Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Dec 2008 09:45:52 -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/Dec/16/t1229446000bar2td3paaw8hcv.htm/, Retrieved Wed, 15 May 2024 11:46:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34031, Retrieved Wed, 15 May 2024 11:46:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper: Central Te...] [2008-12-16 15:47:28] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D  [Central Tendency] [Paper: Central Te...] [2008-12-16 15:59:22] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D      [Central Tendency] [Paper: Central Te...] [2008-12-16 16:45:52] [8da7502cfecb272886bc60b3f290b8b8] [Current]
-    D        [Central Tendency] [Paper: Central Te...] [2008-12-16 16:49:56] [9e54d1454d464f1bf9ee4a54d5d56945]
- RMPD        [Histogram] [Paper: histogram ...] [2008-12-16 17:12:52] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D          [Histogram] [Paper: Histogram ...] [2008-12-16 17:16:37] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D            [Histogram] [] [2008-12-22 22:01:25] [187876c4ad94aebda16017e4a72ae602]
-                 [Histogram] [] [2008-12-22 22:08:37] [187876c4ad94aebda16017e4a72ae602]
- RMPD          [Back to Back Histogram] [Paper: Bihistogra...] [2008-12-16 17:21:03] [9e54d1454d464f1bf9ee4a54d5d56945]
-                 [Back to Back Histogram] [] [2008-12-22 22:11:19] [187876c4ad94aebda16017e4a72ae602]
-               [Histogram] [] [2008-12-22 21:53:40] [84af9210cb1d82626c16de257e3e8f09]
-    D          [Histogram] [] [2008-12-22 22:06:44] [187876c4ad94aebda16017e4a72ae602]
Feedback Forum

Post a new message
Dataseries X:
1,3
1,4
1,3
1
0,8
0,7
0,6
0,8
0,9
1
1,2
1,3
1,3
1,4
1,4
1,8
1,9
2
2,4
2,5
2,5
2,3
1,7
1,1
0,7
0,2
0,3
1,1
1,6
2,2
3
3,8
4,6
5,1
5,3
5,5
5,7
5,9
6,1
6,1
6,3
6,5
6,7
6,6
6,5
6,4
6,3
6,3
6,3
6,2
6
5,6
5,3
5,1
4,5
4
3,5
3,5
3,3
3,1
2,9
2,5
2,6
2,8
2,8
2,9
3,1
3,3
3,5
3,4
3,5
3,7
3,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34031&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34031&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34031&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.295890410958900.23426459916239314.0690929092286
Geometric Mean2.57530720843188
Harmonic Mean1.76042627308944
Quadratic Mean3.84892797741689
Winsorized Mean ( 1 / 24 )3.295890410958900.23374424317677114.1004131959150
Winsorized Mean ( 2 / 24 )3.30136986301370.23181578551091614.241350543655
Winsorized Mean ( 3 / 24 )3.305479452054790.23116153670945614.2994353606907
Winsorized Mean ( 4 / 24 )3.30.23012305622115814.3401537168382
Winsorized Mean ( 5 / 24 )3.30.22779633885098314.4866243972374
Winsorized Mean ( 6 / 24 )3.30.22779633885098314.4866243972374
Winsorized Mean ( 7 / 24 )3.309589041095890.22635659344404414.6211293903132
Winsorized Mean ( 8 / 24 )3.320547945205480.22476064474929514.7737071537116
Winsorized Mean ( 9 / 24 )3.308219178082190.22251291947388414.8675375160428
Winsorized Mean ( 10 / 24 )3.308219178082190.21810859694974215.1677614928883
Winsorized Mean ( 11 / 24 )3.308219178082190.21810859694974215.1677614928883
Winsorized Mean ( 12 / 24 )3.308219178082190.21291762994409515.5375540247692
Winsorized Mean ( 13 / 24 )3.308219178082190.20738600529630915.951988531509
Winsorized Mean ( 14 / 24 )3.269863013698630.20083240901951816.2815505209662
Winsorized Mean ( 15 / 24 )3.249315068493150.19740634917817916.4600332361160
Winsorized Mean ( 16 / 24 )3.227397260273970.19380885735340516.6524755594060
Winsorized Mean ( 17 / 24 )3.204109589041100.18310943526265517.4983314455919
Winsorized Mean ( 18 / 24 )3.204109589041100.18310943526265517.4983314455919
Winsorized Mean ( 19 / 24 )3.152054794520550.17494410489220218.0174964824496
Winsorized Mean ( 20 / 24 )3.206849315068490.16747894262243919.1477762210258
Winsorized Mean ( 21 / 24 )3.091780821917810.14161969977101621.8315730573988
Winsorized Mean ( 22 / 24 )3.091780821917810.13308700740415223.2312746542482
Winsorized Mean ( 23 / 24 )2.965753424657530.10647276858109527.8545722458477
Winsorized Mean ( 24 / 24 )2.932876712328770.093206346965289631.4664913691015
Trimmed Mean ( 1 / 24 )3.291549295774650.23190009018206914.1938249924370
Trimmed Mean ( 2 / 24 )3.286956521739130.22961579760020914.3150277815909
Trimmed Mean ( 3 / 24 )3.279104477611940.22797892133427614.3833669289273
Trimmed Mean ( 4 / 24 )3.269230769230770.22617134286058614.4546640077472
Trimmed Mean ( 5 / 24 )3.260317460317460.22423037494351714.5400348241790
Trimmed Mean ( 6 / 24 )3.250819672131150.22243833738567914.6144756804878
Trimmed Mean ( 7 / 24 )3.240677966101690.22010462742486514.7233522712190
Trimmed Mean ( 8 / 24 )3.228070175438600.21745212917672114.8449692705247
Trimmed Mean ( 9 / 24 )3.212727272727270.21439845446221914.9848434345566
Trimmed Mean ( 10 / 24 )3.198113207547170.21099134599422315.1575563086589
Trimmed Mean ( 11 / 24 )3.182352941176470.20755733216656415.3324043432137
Trimmed Mean ( 12 / 24 )3.165306122448980.20307062501742415.5872181029501
Trimmed Mean ( 13 / 24 )3.14680851063830.1983710504860815.8632446767182
Trimmed Mean ( 14 / 24 )3.126666666666670.19341168736165016.1658621012921
Trimmed Mean ( 15 / 24 )3.109302325581400.18838986558763816.5046156590359
Trimmed Mean ( 16 / 24 )3.092682926829270.18247586689425616.9484490166662
Trimmed Mean ( 17 / 24 )3.076923076923080.17539088939224317.5432320777042
Trimmed Mean ( 18 / 24 )3.062162162162160.16851904622092318.1710152699759
Trimmed Mean ( 19 / 24 )3.045714285714290.15890078597638719.1673959760456
Trimmed Mean ( 20 / 24 )3.033333333333330.14794467297819920.5031602170652
Trimmed Mean ( 21 / 24 )3.012903225806450.13430361491094622.4335229383382
Trimmed Mean ( 22 / 24 )3.003448275862070.12422000570859624.1784586848899
Trimmed Mean ( 23 / 24 )2.992592592592590.11220731803279126.6702087266541
Trimmed Mean ( 24 / 24 )2.9960.10511580915035328.5018973284472
Median3
Midrange3.45
Midmean - Weighted Average at Xnp2.95675675675676
Midmean - Weighted Average at X(n+1)p3.07692307692308
Midmean - Empirical Distribution Function3.07692307692308
Midmean - Empirical Distribution Function - Averaging3.07692307692308
Midmean - Empirical Distribution Function - Interpolation3.07692307692308
Midmean - Closest Observation3.07692307692308
Midmean - True Basic - Statistics Graphics Toolkit3.07692307692308
Midmean - MS Excel (old versions)3.07692307692308
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.29589041095890 & 0.234264599162393 & 14.0690929092286 \tabularnewline
Geometric Mean & 2.57530720843188 &  &  \tabularnewline
Harmonic Mean & 1.76042627308944 &  &  \tabularnewline
Quadratic Mean & 3.84892797741689 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.29589041095890 & 0.233744243176771 & 14.1004131959150 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.3013698630137 & 0.231815785510916 & 14.241350543655 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.30547945205479 & 0.231161536709456 & 14.2994353606907 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.3 & 0.230123056221158 & 14.3401537168382 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.3 & 0.227796338850983 & 14.4866243972374 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.3 & 0.227796338850983 & 14.4866243972374 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.30958904109589 & 0.226356593444044 & 14.6211293903132 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.32054794520548 & 0.224760644749295 & 14.7737071537116 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.30821917808219 & 0.222512919473884 & 14.8675375160428 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.30821917808219 & 0.218108596949742 & 15.1677614928883 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.30821917808219 & 0.218108596949742 & 15.1677614928883 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.30821917808219 & 0.212917629944095 & 15.5375540247692 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.30821917808219 & 0.207386005296309 & 15.951988531509 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.26986301369863 & 0.200832409019518 & 16.2815505209662 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.24931506849315 & 0.197406349178179 & 16.4600332361160 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.22739726027397 & 0.193808857353405 & 16.6524755594060 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.20410958904110 & 0.183109435262655 & 17.4983314455919 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.20410958904110 & 0.183109435262655 & 17.4983314455919 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.15205479452055 & 0.174944104892202 & 18.0174964824496 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.20684931506849 & 0.167478942622439 & 19.1477762210258 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.09178082191781 & 0.141619699771016 & 21.8315730573988 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.09178082191781 & 0.133087007404152 & 23.2312746542482 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.96575342465753 & 0.106472768581095 & 27.8545722458477 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.93287671232877 & 0.0932063469652896 & 31.4664913691015 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.29154929577465 & 0.231900090182069 & 14.1938249924370 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.28695652173913 & 0.229615797600209 & 14.3150277815909 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.27910447761194 & 0.227978921334276 & 14.3833669289273 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.26923076923077 & 0.226171342860586 & 14.4546640077472 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.26031746031746 & 0.224230374943517 & 14.5400348241790 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.25081967213115 & 0.222438337385679 & 14.6144756804878 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.24067796610169 & 0.220104627424865 & 14.7233522712190 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.22807017543860 & 0.217452129176721 & 14.8449692705247 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.21272727272727 & 0.214398454462219 & 14.9848434345566 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.19811320754717 & 0.210991345994223 & 15.1575563086589 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.18235294117647 & 0.207557332166564 & 15.3324043432137 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.16530612244898 & 0.203070625017424 & 15.5872181029501 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.1468085106383 & 0.19837105048608 & 15.8632446767182 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.12666666666667 & 0.193411687361650 & 16.1658621012921 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.10930232558140 & 0.188389865587638 & 16.5046156590359 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.09268292682927 & 0.182475866894256 & 16.9484490166662 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.07692307692308 & 0.175390889392243 & 17.5432320777042 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.06216216216216 & 0.168519046220923 & 18.1710152699759 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.04571428571429 & 0.158900785976387 & 19.1673959760456 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.03333333333333 & 0.147944672978199 & 20.5031602170652 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.01290322580645 & 0.134303614910946 & 22.4335229383382 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.00344827586207 & 0.124220005708596 & 24.1784586848899 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.99259259259259 & 0.112207318032791 & 26.6702087266541 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.996 & 0.105115809150353 & 28.5018973284472 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 3.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.95675675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.07692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.07692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.07692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.07692307692308 &  &  \tabularnewline
Midmean - Closest Observation & 3.07692307692308 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.07692307692308 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.07692307692308 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34031&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]3.29589041095890[/C][C]0.234264599162393[/C][C]14.0690929092286[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.57530720843188[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.76042627308944[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.84892797741689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.29589041095890[/C][C]0.233744243176771[/C][C]14.1004131959150[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.3013698630137[/C][C]0.231815785510916[/C][C]14.241350543655[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.30547945205479[/C][C]0.231161536709456[/C][C]14.2994353606907[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.3[/C][C]0.230123056221158[/C][C]14.3401537168382[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.3[/C][C]0.227796338850983[/C][C]14.4866243972374[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.3[/C][C]0.227796338850983[/C][C]14.4866243972374[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.30958904109589[/C][C]0.226356593444044[/C][C]14.6211293903132[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.32054794520548[/C][C]0.224760644749295[/C][C]14.7737071537116[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.30821917808219[/C][C]0.222512919473884[/C][C]14.8675375160428[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.30821917808219[/C][C]0.218108596949742[/C][C]15.1677614928883[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.30821917808219[/C][C]0.218108596949742[/C][C]15.1677614928883[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.30821917808219[/C][C]0.212917629944095[/C][C]15.5375540247692[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.30821917808219[/C][C]0.207386005296309[/C][C]15.951988531509[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.26986301369863[/C][C]0.200832409019518[/C][C]16.2815505209662[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.24931506849315[/C][C]0.197406349178179[/C][C]16.4600332361160[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.22739726027397[/C][C]0.193808857353405[/C][C]16.6524755594060[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.20410958904110[/C][C]0.183109435262655[/C][C]17.4983314455919[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.20410958904110[/C][C]0.183109435262655[/C][C]17.4983314455919[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.15205479452055[/C][C]0.174944104892202[/C][C]18.0174964824496[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.20684931506849[/C][C]0.167478942622439[/C][C]19.1477762210258[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.09178082191781[/C][C]0.141619699771016[/C][C]21.8315730573988[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.09178082191781[/C][C]0.133087007404152[/C][C]23.2312746542482[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.96575342465753[/C][C]0.106472768581095[/C][C]27.8545722458477[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.93287671232877[/C][C]0.0932063469652896[/C][C]31.4664913691015[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.29154929577465[/C][C]0.231900090182069[/C][C]14.1938249924370[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.28695652173913[/C][C]0.229615797600209[/C][C]14.3150277815909[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.27910447761194[/C][C]0.227978921334276[/C][C]14.3833669289273[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.26923076923077[/C][C]0.226171342860586[/C][C]14.4546640077472[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.26031746031746[/C][C]0.224230374943517[/C][C]14.5400348241790[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.25081967213115[/C][C]0.222438337385679[/C][C]14.6144756804878[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.24067796610169[/C][C]0.220104627424865[/C][C]14.7233522712190[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.22807017543860[/C][C]0.217452129176721[/C][C]14.8449692705247[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.21272727272727[/C][C]0.214398454462219[/C][C]14.9848434345566[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.19811320754717[/C][C]0.210991345994223[/C][C]15.1575563086589[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.18235294117647[/C][C]0.207557332166564[/C][C]15.3324043432137[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.16530612244898[/C][C]0.203070625017424[/C][C]15.5872181029501[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.1468085106383[/C][C]0.19837105048608[/C][C]15.8632446767182[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.12666666666667[/C][C]0.193411687361650[/C][C]16.1658621012921[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.10930232558140[/C][C]0.188389865587638[/C][C]16.5046156590359[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.09268292682927[/C][C]0.182475866894256[/C][C]16.9484490166662[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.07692307692308[/C][C]0.175390889392243[/C][C]17.5432320777042[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.06216216216216[/C][C]0.168519046220923[/C][C]18.1710152699759[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.04571428571429[/C][C]0.158900785976387[/C][C]19.1673959760456[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.03333333333333[/C][C]0.147944672978199[/C][C]20.5031602170652[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.01290322580645[/C][C]0.134303614910946[/C][C]22.4335229383382[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.00344827586207[/C][C]0.124220005708596[/C][C]24.1784586848899[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.99259259259259[/C][C]0.112207318032791[/C][C]26.6702087266541[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.996[/C][C]0.105115809150353[/C][C]28.5018973284472[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.95675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.07692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34031&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34031&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 Mean3.295890410958900.23426459916239314.0690929092286
Geometric Mean2.57530720843188
Harmonic Mean1.76042627308944
Quadratic Mean3.84892797741689
Winsorized Mean ( 1 / 24 )3.295890410958900.23374424317677114.1004131959150
Winsorized Mean ( 2 / 24 )3.30136986301370.23181578551091614.241350543655
Winsorized Mean ( 3 / 24 )3.305479452054790.23116153670945614.2994353606907
Winsorized Mean ( 4 / 24 )3.30.23012305622115814.3401537168382
Winsorized Mean ( 5 / 24 )3.30.22779633885098314.4866243972374
Winsorized Mean ( 6 / 24 )3.30.22779633885098314.4866243972374
Winsorized Mean ( 7 / 24 )3.309589041095890.22635659344404414.6211293903132
Winsorized Mean ( 8 / 24 )3.320547945205480.22476064474929514.7737071537116
Winsorized Mean ( 9 / 24 )3.308219178082190.22251291947388414.8675375160428
Winsorized Mean ( 10 / 24 )3.308219178082190.21810859694974215.1677614928883
Winsorized Mean ( 11 / 24 )3.308219178082190.21810859694974215.1677614928883
Winsorized Mean ( 12 / 24 )3.308219178082190.21291762994409515.5375540247692
Winsorized Mean ( 13 / 24 )3.308219178082190.20738600529630915.951988531509
Winsorized Mean ( 14 / 24 )3.269863013698630.20083240901951816.2815505209662
Winsorized Mean ( 15 / 24 )3.249315068493150.19740634917817916.4600332361160
Winsorized Mean ( 16 / 24 )3.227397260273970.19380885735340516.6524755594060
Winsorized Mean ( 17 / 24 )3.204109589041100.18310943526265517.4983314455919
Winsorized Mean ( 18 / 24 )3.204109589041100.18310943526265517.4983314455919
Winsorized Mean ( 19 / 24 )3.152054794520550.17494410489220218.0174964824496
Winsorized Mean ( 20 / 24 )3.206849315068490.16747894262243919.1477762210258
Winsorized Mean ( 21 / 24 )3.091780821917810.14161969977101621.8315730573988
Winsorized Mean ( 22 / 24 )3.091780821917810.13308700740415223.2312746542482
Winsorized Mean ( 23 / 24 )2.965753424657530.10647276858109527.8545722458477
Winsorized Mean ( 24 / 24 )2.932876712328770.093206346965289631.4664913691015
Trimmed Mean ( 1 / 24 )3.291549295774650.23190009018206914.1938249924370
Trimmed Mean ( 2 / 24 )3.286956521739130.22961579760020914.3150277815909
Trimmed Mean ( 3 / 24 )3.279104477611940.22797892133427614.3833669289273
Trimmed Mean ( 4 / 24 )3.269230769230770.22617134286058614.4546640077472
Trimmed Mean ( 5 / 24 )3.260317460317460.22423037494351714.5400348241790
Trimmed Mean ( 6 / 24 )3.250819672131150.22243833738567914.6144756804878
Trimmed Mean ( 7 / 24 )3.240677966101690.22010462742486514.7233522712190
Trimmed Mean ( 8 / 24 )3.228070175438600.21745212917672114.8449692705247
Trimmed Mean ( 9 / 24 )3.212727272727270.21439845446221914.9848434345566
Trimmed Mean ( 10 / 24 )3.198113207547170.21099134599422315.1575563086589
Trimmed Mean ( 11 / 24 )3.182352941176470.20755733216656415.3324043432137
Trimmed Mean ( 12 / 24 )3.165306122448980.20307062501742415.5872181029501
Trimmed Mean ( 13 / 24 )3.14680851063830.1983710504860815.8632446767182
Trimmed Mean ( 14 / 24 )3.126666666666670.19341168736165016.1658621012921
Trimmed Mean ( 15 / 24 )3.109302325581400.18838986558763816.5046156590359
Trimmed Mean ( 16 / 24 )3.092682926829270.18247586689425616.9484490166662
Trimmed Mean ( 17 / 24 )3.076923076923080.17539088939224317.5432320777042
Trimmed Mean ( 18 / 24 )3.062162162162160.16851904622092318.1710152699759
Trimmed Mean ( 19 / 24 )3.045714285714290.15890078597638719.1673959760456
Trimmed Mean ( 20 / 24 )3.033333333333330.14794467297819920.5031602170652
Trimmed Mean ( 21 / 24 )3.012903225806450.13430361491094622.4335229383382
Trimmed Mean ( 22 / 24 )3.003448275862070.12422000570859624.1784586848899
Trimmed Mean ( 23 / 24 )2.992592592592590.11220731803279126.6702087266541
Trimmed Mean ( 24 / 24 )2.9960.10511580915035328.5018973284472
Median3
Midrange3.45
Midmean - Weighted Average at Xnp2.95675675675676
Midmean - Weighted Average at X(n+1)p3.07692307692308
Midmean - Empirical Distribution Function3.07692307692308
Midmean - Empirical Distribution Function - Averaging3.07692307692308
Midmean - Empirical Distribution Function - Interpolation3.07692307692308
Midmean - Closest Observation3.07692307692308
Midmean - True Basic - Statistics Graphics Toolkit3.07692307692308
Midmean - MS Excel (old versions)3.07692307692308
Number of observations73



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')