.3696969696975.5305356913731524.1151498538803
Trimmed Mean ( 4 / 24 )132.25781255.416245315428624.4187264050343
Trimmed Mean ( 5 / 24 )131.0870967741945.2807526364683324.8235631922843
Trimmed Mean ( 6 / 24 )129.9716666666675.1581590744823725.1972970957104
Trimmed Mean ( 7 / 24 )128.8051724137935.0146225518025325.6859157560111
Trimmed Mean ( 8 / 24 )127.5767857142864.8419031295605526.3484795751923
Trimmed Mean ( 9 / 24 )126.2925925925934.6349490055533527.2478925747134
Trimmed Mean ( 10 / 24 )125.0153846153854.41434175806328.3202777372273
Trimmed Mean ( 11 / 24 )123.8524.2229298659889229.3284529770414
Trimmed Mean ( 12 / 24 )122.63.9764298913536830.8316764911612
Trimmed Mean ( 13 / 24 )121.6391304347833.8323659500975831.7399569922819
Trimmed Mean ( 14 / 24 )120.8295454545453.7401351282321532.3061978543161
Trimmed Mean ( 15 / 24 )120.0761904761903.664345917748832.7687923497025
Trimmed Mean ( 16 / 24 )119.253.5595735843727333.5012037743882
Trimmed Mean ( 17 / 24 )118.4315789473683.4501656530687534.3263457051778
Trimmed Mean ( 18 / 24 )117.5194444444443.2969919417853535.6444439414695
Trimmed Mean ( 19 / 24 )116.6617647058823.1519284047316337.0128219063452
Trimmed Mean ( 20 / 24 )115.7156252.9507418059093439.2157744090861
Trimmed Mean ( 21 / 24 )114.782.7271786608647142.0874516389793
Trimmed Mean ( 22 / 24 )113.8857142857142.4900633971536345.73607018034
Trimmed Mean ( 23 / 24 )113.0076923076922.2244025858430750.8036148793009
Trimmed Mean ( 24 / 24 )112.0251.8295407081829461.2312147518491
Median109.55
Midrange168.4
Midmean - Weighted Average at Xnp117.037837837838
Midmean - Weighted Average at X(n+1)p117.037837837838
Midmean - Empirical Distribution Function117.037837837838
Midmean - Empirical Distribution Function - Averaging117.037837837838
Midmean - Empirical Distribution Function - Interpolation117.037837837838
Midmean - Closest Observation117.037837837838
Midmean - True Basic - Statistics Graphics Toolkit117.037837837838
Midmean - MS Excel (old versions)118.431578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 136.319444444444 & 5.76718892275694 & 23.6370693365943 \tabularnewline
Geometric Mean & 129.096947736812 &  &  \tabularnewline
Harmonic Mean & 123.353329622673 &  &  \tabularnewline
Quadratic Mean & 144.722092876888 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 136.331944444444 & 5.76493902938063 & 23.6484624988465 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 136.343055555556 & 5.75597016944197 & 23.6872415147999 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 136.334722222222 & 5.75236875741567 & 23.7006228167250 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 136.290277777778 & 5.73325661856438 & 23.7718781567299 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 135.734722222222 & 5.59334683297088 & 24.267174247467 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 135.609722222222 & 5.5549725217343 & 24.4123119766368 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 135.493055555556 & 5.52076614854643 & 24.542437029547 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 135.281944444444 & 5.47101243101319 & 24.7270402234110 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 134.594444444444 & 5.30761363289484 & 25.3587494783480 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 133.094444444444 & 4.96800281712461 & 26.7903319188287 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 133.033333333333 & 4.94505688915029 & 26.9022857199511 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 129.966666666667 & 4.29933075186453 & 30.2295110954892 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 128.070833333333 & 3.91150415811507 & 32.7420931069775 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 126.981944444444 & 3.70649533835229 & 34.2593023470235 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 126.961111111111 & 3.69088436138999 & 34.3985610709563 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 126.161111111111 & 3.54914058430348 & 35.5469466802962 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 126.184722222222 & 3.52671098539419 & 35.7797173470732 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 124.809722222222 & 3.28945365064276 & 37.9423866324532 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 124.651388888889 & 3.24067398722143 & 38.4646494465077 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 123.5125 & 3.03432691351395 & 40.7050734876039 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 122.083333333333 & 2.78343875429378 & 43.8606141935063 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 120.861111111111 & 2.54508221637122 & 47.4880969792147 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 120.541666666667 & 2.42541943358154 & 49.6993076734223 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 114.041666666667 & 1.41907107474572 & 80.363604541162 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 135.402857142857 & 5.70218438091842 & 23.7457872453168 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 134.419117647059 & 5.62337021842681 & 23.9036578467821 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 133.369696969697 & 5.53053569137315 & 24.1151498538803 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 132.2578125 & 5.4162453154286 & 24.4187264050343 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 131.087096774194 & 5.28075263646833 & 24.8235631922843 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 129.971666666667 & 5.15815907448237 & 25.1972970957104 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 128.805172413793 & 5.01462255180253 & 25.6859157560111 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 127.576785714286 & 4.84190312956055 & 26.3484795751923 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 126.292592592593 & 4.63494900555335 & 27.2478925747134 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 125.015384615385 & 4.414341758063 & 28.3202777372273 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 123.852 & 4.22292986598892 & 29.3284529770414 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 122.6 & 3.97642989135368 & 30.8316764911612 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 121.639130434783 & 3.83236595009758 & 31.7399569922819 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 120.829545454545 & 3.74013512823215 & 32.3061978543161 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 120.076190476190 & 3.6643459177488 & 32.7687923497025 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 119.25 & 3.55957358437273 & 33.5012037743882 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 118.431578947368 & 3.45016565306875 & 34.3263457051778 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 117.519444444444 & 3.29699194178535 & 35.6444439414695 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 116.661764705882 & 3.15192840473163 & 37.0128219063452 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 115.715625 & 2.95074180590934 & 39.2157744090861 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 114.78 & 2.72717866086471 & 42.0874516389793 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 113.885714285714 & 2.49006339715363 & 45.73607018034 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 113.007692307692 & 2.22440258584307 & 50.8036148793009 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.025 & 1.82954070818294 & 61.2312147518491 \tabularnewline
Median & 109.55 &  &  \tabularnewline
Midrange & 168.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117.037837837838 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117.037837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117.037837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117.037837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117.037837837838 &  &  \tabularnewline
Midmean - Closest Observation & 117.037837837838 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117.037837837838 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.431578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10458&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]136.319444444444[/C][C]5.76718892275694[/C][C]23.6370693365943[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]129.096947736812[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]123.353329622673[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]144.722092876888[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]136.331944444444[/C][C]5.76493902938063[/C][C]23.6484624988465[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]136.343055555556[/C][C]5.75597016944197[/C][C]23.6872415147999[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]136.334722222222[/C][C]5.75236875741567[/C][C]23.7006228167250[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]136.290277777778[/C][C]5.73325661856438[/C][C]23.7718781567299[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]135.734722222222[/C][C]5.59334683297088[/C][C]24.267174247467[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]135.609722222222[/C][C]5.5549725217343[/C][C]24.4123119766368[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]135.493055555556[/C][C]5.52076614854643[/C][C]24.542437029547[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]135.281944444444[/C][C]5.47101243101319[/C][C]24.7270402234110[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]134.594444444444[/C][C]5.30761363289484[/C][C]25.3587494783480[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]133.094444444444[/C][C]4.96800281712461[/C][C]26.7903319188287[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]133.033333333333[/C][C]4.94505688915029[/C][C]26.9022857199511[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]129.966666666667[/C][C]4.29933075186453[/C][C]30.2295110954892[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]128.070833333333[/C][C]3.91150415811507[/C][C]32.7420931069775[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]126.981944444444[/C][C]3.70649533835229[/C][C]34.2593023470235[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]126.961111111111[/C][C]3.69088436138999[/C][C]34.3985610709563[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]126.161111111111[/C][C]3.54914058430348[/C][C]35.5469466802962[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]126.184722222222[/C][C]3.52671098539419[/C][C]35.7797173470732[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]124.809722222222[/C][C]3.28945365064276[/C][C]37.9423866324532[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]124.651388888889[/C][C]3.24067398722143[/C][C]38.4646494465077[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]123.5125[/C][C]3.03432691351395[/C][C]40.7050734876039[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]122.083333333333[/C][C]2.78343875429378[/C][C]43.8606141935063[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]120.861111111111[/C][C]2.54508221637122[/C][C]47.4880969792147[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]120.541666666667[/C][C]2.42541943358154[/C][C]49.6993076734223[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]114.041666666667[/C][C]1.41907107474572[/C][C]80.363604541162[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]135.402857142857[/C][C]5.70218438091842[/C][C]23.7457872453168[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]134.419117647059[/C][C]5.62337021842681[/C][C]23.9036578467821[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]133.369696969697[/C][C]5.53053569137315[/C][C]24.1151498538803[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]132.2578125[/C][C]5.4162453154286[/C][C]24.4187264050343[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]131.087096774194[/C][C]5.28075263646833[/C][C]24.8235631922843[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]129.971666666667[/C][C]5.15815907448237[/C][C]25.1972970957104[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]128.805172413793[/C][C]5.01462255180253[/C][C]25.6859157560111[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]127.576785714286[/C][C]4.84190312956055[/C][C]26.3484795751923[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]126.292592592593[/C][C]4.63494900555335[/C][C]27.2478925747134[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]125.015384615385[/C][C]4.414341758063[/C][C]28.3202777372273[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]123.852[/C][C]4.22292986598892[/C][C]29.3284529770414[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]122.6[/C][C]3.97642989135368[/C][C]30.8316764911612[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]121.639130434783[/C][C]3.83236595009758[/C][C]31.7399569922819[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]120.829545454545[/C][C]3.74013512823215[/C][C]32.3061978543161[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]120.076190476190[/C][C]3.6643459177488[/C][C]32.7687923497025[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]119.25[/C][C]3.55957358437273[/C][C]33.5012037743882[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]118.431578947368[/C][C]3.45016565306875[/C][C]34.3263457051778[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]117.519444444444[/C][C]3.29699194178535[/C][C]35.6444439414695[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]116.661764705882[/C][C]3.15192840473163[/C][C]37.0128219063452[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]115.715625[/C][C]2.95074180590934[/C][C]39.2157744090861[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]114.78[/C][C]2.72717866086471[/C][C]42.0874516389793[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]113.885714285714[/C][C]2.49006339715363[/C][C]45.73607018034[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]113.007692307692[/C][C]2.22440258584307[/C][C]50.8036148793009[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.025[/C][C]1.82954070818294[/C][C]61.2312147518491[/C][/ROW]
[ROW][C]Median[/C][C]109.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]168.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117.037837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.431578947368[/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=10458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10458&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 Mean136.3194444444445.7671889227569423.6370693365943
Geometric Mean129.096947736812
Harmonic Mean123.353329622673
Quadratic Mean144.722092876888
Winsorized Mean ( 1 / 24 )136.3319444444445.7649390293806323.6484624988465
Winsorized Mean ( 2 / 24 )136.3430555555565.7559701694419723.6872415147999
Winsorized Mean ( 3 / 24 )136.3347222222225.7523687574156723.7006228167250
Winsorized Mean ( 4 / 24 )136.2902777777785.7332566185643823.7718781567299
Winsorized Mean ( 5 / 24 )135.7347222222225.5933468329708824.267174247467
Winsorized Mean ( 6 / 24 )135.6097222222225.554972521734324.4123119766368
Winsorized Mean ( 7 / 24 )135.4930555555565.5207661485464324.542437029547
Winsorized Mean ( 8 / 24 )135.2819444444445.4710124310131924.7270402234110
Winsorized Mean ( 9 / 24 )134.5944444444445.3076136328948425.3587494783480
Winsorized Mean ( 10 / 24 )133.0944444444444.9680028171246126.7903319188287
Winsorized Mean ( 11 / 24 )133.0333333333334.9450568891502926.9022857199511
Winsorized Mean ( 12 / 24 )129.9666666666674.2993307518645330.2295110954892
Winsorized Mean ( 13 / 24 )128.0708333333333.9115041581150732.7420931069775
Winsorized Mean ( 14 / 24 )126.9819444444443.7064953383522934.2593023470235
Winsorized Mean ( 15 / 24 )126.9611111111113.6908843613899934.3985610709563
Winsorized Mean ( 16 / 24 )126.1611111111113.5491405843034835.5469466802962
Winsorized Mean ( 17 / 24 )126.1847222222223.5267109853941935.7797173470732
Winsorized Mean ( 18 / 24 )124.8097222222223.2894536506427637.9423866324532
Winsorized Mean ( 19 / 24 )124.6513888888893.2406739872214338.4646494465077
Winsorized Mean ( 20 / 24 )123.51253.0343269135139540.7050734876039
Winsorized Mean ( 21 / 24 )122.0833333333332.7834387542937843.8606141935063
Winsorized Mean ( 22 / 24 )120.8611111111112.5450822163712247.4880969792147
Winsorized Mean ( 23 / 24 )120.5416666666672.4254194335815449.6993076734223
Winsorized Mean ( 24 / 24 )114.0416666666671.4190710747457280.363604541162
Trimmed Mean ( 1 / 24 )135.4028571428575.7021843809184223.7457872453168
Trimmed Mean ( 2 / 24 )134.4191176470595.6233702184268123.9036578467821
Trimmed Mean ( 3 / 24 )133.3696969696975.5305356913731524.1151498538803
Trimmed Mean ( 4 / 24 )132.25781255.416245315428624.4187264050343
Trimmed Mean ( 5 / 24 )131.0870967741945.2807526364683324.8235631922843
Trimmed Mean ( 6 / 24 )129.9716666666675.1581590744823725.1972970957104
Trimmed Mean ( 7 / 24 )128.8051724137935.0146225518025325.6859157560111
Trimmed Mean ( 8 / 24 )127.5767857142864.8419031295605526.3484795751923
Trimmed Mean ( 9 / 24 )126.2925925925934.6349490055533527.2478925747134
Trimmed Mean ( 10 / 24 )125.0153846153854.41434175806328.3202777372273
Trimmed Mean ( 11 / 24 )123.8524.2229298659889229.3284529770414
Trimmed Mean ( 12 / 24 )122.63.9764298913536830.8316764911612
Trimmed Mean ( 13 / 24 )121.6391304347833.8323659500975831.7399569922819
Trimmed Mean ( 14 / 24 )120.8295454545453.7401351282321532.3061978543161
Trimmed Mean ( 15 / 24 )120.0761904761903.664345917748832.7687923497025
Trimmed Mean ( 16 / 24 )119.253.5595735843727333.5012037743882
Trimmed Mean ( 17 / 24 )118.4315789473683.4501656530687534.3263457051778
Trimmed Mean ( 18 / 24 )117.5194444444443.2969919417853535.6444439414695
Trimmed Mean ( 19 / 24 )116.6617647058823.1519284047316337.0128219063452
Trimmed Mean ( 20 / 24 )115.7156252.9507418059093439.2157744090861
Trimmed Mean ( 21 / 24 )114.782.7271786608647142.0874516389793
Trimmed Mean ( 22 / 24 )113.8857142857142.4900633971536345.73607018034
Trimmed Mean ( 23 / 24 )113.0076923076922.2244025858430750.8036148793009
Trimmed Mean ( 24 / 24 )112.0251.8295407081829461.2312147518491
Median109.55
Midrange168.4
Midmean - Weighted Average at Xnp117.037837837838
Midmean - Weighted Average at X(n+1)p117.037837837838
Midmean - Empirical Distribution Function117.037837837838
Midmean - Empirical Distribution Function - Averaging117.037837837838
Midmean - Empirical Distribution Function - Interpolation117.037837837838
Midmean - Closest Observation117.037837837838
Midmean - True Basic - Statistics Graphics Toolkit117.037837837838
Midmean - MS Excel (old versions)118.431578947368
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')