Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Dec 2014 14:47:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/26/t1419605311pd9rs0a7fhmv0z3.htm/, Retrieved Thu, 31 Oct 2024 23:18:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271541, Retrieved Thu, 31 Oct 2024 23:18:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Data reeks - aant...] [2014-09-23 14:19:26] [7374732ae26351929a6f66a8cd8fe417]
- RMPD    [Central Tendency] [Trimmed Mean Plot...] [2014-12-26 14:47:08] [be7d2a6a6c016378f31f309d9b06695b] [Current]
Feedback Forum

Post a new message
Dataseries X:
71
77
76
69
74
101
105
73
68
65
70
65
80
92
93
90
96
125
134
100
97
97
101
90
108
113
112
103
103
125
128
91
84
83
83
69
77
83
78
70
75
101
117
80
87
81
78
73
93
105
102
97
100
127
138
107
107
106
109
107
129
138
137
134
134
166
180
131
135
127
121
116




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271541&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271541&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.7916666666672.9000659360590134.7549569178539
Geometric Mean97.9885755176075
Harmonic Mean95.3447967484864
Quadratic Mean103.711606015056
Winsorized Mean ( 1 / 24 )100.5972222222222.8309614293253735.5346495293632
Winsorized Mean ( 2 / 24 )99.90277777777782.6079329832865438.3072641889284
Winsorized Mean ( 3 / 24 )99.94444444444442.6008522204554938.4275752610585
Winsorized Mean ( 4 / 24 )99.88888888888892.5895204989604938.5742800371679
Winsorized Mean ( 5 / 24 )99.81944444444442.5504553575517139.1378912588635
Winsorized Mean ( 6 / 24 )99.73611111111112.5344259639930839.3525447292898
Winsorized Mean ( 7 / 24 )99.83333333333332.5185539980317239.6391474676954
Winsorized Mean ( 8 / 24 )100.0555555555562.4835837294508240.2867655996765
Winsorized Mean ( 9 / 24 )99.68055555555562.4131896947184241.3065561210208
Winsorized Mean ( 10 / 24 )99.54166666666672.3416967401540742.5083508721618
Winsorized Mean ( 11 / 24 )99.54166666666672.2915386221163843.4387907347308
Winsorized Mean ( 12 / 24 )99.54166666666672.2376366553245344.4851787844125
Winsorized Mean ( 13 / 24 )99.72222222222222.2111913229291445.0988664744403
Winsorized Mean ( 14 / 24 )99.33333333333332.1446151220928346.3175570805444
Winsorized Mean ( 15 / 24 )99.54166666666672.1143871038024647.0782604035248
Winsorized Mean ( 16 / 24 )98.65277777777781.9677723996519250.1342420471131
Winsorized Mean ( 17 / 24 )98.18055555555561.7510701388067556.0688880357812
Winsorized Mean ( 18 / 24 )97.93055555555561.7135799302006857.1496863552123
Winsorized Mean ( 19 / 24 )97.40277777777781.5599220169082162.4407994258786
Winsorized Mean ( 20 / 24 )97.68055555555561.4398240400786767.842009048702
Winsorized Mean ( 21 / 24 )96.80555555555561.3214906709704873.254815703287
Winsorized Mean ( 22 / 24 )96.51.282328427971275.253732113445
Winsorized Mean ( 23 / 24 )96.51.1951584647520880.7424311051655
Winsorized Mean ( 24 / 24 )97.51.0509329635598692.7747091210603
Trimmed Mean ( 1 / 24 )100.1714285714292.7077047822490336.9949594313697
Trimmed Mean ( 2 / 24 )99.72058823529412.5586917054031938.973272170584
Trimmed Mean ( 3 / 24 )99.62121212121212.5251891988951739.4509893218293
Trimmed Mean ( 4 / 24 )99.52.4872691725078640.0037121433368
Trimmed Mean ( 5 / 24 )99.38709677419362.4448820737788540.6510800009994
Trimmed Mean ( 6 / 24 )99.28333333333332.4049256970406141.2833267387458
Trimmed Mean ( 7 / 24 )99.18965517241382.3598600469837442.0320074909498
Trimmed Mean ( 8 / 24 )99.07142857142862.3077870919119842.9291891434183
Trimmed Mean ( 9 / 24 )98.90740740740742.2510605495736143.938137259854
Trimmed Mean ( 10 / 24 )98.78846153846152.1969979068632144.965205123708
Trimmed Mean ( 11 / 24 )98.682.1450350836767446.0039095635003
Trimmed Mean ( 12 / 24 )98.56252.0897220305326847.1653638904673
Trimmed Mean ( 13 / 24 )98.43478260869572.0303618520247948.4813987765437
Trimmed Mean ( 14 / 24 )98.27272727272731.9584380334950150.1791354089212
Trimmed Mean ( 15 / 24 )98.14285714285711.8804487777586552.1911887756047
Trimmed Mean ( 16 / 24 )97.9751.7832869033016554.9406827463406
Trimmed Mean ( 17 / 24 )97.89473684210531.6933429500944957.8115241431999
Trimmed Mean ( 18 / 24 )97.86111111111111.6296619465290160.0499455236982
Trimmed Mean ( 19 / 24 )97.85294117647061.5507644902922863.0998077329123
Trimmed Mean ( 20 / 24 )97.906251.4840274423327865.973342006465
Trimmed Mean ( 21 / 24 )97.93333333333331.4238795420229868.7792263622205
Trimmed Mean ( 22 / 24 )98.07142857142861.369478883074471.6122240244145
Trimmed Mean ( 23 / 24 )98.26923076923081.2956230367103175.8470851357694
Trimmed Mean ( 24 / 24 )98.51.2113592796308781.3136132741849
Median100
Midrange122.5
Midmean - Weighted Average at Xnp97.3783783783784
Midmean - Weighted Average at X(n+1)p97.3783783783784
Midmean - Empirical Distribution Function97.3783783783784
Midmean - Empirical Distribution Function - Averaging97.3783783783784
Midmean - Empirical Distribution Function - Interpolation97.3783783783784
Midmean - Closest Observation97.3783783783784
Midmean - True Basic - Statistics Graphics Toolkit97.3783783783784
Midmean - MS Excel (old versions)97.8947368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.791666666667 & 2.90006593605901 & 34.7549569178539 \tabularnewline
Geometric Mean & 97.9885755176075 &  &  \tabularnewline
Harmonic Mean & 95.3447967484864 &  &  \tabularnewline
Quadratic Mean & 103.711606015056 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.597222222222 & 2.83096142932537 & 35.5346495293632 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.9027777777778 & 2.60793298328654 & 38.3072641889284 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.9444444444444 & 2.60085222045549 & 38.4275752610585 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.8888888888889 & 2.58952049896049 & 38.5742800371679 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.8194444444444 & 2.55045535755171 & 39.1378912588635 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.7361111111111 & 2.53442596399308 & 39.3525447292898 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.8333333333333 & 2.51855399803172 & 39.6391474676954 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.055555555556 & 2.48358372945082 & 40.2867655996765 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.6805555555556 & 2.41318969471842 & 41.3065561210208 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.5416666666667 & 2.34169674015407 & 42.5083508721618 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.5416666666667 & 2.29153862211638 & 43.4387907347308 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.5416666666667 & 2.23763665532453 & 44.4851787844125 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.7222222222222 & 2.21119132292914 & 45.0988664744403 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.3333333333333 & 2.14461512209283 & 46.3175570805444 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.5416666666667 & 2.11438710380246 & 47.0782604035248 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.6527777777778 & 1.96777239965192 & 50.1342420471131 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.1805555555556 & 1.75107013880675 & 56.0688880357812 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.9305555555556 & 1.71357993020068 & 57.1496863552123 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.4027777777778 & 1.55992201690821 & 62.4407994258786 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.6805555555556 & 1.43982404007867 & 67.842009048702 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 96.8055555555556 & 1.32149067097048 & 73.254815703287 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 96.5 & 1.2823284279712 & 75.253732113445 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 96.5 & 1.19515846475208 & 80.7424311051655 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.5 & 1.05093296355986 & 92.7747091210603 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.171428571429 & 2.70770478224903 & 36.9949594313697 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.7205882352941 & 2.55869170540319 & 38.973272170584 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.6212121212121 & 2.52518919889517 & 39.4509893218293 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.5 & 2.48726917250786 & 40.0037121433368 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.3870967741936 & 2.44488207377885 & 40.6510800009994 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.2833333333333 & 2.40492569704061 & 41.2833267387458 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.1896551724138 & 2.35986004698374 & 42.0320074909498 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.0714285714286 & 2.30778709191198 & 42.9291891434183 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.9074074074074 & 2.25106054957361 & 43.938137259854 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.7884615384615 & 2.19699790686321 & 44.965205123708 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.68 & 2.14503508367674 & 46.0039095635003 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.5625 & 2.08972203053268 & 47.1653638904673 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.4347826086957 & 2.03036185202479 & 48.4813987765437 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.2727272727273 & 1.95843803349501 & 50.1791354089212 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.1428571428571 & 1.88044877775865 & 52.1911887756047 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.975 & 1.78328690330165 & 54.9406827463406 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.8947368421053 & 1.69334295009449 & 57.8115241431999 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.8611111111111 & 1.62966194652901 & 60.0499455236982 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.8529411764706 & 1.55076449029228 & 63.0998077329123 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.90625 & 1.48402744233278 & 65.973342006465 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.9333333333333 & 1.42387954202298 & 68.7792263622205 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.0714285714286 & 1.3694788830744 & 71.6122240244145 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.2692307692308 & 1.29562303671031 & 75.8470851357694 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.5 & 1.21135927963087 & 81.3136132741849 \tabularnewline
Median & 100 &  &  \tabularnewline
Midrange & 122.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.3783783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.3783783783784 &  &  \tabularnewline
Midmean - Closest Observation & 97.3783783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.3783783783784 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.8947368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271541&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]100.791666666667[/C][C]2.90006593605901[/C][C]34.7549569178539[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.9885755176075[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.3447967484864[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.711606015056[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.597222222222[/C][C]2.83096142932537[/C][C]35.5346495293632[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.9027777777778[/C][C]2.60793298328654[/C][C]38.3072641889284[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.9444444444444[/C][C]2.60085222045549[/C][C]38.4275752610585[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.8888888888889[/C][C]2.58952049896049[/C][C]38.5742800371679[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.8194444444444[/C][C]2.55045535755171[/C][C]39.1378912588635[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.7361111111111[/C][C]2.53442596399308[/C][C]39.3525447292898[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.8333333333333[/C][C]2.51855399803172[/C][C]39.6391474676954[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.055555555556[/C][C]2.48358372945082[/C][C]40.2867655996765[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.6805555555556[/C][C]2.41318969471842[/C][C]41.3065561210208[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.5416666666667[/C][C]2.34169674015407[/C][C]42.5083508721618[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.5416666666667[/C][C]2.29153862211638[/C][C]43.4387907347308[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.5416666666667[/C][C]2.23763665532453[/C][C]44.4851787844125[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.7222222222222[/C][C]2.21119132292914[/C][C]45.0988664744403[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.3333333333333[/C][C]2.14461512209283[/C][C]46.3175570805444[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.5416666666667[/C][C]2.11438710380246[/C][C]47.0782604035248[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.6527777777778[/C][C]1.96777239965192[/C][C]50.1342420471131[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.1805555555556[/C][C]1.75107013880675[/C][C]56.0688880357812[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.9305555555556[/C][C]1.71357993020068[/C][C]57.1496863552123[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.4027777777778[/C][C]1.55992201690821[/C][C]62.4407994258786[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.6805555555556[/C][C]1.43982404007867[/C][C]67.842009048702[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]96.8055555555556[/C][C]1.32149067097048[/C][C]73.254815703287[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]96.5[/C][C]1.2823284279712[/C][C]75.253732113445[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]96.5[/C][C]1.19515846475208[/C][C]80.7424311051655[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.5[/C][C]1.05093296355986[/C][C]92.7747091210603[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.171428571429[/C][C]2.70770478224903[/C][C]36.9949594313697[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.7205882352941[/C][C]2.55869170540319[/C][C]38.973272170584[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.6212121212121[/C][C]2.52518919889517[/C][C]39.4509893218293[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.5[/C][C]2.48726917250786[/C][C]40.0037121433368[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.3870967741936[/C][C]2.44488207377885[/C][C]40.6510800009994[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.2833333333333[/C][C]2.40492569704061[/C][C]41.2833267387458[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.1896551724138[/C][C]2.35986004698374[/C][C]42.0320074909498[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.0714285714286[/C][C]2.30778709191198[/C][C]42.9291891434183[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.9074074074074[/C][C]2.25106054957361[/C][C]43.938137259854[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.7884615384615[/C][C]2.19699790686321[/C][C]44.965205123708[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.68[/C][C]2.14503508367674[/C][C]46.0039095635003[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.5625[/C][C]2.08972203053268[/C][C]47.1653638904673[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.4347826086957[/C][C]2.03036185202479[/C][C]48.4813987765437[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.2727272727273[/C][C]1.95843803349501[/C][C]50.1791354089212[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.1428571428571[/C][C]1.88044877775865[/C][C]52.1911887756047[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.975[/C][C]1.78328690330165[/C][C]54.9406827463406[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.8947368421053[/C][C]1.69334295009449[/C][C]57.8115241431999[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.8611111111111[/C][C]1.62966194652901[/C][C]60.0499455236982[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.8529411764706[/C][C]1.55076449029228[/C][C]63.0998077329123[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.90625[/C][C]1.48402744233278[/C][C]65.973342006465[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.9333333333333[/C][C]1.42387954202298[/C][C]68.7792263622205[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.0714285714286[/C][C]1.3694788830744[/C][C]71.6122240244145[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.2692307692308[/C][C]1.29562303671031[/C][C]75.8470851357694[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.5[/C][C]1.21135927963087[/C][C]81.3136132741849[/C][/ROW]
[ROW][C]Median[/C][C]100[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.8947368421053[/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=271541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271541&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 Mean100.7916666666672.9000659360590134.7549569178539
Geometric Mean97.9885755176075
Harmonic Mean95.3447967484864
Quadratic Mean103.711606015056
Winsorized Mean ( 1 / 24 )100.5972222222222.8309614293253735.5346495293632
Winsorized Mean ( 2 / 24 )99.90277777777782.6079329832865438.3072641889284
Winsorized Mean ( 3 / 24 )99.94444444444442.6008522204554938.4275752610585
Winsorized Mean ( 4 / 24 )99.88888888888892.5895204989604938.5742800371679
Winsorized Mean ( 5 / 24 )99.81944444444442.5504553575517139.1378912588635
Winsorized Mean ( 6 / 24 )99.73611111111112.5344259639930839.3525447292898
Winsorized Mean ( 7 / 24 )99.83333333333332.5185539980317239.6391474676954
Winsorized Mean ( 8 / 24 )100.0555555555562.4835837294508240.2867655996765
Winsorized Mean ( 9 / 24 )99.68055555555562.4131896947184241.3065561210208
Winsorized Mean ( 10 / 24 )99.54166666666672.3416967401540742.5083508721618
Winsorized Mean ( 11 / 24 )99.54166666666672.2915386221163843.4387907347308
Winsorized Mean ( 12 / 24 )99.54166666666672.2376366553245344.4851787844125
Winsorized Mean ( 13 / 24 )99.72222222222222.2111913229291445.0988664744403
Winsorized Mean ( 14 / 24 )99.33333333333332.1446151220928346.3175570805444
Winsorized Mean ( 15 / 24 )99.54166666666672.1143871038024647.0782604035248
Winsorized Mean ( 16 / 24 )98.65277777777781.9677723996519250.1342420471131
Winsorized Mean ( 17 / 24 )98.18055555555561.7510701388067556.0688880357812
Winsorized Mean ( 18 / 24 )97.93055555555561.7135799302006857.1496863552123
Winsorized Mean ( 19 / 24 )97.40277777777781.5599220169082162.4407994258786
Winsorized Mean ( 20 / 24 )97.68055555555561.4398240400786767.842009048702
Winsorized Mean ( 21 / 24 )96.80555555555561.3214906709704873.254815703287
Winsorized Mean ( 22 / 24 )96.51.282328427971275.253732113445
Winsorized Mean ( 23 / 24 )96.51.1951584647520880.7424311051655
Winsorized Mean ( 24 / 24 )97.51.0509329635598692.7747091210603
Trimmed Mean ( 1 / 24 )100.1714285714292.7077047822490336.9949594313697
Trimmed Mean ( 2 / 24 )99.72058823529412.5586917054031938.973272170584
Trimmed Mean ( 3 / 24 )99.62121212121212.5251891988951739.4509893218293
Trimmed Mean ( 4 / 24 )99.52.4872691725078640.0037121433368
Trimmed Mean ( 5 / 24 )99.38709677419362.4448820737788540.6510800009994
Trimmed Mean ( 6 / 24 )99.28333333333332.4049256970406141.2833267387458
Trimmed Mean ( 7 / 24 )99.18965517241382.3598600469837442.0320074909498
Trimmed Mean ( 8 / 24 )99.07142857142862.3077870919119842.9291891434183
Trimmed Mean ( 9 / 24 )98.90740740740742.2510605495736143.938137259854
Trimmed Mean ( 10 / 24 )98.78846153846152.1969979068632144.965205123708
Trimmed Mean ( 11 / 24 )98.682.1450350836767446.0039095635003
Trimmed Mean ( 12 / 24 )98.56252.0897220305326847.1653638904673
Trimmed Mean ( 13 / 24 )98.43478260869572.0303618520247948.4813987765437
Trimmed Mean ( 14 / 24 )98.27272727272731.9584380334950150.1791354089212
Trimmed Mean ( 15 / 24 )98.14285714285711.8804487777586552.1911887756047
Trimmed Mean ( 16 / 24 )97.9751.7832869033016554.9406827463406
Trimmed Mean ( 17 / 24 )97.89473684210531.6933429500944957.8115241431999
Trimmed Mean ( 18 / 24 )97.86111111111111.6296619465290160.0499455236982
Trimmed Mean ( 19 / 24 )97.85294117647061.5507644902922863.0998077329123
Trimmed Mean ( 20 / 24 )97.906251.4840274423327865.973342006465
Trimmed Mean ( 21 / 24 )97.93333333333331.4238795420229868.7792263622205
Trimmed Mean ( 22 / 24 )98.07142857142861.369478883074471.6122240244145
Trimmed Mean ( 23 / 24 )98.26923076923081.2956230367103175.8470851357694
Trimmed Mean ( 24 / 24 )98.51.2113592796308781.3136132741849
Median100
Midrange122.5
Midmean - Weighted Average at Xnp97.3783783783784
Midmean - Weighted Average at X(n+1)p97.3783783783784
Midmean - Empirical Distribution Function97.3783783783784
Midmean - Empirical Distribution Function - Averaging97.3783783783784
Midmean - Empirical Distribution Function - Interpolation97.3783783783784
Midmean - Closest Observation97.3783783783784
Midmean - True Basic - Statistics Graphics Toolkit97.3783783783784
Midmean - MS Excel (old versions)97.8947368421053
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')