Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Nov 2008 02:55:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/04/t1225792573nsckqew5n65g7ic.htm/, Retrieved Mon, 20 May 2024 09:26:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21466, Retrieved Mon, 20 May 2024 09:26:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5-oefening...] [2008-11-04 09:55:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
113,9000
112,0000
113,8500
113,0800
111,7200
110,6900
113,5300
113,9900
112,7400
112,1500
115,8200
118,3800
118,8100
123,8500
117,9600
120,1600
118,7400
119,8400
124,8100
121,3300
120,2000
118,3200
129,5800
130,2000
127,1900
133,1000
129,1200
123,2800
123,3600
124,1300
126,9700
127,1400
123,7000
123,6700
130,1900
134,0100
124,9600
129,9600
128,3200
132,3800
126,2500
128,9100
131,4200
129,4400
126,8600
126,7100
131,6300
132,7800
126,6100
132,8400
123,1400
128,1300
125,4900
126,4800
130,8600
127,3200
126,5600
126,6400
129,2600
126,4700
135,4000
135,5000
132,2200
122,6200
125,1600
128,5000
133,8600
128,8700
125,0700
125,2500
132,1600
130,2400




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21466&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21466&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean124.80250.771037772661048161.863016865276
Geometric Mean124.629577037281
Harmonic Mean124.452844358790
Quadratic Mean124.971490559958
Winsorized Mean ( 1 / 24 )124.8154166666670.767203296003268162.688843122664
Winsorized Mean ( 2 / 24 )124.7845833333330.75828279606406164.562065737268
Winsorized Mean ( 3 / 24 )124.7845833333330.755740833392926165.11557642467
Winsorized Mean ( 4 / 24 )124.7751388888890.741220364558536168.337440328159
Winsorized Mean ( 5 / 24 )124.7806944444440.733040042886682170.223571898014
Winsorized Mean ( 6 / 24 )124.8131944444440.723933510183784172.409748531683
Winsorized Mean ( 7 / 24 )124.8054166666670.711212071757294175.482702871300
Winsorized Mean ( 8 / 24 )124.7931944444440.707359032401114176.421292057072
Winsorized Mean ( 9 / 24 )124.7969444444440.703815380024057177.314886810485
Winsorized Mean ( 10 / 24 )124.97750.639809450249923195.335501767255
Winsorized Mean ( 11 / 24 )125.2723611111110.572477746697487218.824857094940
Winsorized Mean ( 12 / 24 )125.2390277777780.547935917733255228.565099904158
Winsorized Mean ( 13 / 24 )125.1379166666670.530320714429092235.96648831902
Winsorized Mean ( 14 / 24 )125.2001388888890.51681867720867242.251575668846
Winsorized Mean ( 15 / 24 )125.2126388888890.513971578753015243.617826481139
Winsorized Mean ( 16 / 24 )125.3904166666670.467717940525774268.089816109495
Winsorized Mean ( 17 / 24 )125.376250.442962508503542283.040319650433
Winsorized Mean ( 18 / 24 )125.351250.436655150615984287.071502129698
Winsorized Mean ( 19 / 24 )125.6019444444440.381979474848264328.81856935988
Winsorized Mean ( 20 / 24 )125.9213888888890.322382520094897390.596204942570
Winsorized Mean ( 21 / 24 )126.0118055555560.292376555708907430.991483739257
Winsorized Mean ( 22 / 24 )126.0423611111110.284787245428352442.584291025848
Winsorized Mean ( 23 / 24 )125.9497222222220.264999407403464475.283033484156
Winsorized Mean ( 24 / 24 )125.9930555555560.242802466040225518.91176234875
Trimmed Mean ( 1 / 24 )124.8512857142860.751163953162826166.210432740537
Trimmed Mean ( 2 / 24 )124.8892647058820.732044394447727170.603402816986
Trimmed Mean ( 3 / 24 )124.9463636363640.71480744261441174.797233754831
Trimmed Mean ( 4 / 24 )125.007031250.6951751834601179.820905901447
Trimmed Mean ( 5 / 24 )125.0743548387100.676781493465815184.807587155200
Trimmed Mean ( 6 / 24 )125.1448333333330.656951893588596190.493146537306
Trimmed Mean ( 7 / 24 )125.2134482758620.635304470009684197.092030965804
Trimmed Mean ( 8 / 24 )125.2883928571430.611984889507973204.724650894359
Trimmed Mean ( 9 / 24 )125.3709259259260.583798273443292214.750422584290
Trimmed Mean ( 10 / 24 )125.4592307692310.549030947084268228.510307907971
Trimmed Mean ( 11 / 24 )125.52860.522229053663042240.370770487609
Trimmed Mean ( 12 / 24 )125.5635416666670.505344178197631248.471333170402
Trimmed Mean ( 13 / 24 )125.6058695652170.48926500886257256.72359005853
Trimmed Mean ( 14 / 24 )125.6647727272730.472094483931555266.185640808063
Trimmed Mean ( 15 / 24 )125.7216666666670.452775274380354277.669019887897
Trimmed Mean ( 16 / 24 )125.782750.427524926173902294.211500428015
Trimmed Mean ( 17 / 24 )125.8292105263160.406460344442606309.573153314304
Trimmed Mean ( 18 / 24 )125.88250.384186085657326327.660226904419
Trimmed Mean ( 19 / 24 )125.9450.354365756142661355.409623579139
Trimmed Mean ( 20 / 24 )125.9856250.330802706983453380.848228688472
Trimmed Mean ( 21 / 24 )125.9933333333330.316956552130883397.509792702774
Trimmed Mean ( 22 / 24 )125.9910714285710.305922293313981411.840111630118
Trimmed Mean ( 23 / 24 )125.9846153846150.291187611089605432.657883050688
Trimmed Mean ( 24 / 24 )125.9891666666670.2755014641763457.308519369767
Median126.475
Midrange123.095
Midmean - Weighted Average at Xnp125.727837837838
Midmean - Weighted Average at X(n+1)p125.8825
Midmean - Empirical Distribution Function125.727837837838
Midmean - Empirical Distribution Function - Averaging125.8825
Midmean - Empirical Distribution Function - Interpolation125.8825
Midmean - Closest Observation125.727837837838
Midmean - True Basic - Statistics Graphics Toolkit125.8825
Midmean - MS Excel (old versions)125.829210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 124.8025 & 0.771037772661048 & 161.863016865276 \tabularnewline
Geometric Mean & 124.629577037281 &  &  \tabularnewline
Harmonic Mean & 124.452844358790 &  &  \tabularnewline
Quadratic Mean & 124.971490559958 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 124.815416666667 & 0.767203296003268 & 162.688843122664 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 124.784583333333 & 0.75828279606406 & 164.562065737268 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 124.784583333333 & 0.755740833392926 & 165.11557642467 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 124.775138888889 & 0.741220364558536 & 168.337440328159 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 124.780694444444 & 0.733040042886682 & 170.223571898014 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 124.813194444444 & 0.723933510183784 & 172.409748531683 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 124.805416666667 & 0.711212071757294 & 175.482702871300 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 124.793194444444 & 0.707359032401114 & 176.421292057072 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 124.796944444444 & 0.703815380024057 & 177.314886810485 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 124.9775 & 0.639809450249923 & 195.335501767255 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 125.272361111111 & 0.572477746697487 & 218.824857094940 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 125.239027777778 & 0.547935917733255 & 228.565099904158 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 125.137916666667 & 0.530320714429092 & 235.96648831902 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 125.200138888889 & 0.51681867720867 & 242.251575668846 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 125.212638888889 & 0.513971578753015 & 243.617826481139 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 125.390416666667 & 0.467717940525774 & 268.089816109495 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 125.37625 & 0.442962508503542 & 283.040319650433 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 125.35125 & 0.436655150615984 & 287.071502129698 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 125.601944444444 & 0.381979474848264 & 328.81856935988 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 125.921388888889 & 0.322382520094897 & 390.596204942570 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 126.011805555556 & 0.292376555708907 & 430.991483739257 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 126.042361111111 & 0.284787245428352 & 442.584291025848 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 125.949722222222 & 0.264999407403464 & 475.283033484156 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 125.993055555556 & 0.242802466040225 & 518.91176234875 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 124.851285714286 & 0.751163953162826 & 166.210432740537 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 124.889264705882 & 0.732044394447727 & 170.603402816986 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 124.946363636364 & 0.71480744261441 & 174.797233754831 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 125.00703125 & 0.6951751834601 & 179.820905901447 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 125.074354838710 & 0.676781493465815 & 184.807587155200 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 125.144833333333 & 0.656951893588596 & 190.493146537306 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 125.213448275862 & 0.635304470009684 & 197.092030965804 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 125.288392857143 & 0.611984889507973 & 204.724650894359 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 125.370925925926 & 0.583798273443292 & 214.750422584290 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 125.459230769231 & 0.549030947084268 & 228.510307907971 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 125.5286 & 0.522229053663042 & 240.370770487609 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 125.563541666667 & 0.505344178197631 & 248.471333170402 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 125.605869565217 & 0.48926500886257 & 256.72359005853 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 125.664772727273 & 0.472094483931555 & 266.185640808063 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 125.721666666667 & 0.452775274380354 & 277.669019887897 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 125.78275 & 0.427524926173902 & 294.211500428015 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 125.829210526316 & 0.406460344442606 & 309.573153314304 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 125.8825 & 0.384186085657326 & 327.660226904419 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 125.945 & 0.354365756142661 & 355.409623579139 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 125.985625 & 0.330802706983453 & 380.848228688472 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 125.993333333333 & 0.316956552130883 & 397.509792702774 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 125.991071428571 & 0.305922293313981 & 411.840111630118 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 125.984615384615 & 0.291187611089605 & 432.657883050688 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 125.989166666667 & 0.2755014641763 & 457.308519369767 \tabularnewline
Median & 126.475 &  &  \tabularnewline
Midrange & 123.095 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 125.727837837838 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 125.8825 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 125.727837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 125.8825 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 125.8825 &  &  \tabularnewline
Midmean - Closest Observation & 125.727837837838 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 125.8825 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 125.829210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21466&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]124.8025[/C][C]0.771037772661048[/C][C]161.863016865276[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]124.629577037281[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]124.452844358790[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]124.971490559958[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]124.815416666667[/C][C]0.767203296003268[/C][C]162.688843122664[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]124.784583333333[/C][C]0.75828279606406[/C][C]164.562065737268[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]124.784583333333[/C][C]0.755740833392926[/C][C]165.11557642467[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]124.775138888889[/C][C]0.741220364558536[/C][C]168.337440328159[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]124.780694444444[/C][C]0.733040042886682[/C][C]170.223571898014[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]124.813194444444[/C][C]0.723933510183784[/C][C]172.409748531683[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]124.805416666667[/C][C]0.711212071757294[/C][C]175.482702871300[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]124.793194444444[/C][C]0.707359032401114[/C][C]176.421292057072[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]124.796944444444[/C][C]0.703815380024057[/C][C]177.314886810485[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]124.9775[/C][C]0.639809450249923[/C][C]195.335501767255[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]125.272361111111[/C][C]0.572477746697487[/C][C]218.824857094940[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]125.239027777778[/C][C]0.547935917733255[/C][C]228.565099904158[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]125.137916666667[/C][C]0.530320714429092[/C][C]235.96648831902[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]125.200138888889[/C][C]0.51681867720867[/C][C]242.251575668846[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]125.212638888889[/C][C]0.513971578753015[/C][C]243.617826481139[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]125.390416666667[/C][C]0.467717940525774[/C][C]268.089816109495[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]125.37625[/C][C]0.442962508503542[/C][C]283.040319650433[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]125.35125[/C][C]0.436655150615984[/C][C]287.071502129698[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]125.601944444444[/C][C]0.381979474848264[/C][C]328.81856935988[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]125.921388888889[/C][C]0.322382520094897[/C][C]390.596204942570[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]126.011805555556[/C][C]0.292376555708907[/C][C]430.991483739257[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]126.042361111111[/C][C]0.284787245428352[/C][C]442.584291025848[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]125.949722222222[/C][C]0.264999407403464[/C][C]475.283033484156[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]125.993055555556[/C][C]0.242802466040225[/C][C]518.91176234875[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]124.851285714286[/C][C]0.751163953162826[/C][C]166.210432740537[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]124.889264705882[/C][C]0.732044394447727[/C][C]170.603402816986[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]124.946363636364[/C][C]0.71480744261441[/C][C]174.797233754831[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]125.00703125[/C][C]0.6951751834601[/C][C]179.820905901447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]125.074354838710[/C][C]0.676781493465815[/C][C]184.807587155200[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]125.144833333333[/C][C]0.656951893588596[/C][C]190.493146537306[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]125.213448275862[/C][C]0.635304470009684[/C][C]197.092030965804[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]125.288392857143[/C][C]0.611984889507973[/C][C]204.724650894359[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]125.370925925926[/C][C]0.583798273443292[/C][C]214.750422584290[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]125.459230769231[/C][C]0.549030947084268[/C][C]228.510307907971[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]125.5286[/C][C]0.522229053663042[/C][C]240.370770487609[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]125.563541666667[/C][C]0.505344178197631[/C][C]248.471333170402[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]125.605869565217[/C][C]0.48926500886257[/C][C]256.72359005853[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]125.664772727273[/C][C]0.472094483931555[/C][C]266.185640808063[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]125.721666666667[/C][C]0.452775274380354[/C][C]277.669019887897[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]125.78275[/C][C]0.427524926173902[/C][C]294.211500428015[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]125.829210526316[/C][C]0.406460344442606[/C][C]309.573153314304[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]125.8825[/C][C]0.384186085657326[/C][C]327.660226904419[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]125.945[/C][C]0.354365756142661[/C][C]355.409623579139[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]125.985625[/C][C]0.330802706983453[/C][C]380.848228688472[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]125.993333333333[/C][C]0.316956552130883[/C][C]397.509792702774[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]125.991071428571[/C][C]0.305922293313981[/C][C]411.840111630118[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]125.984615384615[/C][C]0.291187611089605[/C][C]432.657883050688[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]125.989166666667[/C][C]0.2755014641763[/C][C]457.308519369767[/C][/ROW]
[ROW][C]Median[/C][C]126.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]123.095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]125.727837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]125.8825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]125.727837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]125.8825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]125.8825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]125.727837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]125.8825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]125.829210526316[/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=21466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21466&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 Mean124.80250.771037772661048161.863016865276
Geometric Mean124.629577037281
Harmonic Mean124.452844358790
Quadratic Mean124.971490559958
Winsorized Mean ( 1 / 24 )124.8154166666670.767203296003268162.688843122664
Winsorized Mean ( 2 / 24 )124.7845833333330.75828279606406164.562065737268
Winsorized Mean ( 3 / 24 )124.7845833333330.755740833392926165.11557642467
Winsorized Mean ( 4 / 24 )124.7751388888890.741220364558536168.337440328159
Winsorized Mean ( 5 / 24 )124.7806944444440.733040042886682170.223571898014
Winsorized Mean ( 6 / 24 )124.8131944444440.723933510183784172.409748531683
Winsorized Mean ( 7 / 24 )124.8054166666670.711212071757294175.482702871300
Winsorized Mean ( 8 / 24 )124.7931944444440.707359032401114176.421292057072
Winsorized Mean ( 9 / 24 )124.7969444444440.703815380024057177.314886810485
Winsorized Mean ( 10 / 24 )124.97750.639809450249923195.335501767255
Winsorized Mean ( 11 / 24 )125.2723611111110.572477746697487218.824857094940
Winsorized Mean ( 12 / 24 )125.2390277777780.547935917733255228.565099904158
Winsorized Mean ( 13 / 24 )125.1379166666670.530320714429092235.96648831902
Winsorized Mean ( 14 / 24 )125.2001388888890.51681867720867242.251575668846
Winsorized Mean ( 15 / 24 )125.2126388888890.513971578753015243.617826481139
Winsorized Mean ( 16 / 24 )125.3904166666670.467717940525774268.089816109495
Winsorized Mean ( 17 / 24 )125.376250.442962508503542283.040319650433
Winsorized Mean ( 18 / 24 )125.351250.436655150615984287.071502129698
Winsorized Mean ( 19 / 24 )125.6019444444440.381979474848264328.81856935988
Winsorized Mean ( 20 / 24 )125.9213888888890.322382520094897390.596204942570
Winsorized Mean ( 21 / 24 )126.0118055555560.292376555708907430.991483739257
Winsorized Mean ( 22 / 24 )126.0423611111110.284787245428352442.584291025848
Winsorized Mean ( 23 / 24 )125.9497222222220.264999407403464475.283033484156
Winsorized Mean ( 24 / 24 )125.9930555555560.242802466040225518.91176234875
Trimmed Mean ( 1 / 24 )124.8512857142860.751163953162826166.210432740537
Trimmed Mean ( 2 / 24 )124.8892647058820.732044394447727170.603402816986
Trimmed Mean ( 3 / 24 )124.9463636363640.71480744261441174.797233754831
Trimmed Mean ( 4 / 24 )125.007031250.6951751834601179.820905901447
Trimmed Mean ( 5 / 24 )125.0743548387100.676781493465815184.807587155200
Trimmed Mean ( 6 / 24 )125.1448333333330.656951893588596190.493146537306
Trimmed Mean ( 7 / 24 )125.2134482758620.635304470009684197.092030965804
Trimmed Mean ( 8 / 24 )125.2883928571430.611984889507973204.724650894359
Trimmed Mean ( 9 / 24 )125.3709259259260.583798273443292214.750422584290
Trimmed Mean ( 10 / 24 )125.4592307692310.549030947084268228.510307907971
Trimmed Mean ( 11 / 24 )125.52860.522229053663042240.370770487609
Trimmed Mean ( 12 / 24 )125.5635416666670.505344178197631248.471333170402
Trimmed Mean ( 13 / 24 )125.6058695652170.48926500886257256.72359005853
Trimmed Mean ( 14 / 24 )125.6647727272730.472094483931555266.185640808063
Trimmed Mean ( 15 / 24 )125.7216666666670.452775274380354277.669019887897
Trimmed Mean ( 16 / 24 )125.782750.427524926173902294.211500428015
Trimmed Mean ( 17 / 24 )125.8292105263160.406460344442606309.573153314304
Trimmed Mean ( 18 / 24 )125.88250.384186085657326327.660226904419
Trimmed Mean ( 19 / 24 )125.9450.354365756142661355.409623579139
Trimmed Mean ( 20 / 24 )125.9856250.330802706983453380.848228688472
Trimmed Mean ( 21 / 24 )125.9933333333330.316956552130883397.509792702774
Trimmed Mean ( 22 / 24 )125.9910714285710.305922293313981411.840111630118
Trimmed Mean ( 23 / 24 )125.9846153846150.291187611089605432.657883050688
Trimmed Mean ( 24 / 24 )125.9891666666670.2755014641763457.308519369767
Median126.475
Midrange123.095
Midmean - Weighted Average at Xnp125.727837837838
Midmean - Weighted Average at X(n+1)p125.8825
Midmean - Empirical Distribution Function125.727837837838
Midmean - Empirical Distribution Function - Averaging125.8825
Midmean - Empirical Distribution Function - Interpolation125.8825
Midmean - Closest Observation125.727837837838
Midmean - True Basic - Statistics Graphics Toolkit125.8825
Midmean - MS Excel (old versions)125.829210526316
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')