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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Dec 2009 03:53:40 -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/2009/Dec/20/t126130646284wiurl292ygx3f.htm/, Retrieved Sat, 27 Apr 2024 07:42:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69829, Retrieved Sat, 27 Apr 2024 07:42:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2009-12-20 10:50:56] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
-    D    [Central Tendency] [Paper central ten...] [2009-12-20 10:53:40] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
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Dataseries X:
14.3
14.2
15.9
15.3
15.5
15.1
15
12.1
15.8
16.9
15.1
13.7
14.8
14.7
16
15.4
15
15.5
15.1
11.7
16.3
16.7
15
14.9
14.6
15.3
17.9
16.4
15.4
17.9
15.9
13.9
17.8
17.9
17.4
16.7
16
16.6
19.1
17.8
17.2
18.6
16.3
15.1
19.2
17.7
19.1
18
17.5
17.8
21.1
17.2
19.4
19.8
17.6
16.2
19.5
19.9
20
17.3
18.9
18.6
21.4
18.6
19.8
20.8
19.6
17.7
19.8
22.2
20.7
17.9




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69829&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69829&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.04305555555560.25865175278935465.8919004868891
Geometric Mean16.902294693916
Harmonic Mean16.7597278440542
Quadratic Mean17.1818419980060
Winsorized Mean ( 1 / 24 )17.03750.25417821108239367.0297423506425
Winsorized Mean ( 2 / 24 )17.07361111111110.24170100982748570.6393867501733
Winsorized Mean ( 3 / 24 )17.06944444444440.23724618996174671.9482342253704
Winsorized Mean ( 4 / 24 )17.08055555555560.23300311046646173.3061267781409
Winsorized Mean ( 5 / 24 )17.03888888888890.22189040171636176.7896617298004
Winsorized Mean ( 6 / 24 )17.05555555555560.21615947216272778.9026517547933
Winsorized Mean ( 7 / 24 )17.05555555555560.21283988641505680.1332675131001
Winsorized Mean ( 8 / 24 )17.06666666666670.21113376041915380.8334329516278
Winsorized Mean ( 9 / 24 )17.07916666666670.20927194664498781.6123084841377
Winsorized Mean ( 10 / 24 )17.06527777777780.20225798654919784.373814201037
Winsorized Mean ( 11 / 24 )17.050.19958877912140785.4256440419867
Winsorized Mean ( 12 / 24 )17.03333333333330.19673588341918286.5796978024627
Winsorized Mean ( 13 / 24 )17.01527777777780.18811164943578590.4530784181244
Winsorized Mean ( 14 / 24 )16.99583333333330.18496327829936691.8876086626518
Winsorized Mean ( 15 / 24 )16.99583333333330.18496327829936691.8876086626518
Winsorized Mean ( 16 / 24 )16.95138888888890.17797321209556695.2468559132738
Winsorized Mean ( 17 / 24 )16.92777777777780.16046224091626105.493838806675
Winsorized Mean ( 18 / 24 )16.92777777777780.16046224091626105.493838806675
Winsorized Mean ( 19 / 24 )16.95416666666670.156733797174824108.171734318130
Winsorized Mean ( 20 / 24 )16.78750.133625523446802125.630939112342
Winsorized Mean ( 21 / 24 )16.78750.125705170562325133.546614867975
Winsorized Mean ( 22 / 24 )16.78750.125705170562325133.546614867975
Winsorized Mean ( 23 / 24 )16.88333333333330.112257389243424150.398414279195
Winsorized Mean ( 24 / 24 )16.91666666666670.107776648429944156.960407593883
Trimmed Mean ( 1 / 24 )17.04571428571430.24370064209538969.945299032254
Trimmed Mean ( 2 / 24 )17.05441176470590.23115006037329373.7806935337334
Trimmed Mean ( 3 / 24 )17.04393939393940.22428470904794675.9924270641914
Trimmed Mean ( 4 / 24 )17.0343750.21810669295986578.1011108317276
Trimmed Mean ( 5 / 24 )17.02096774193550.21221474582035380.2063385187395
Trimmed Mean ( 6 / 24 )17.01666666666670.20860265078222581.5745466457737
Trimmed Mean ( 7 / 24 )17.00862068965520.20570043946741582.6863604846574
Trimmed Mean ( 8 / 24 )170.20286903202767183.797905624557
Trimmed Mean ( 9 / 24 )16.98888888888890.19964445452525985.0957214378298
Trimmed Mean ( 10 / 24 )16.9750.19592136431608286.6419038028646
Trimmed Mean ( 11 / 24 )16.9620.19272249267709688.0125602589604
Trimmed Mean ( 12 / 24 )16.950.18913296009882889.6194930335946
Trimmed Mean ( 13 / 24 )16.93913043478260.18505719864865291.5345663852996
Trimmed Mean ( 14 / 24 )16.92954545454550.18159440510278993.22724147235
Trimmed Mean ( 15 / 24 )16.92142857142860.17762583553118195.2644558761733
Trimmed Mean ( 16 / 24 )16.91250.17220990099294598.208639006725
Trimmed Mean ( 17 / 24 )16.90789473684210.166607074270498101.483654345859
Trimmed Mean ( 18 / 24 )16.90555555555560.163248007083022103.55750038013
Trimmed Mean ( 19 / 24 )16.90294117647060.158338369041845106.752022764637
Trimmed Mean ( 20 / 24 )16.8968750.152233663181457110.993026423200
Trimmed Mean ( 21 / 24 )16.910.149815979075020112.871805159931
Trimmed Mean ( 22 / 24 )16.9250.147969055108970114.382023913959
Trimmed Mean ( 23 / 24 )16.94230769230770.144453673907331117.285405307008
Trimmed Mean ( 24 / 24 )16.950.143329962885886118.258594774736
Median17.05
Midrange16.95
Midmean - Weighted Average at Xnp16.9078947368421
Midmean - Weighted Average at X(n+1)p16.9078947368421
Midmean - Empirical Distribution Function16.9078947368421
Midmean - Empirical Distribution Function - Averaging16.9078947368421
Midmean - Empirical Distribution Function - Interpolation16.9078947368421
Midmean - Closest Observation16.9078947368421
Midmean - True Basic - Statistics Graphics Toolkit16.9078947368421
Midmean - MS Excel (old versions)16.9078947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.0430555555556 & 0.258651752789354 & 65.8919004868891 \tabularnewline
Geometric Mean & 16.902294693916 &  &  \tabularnewline
Harmonic Mean & 16.7597278440542 &  &  \tabularnewline
Quadratic Mean & 17.1818419980060 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17.0375 & 0.254178211082393 & 67.0297423506425 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17.0736111111111 & 0.241701009827485 & 70.6393867501733 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17.0694444444444 & 0.237246189961746 & 71.9482342253704 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17.0805555555556 & 0.233003110466461 & 73.3061267781409 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17.0388888888889 & 0.221890401716361 & 76.7896617298004 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17.0555555555556 & 0.216159472162727 & 78.9026517547933 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17.0555555555556 & 0.212839886415056 & 80.1332675131001 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17.0666666666667 & 0.211133760419153 & 80.8334329516278 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17.0791666666667 & 0.209271946644987 & 81.6123084841377 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17.0652777777778 & 0.202257986549197 & 84.373814201037 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17.05 & 0.199588779121407 & 85.4256440419867 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17.0333333333333 & 0.196735883419182 & 86.5796978024627 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17.0152777777778 & 0.188111649435785 & 90.4530784181244 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.9958333333333 & 0.184963278299366 & 91.8876086626518 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.9958333333333 & 0.184963278299366 & 91.8876086626518 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.9513888888889 & 0.177973212095566 & 95.2468559132738 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.9277777777778 & 0.16046224091626 & 105.493838806675 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.9277777777778 & 0.16046224091626 & 105.493838806675 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.9541666666667 & 0.156733797174824 & 108.171734318130 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.7875 & 0.133625523446802 & 125.630939112342 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.7875 & 0.125705170562325 & 133.546614867975 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.7875 & 0.125705170562325 & 133.546614867975 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.8833333333333 & 0.112257389243424 & 150.398414279195 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.9166666666667 & 0.107776648429944 & 156.960407593883 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17.0457142857143 & 0.243700642095389 & 69.945299032254 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17.0544117647059 & 0.231150060373293 & 73.7806935337334 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17.0439393939394 & 0.224284709047946 & 75.9924270641914 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17.034375 & 0.218106692959865 & 78.1011108317276 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17.0209677419355 & 0.212214745820353 & 80.2063385187395 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17.0166666666667 & 0.208602650782225 & 81.5745466457737 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17.0086206896552 & 0.205700439467415 & 82.6863604846574 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17 & 0.202869032027671 & 83.797905624557 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.9888888888889 & 0.199644454525259 & 85.0957214378298 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.975 & 0.195921364316082 & 86.6419038028646 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.962 & 0.192722492677096 & 88.0125602589604 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.95 & 0.189132960098828 & 89.6194930335946 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.9391304347826 & 0.185057198648652 & 91.5345663852996 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.9295454545455 & 0.181594405102789 & 93.22724147235 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.9214285714286 & 0.177625835531181 & 95.2644558761733 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.9125 & 0.172209900992945 & 98.208639006725 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.9078947368421 & 0.166607074270498 & 101.483654345859 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.9055555555556 & 0.163248007083022 & 103.55750038013 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.9029411764706 & 0.158338369041845 & 106.752022764637 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.896875 & 0.152233663181457 & 110.993026423200 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.91 & 0.149815979075020 & 112.871805159931 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.925 & 0.147969055108970 & 114.382023913959 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.9423076923077 & 0.144453673907331 & 117.285405307008 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.95 & 0.143329962885886 & 118.258594774736 \tabularnewline
Median & 17.05 &  &  \tabularnewline
Midrange & 16.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.9078947368421 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.9078947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.9078947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.9078947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.9078947368421 &  &  \tabularnewline
Midmean - Closest Observation & 16.9078947368421 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.9078947368421 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.9078947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69829&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]17.0430555555556[/C][C]0.258651752789354[/C][C]65.8919004868891[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.902294693916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.7597278440542[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.1818419980060[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17.0375[/C][C]0.254178211082393[/C][C]67.0297423506425[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17.0736111111111[/C][C]0.241701009827485[/C][C]70.6393867501733[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17.0694444444444[/C][C]0.237246189961746[/C][C]71.9482342253704[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17.0805555555556[/C][C]0.233003110466461[/C][C]73.3061267781409[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17.0388888888889[/C][C]0.221890401716361[/C][C]76.7896617298004[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17.0555555555556[/C][C]0.216159472162727[/C][C]78.9026517547933[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17.0555555555556[/C][C]0.212839886415056[/C][C]80.1332675131001[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17.0666666666667[/C][C]0.211133760419153[/C][C]80.8334329516278[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17.0791666666667[/C][C]0.209271946644987[/C][C]81.6123084841377[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17.0652777777778[/C][C]0.202257986549197[/C][C]84.373814201037[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17.05[/C][C]0.199588779121407[/C][C]85.4256440419867[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17.0333333333333[/C][C]0.196735883419182[/C][C]86.5796978024627[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17.0152777777778[/C][C]0.188111649435785[/C][C]90.4530784181244[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.9958333333333[/C][C]0.184963278299366[/C][C]91.8876086626518[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.9958333333333[/C][C]0.184963278299366[/C][C]91.8876086626518[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.9513888888889[/C][C]0.177973212095566[/C][C]95.2468559132738[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.9277777777778[/C][C]0.16046224091626[/C][C]105.493838806675[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.9277777777778[/C][C]0.16046224091626[/C][C]105.493838806675[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.9541666666667[/C][C]0.156733797174824[/C][C]108.171734318130[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.7875[/C][C]0.133625523446802[/C][C]125.630939112342[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.7875[/C][C]0.125705170562325[/C][C]133.546614867975[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.7875[/C][C]0.125705170562325[/C][C]133.546614867975[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.8833333333333[/C][C]0.112257389243424[/C][C]150.398414279195[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.9166666666667[/C][C]0.107776648429944[/C][C]156.960407593883[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17.0457142857143[/C][C]0.243700642095389[/C][C]69.945299032254[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17.0544117647059[/C][C]0.231150060373293[/C][C]73.7806935337334[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17.0439393939394[/C][C]0.224284709047946[/C][C]75.9924270641914[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17.034375[/C][C]0.218106692959865[/C][C]78.1011108317276[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17.0209677419355[/C][C]0.212214745820353[/C][C]80.2063385187395[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17.0166666666667[/C][C]0.208602650782225[/C][C]81.5745466457737[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17.0086206896552[/C][C]0.205700439467415[/C][C]82.6863604846574[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17[/C][C]0.202869032027671[/C][C]83.797905624557[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.9888888888889[/C][C]0.199644454525259[/C][C]85.0957214378298[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.975[/C][C]0.195921364316082[/C][C]86.6419038028646[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.962[/C][C]0.192722492677096[/C][C]88.0125602589604[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.95[/C][C]0.189132960098828[/C][C]89.6194930335946[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.9391304347826[/C][C]0.185057198648652[/C][C]91.5345663852996[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.9295454545455[/C][C]0.181594405102789[/C][C]93.22724147235[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.9214285714286[/C][C]0.177625835531181[/C][C]95.2644558761733[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.9125[/C][C]0.172209900992945[/C][C]98.208639006725[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.9078947368421[/C][C]0.166607074270498[/C][C]101.483654345859[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.9055555555556[/C][C]0.163248007083022[/C][C]103.55750038013[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.9029411764706[/C][C]0.158338369041845[/C][C]106.752022764637[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.896875[/C][C]0.152233663181457[/C][C]110.993026423200[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.91[/C][C]0.149815979075020[/C][C]112.871805159931[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.925[/C][C]0.147969055108970[/C][C]114.382023913959[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.9423076923077[/C][C]0.144453673907331[/C][C]117.285405307008[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.95[/C][C]0.143329962885886[/C][C]118.258594774736[/C][/ROW]
[ROW][C]Median[/C][C]17.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.9078947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.9078947368421[/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=69829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69829&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 Mean17.04305555555560.25865175278935465.8919004868891
Geometric Mean16.902294693916
Harmonic Mean16.7597278440542
Quadratic Mean17.1818419980060
Winsorized Mean ( 1 / 24 )17.03750.25417821108239367.0297423506425
Winsorized Mean ( 2 / 24 )17.07361111111110.24170100982748570.6393867501733
Winsorized Mean ( 3 / 24 )17.06944444444440.23724618996174671.9482342253704
Winsorized Mean ( 4 / 24 )17.08055555555560.23300311046646173.3061267781409
Winsorized Mean ( 5 / 24 )17.03888888888890.22189040171636176.7896617298004
Winsorized Mean ( 6 / 24 )17.05555555555560.21615947216272778.9026517547933
Winsorized Mean ( 7 / 24 )17.05555555555560.21283988641505680.1332675131001
Winsorized Mean ( 8 / 24 )17.06666666666670.21113376041915380.8334329516278
Winsorized Mean ( 9 / 24 )17.07916666666670.20927194664498781.6123084841377
Winsorized Mean ( 10 / 24 )17.06527777777780.20225798654919784.373814201037
Winsorized Mean ( 11 / 24 )17.050.19958877912140785.4256440419867
Winsorized Mean ( 12 / 24 )17.03333333333330.19673588341918286.5796978024627
Winsorized Mean ( 13 / 24 )17.01527777777780.18811164943578590.4530784181244
Winsorized Mean ( 14 / 24 )16.99583333333330.18496327829936691.8876086626518
Winsorized Mean ( 15 / 24 )16.99583333333330.18496327829936691.8876086626518
Winsorized Mean ( 16 / 24 )16.95138888888890.17797321209556695.2468559132738
Winsorized Mean ( 17 / 24 )16.92777777777780.16046224091626105.493838806675
Winsorized Mean ( 18 / 24 )16.92777777777780.16046224091626105.493838806675
Winsorized Mean ( 19 / 24 )16.95416666666670.156733797174824108.171734318130
Winsorized Mean ( 20 / 24 )16.78750.133625523446802125.630939112342
Winsorized Mean ( 21 / 24 )16.78750.125705170562325133.546614867975
Winsorized Mean ( 22 / 24 )16.78750.125705170562325133.546614867975
Winsorized Mean ( 23 / 24 )16.88333333333330.112257389243424150.398414279195
Winsorized Mean ( 24 / 24 )16.91666666666670.107776648429944156.960407593883
Trimmed Mean ( 1 / 24 )17.04571428571430.24370064209538969.945299032254
Trimmed Mean ( 2 / 24 )17.05441176470590.23115006037329373.7806935337334
Trimmed Mean ( 3 / 24 )17.04393939393940.22428470904794675.9924270641914
Trimmed Mean ( 4 / 24 )17.0343750.21810669295986578.1011108317276
Trimmed Mean ( 5 / 24 )17.02096774193550.21221474582035380.2063385187395
Trimmed Mean ( 6 / 24 )17.01666666666670.20860265078222581.5745466457737
Trimmed Mean ( 7 / 24 )17.00862068965520.20570043946741582.6863604846574
Trimmed Mean ( 8 / 24 )170.20286903202767183.797905624557
Trimmed Mean ( 9 / 24 )16.98888888888890.19964445452525985.0957214378298
Trimmed Mean ( 10 / 24 )16.9750.19592136431608286.6419038028646
Trimmed Mean ( 11 / 24 )16.9620.19272249267709688.0125602589604
Trimmed Mean ( 12 / 24 )16.950.18913296009882889.6194930335946
Trimmed Mean ( 13 / 24 )16.93913043478260.18505719864865291.5345663852996
Trimmed Mean ( 14 / 24 )16.92954545454550.18159440510278993.22724147235
Trimmed Mean ( 15 / 24 )16.92142857142860.17762583553118195.2644558761733
Trimmed Mean ( 16 / 24 )16.91250.17220990099294598.208639006725
Trimmed Mean ( 17 / 24 )16.90789473684210.166607074270498101.483654345859
Trimmed Mean ( 18 / 24 )16.90555555555560.163248007083022103.55750038013
Trimmed Mean ( 19 / 24 )16.90294117647060.158338369041845106.752022764637
Trimmed Mean ( 20 / 24 )16.8968750.152233663181457110.993026423200
Trimmed Mean ( 21 / 24 )16.910.149815979075020112.871805159931
Trimmed Mean ( 22 / 24 )16.9250.147969055108970114.382023913959
Trimmed Mean ( 23 / 24 )16.94230769230770.144453673907331117.285405307008
Trimmed Mean ( 24 / 24 )16.950.143329962885886118.258594774736
Median17.05
Midrange16.95
Midmean - Weighted Average at Xnp16.9078947368421
Midmean - Weighted Average at X(n+1)p16.9078947368421
Midmean - Empirical Distribution Function16.9078947368421
Midmean - Empirical Distribution Function - Averaging16.9078947368421
Midmean - Empirical Distribution Function - Interpolation16.9078947368421
Midmean - Closest Observation16.9078947368421
Midmean - True Basic - Statistics Graphics Toolkit16.9078947368421
Midmean - MS Excel (old versions)16.9078947368421
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')