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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 computationMon, 22 Dec 2008 03:25:05 -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/22/t1229941550wswbn0vcjg5ioxp.htm/, Retrieved Mon, 13 May 2024 19:15:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35980, Retrieved Mon, 13 May 2024 19:15:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2008-12-20 12:03:40] [d2d412c7f4d35ffbf5ee5ee89db327d4]
-    D    [Central Tendency] [aantal faillissem...] [2008-12-22 10:25:05] [f6a332ba2d530c028d935c5a5bbb53af] [Current]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35980&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]1 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=35980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35980&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51.95833333333331.4226863957298136.5212836007191
Geometric Mean50.3924882719918
Harmonic Mean48.6041484816367
Quadratic Mean53.3233063491003
Winsorized Mean ( 1 / 24 )521.3977961638972837.2014184493222
Winsorized Mean ( 2 / 24 )521.3977961638972837.2014184493222
Winsorized Mean ( 3 / 24 )51.95833333333331.3712960497372737.8899460428608
Winsorized Mean ( 4 / 24 )52.06944444444441.3447757823838538.7197963605071
Winsorized Mean ( 5 / 24 )52.41666666666671.2709511797895541.2420771939848
Winsorized Mean ( 6 / 24 )52.41666666666671.2391548308567742.300336779081
Winsorized Mean ( 7 / 24 )52.1251.1875952313350843.891216994364
Winsorized Mean ( 8 / 24 )52.1251.1487452329949645.375596348811
Winsorized Mean ( 9 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 10 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 11 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 12 / 24 )52.251.0313455817136150.6619710467805
Winsorized Mean ( 13 / 24 )52.251.0313455817136150.6619710467805
Winsorized Mean ( 14 / 24 )52.05555555555561.0034932898731251.8743434369525
Winsorized Mean ( 15 / 24 )52.26388888888890.96879986732281853.947043813409
Winsorized Mean ( 16 / 24 )52.48611111111110.9330048582691456.2549172664337
Winsorized Mean ( 17 / 24 )52.72222222222220.826787015656163.7675982131677
Winsorized Mean ( 18 / 24 )52.97222222222220.79043881114950967.0162212115907
Winsorized Mean ( 19 / 24 )52.70833333333330.75356157475574469.945622360612
Winsorized Mean ( 20 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 21 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 22 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 23 / 24 )52.43055555555560.62979813595592483.249778877124
Winsorized Mean ( 24 / 24 )52.76388888888890.58257598574678790.5699688620918
Trimmed Mean ( 1 / 24 )52.07142857142861.3622113048862938.2256617491331
Trimmed Mean ( 2 / 24 )52.14705882352941.3198465979387939.5099391891208
Trimmed Mean ( 3 / 24 )52.22727272727271.2691049017068541.1528413900468
Trimmed Mean ( 4 / 24 )52.3281251.2204959893704942.8744751770877
Trimmed Mean ( 5 / 24 )52.40322580645161.1720027824915044.712543851688
Trimmed Mean ( 6 / 24 )52.41.1377448206149646.0560215705289
Trimmed Mean ( 7 / 24 )52.39655172413791.1051602154157147.410819710361
Trimmed Mean ( 8 / 24 )52.44642857142861.0786955936099348.6202306583205
Trimmed Mean ( 9 / 24 )52.51.0553348550031349.7472434944301
Trimmed Mean ( 10 / 24 )52.53846153846151.0408190657593850.4779968650265
Trimmed Mean ( 11 / 24 )52.581.0218390783488451.4562430759276
Trimmed Mean ( 12 / 24 )52.6250.99717019823865552.7743409228974
Trimmed Mean ( 13 / 24 )52.67391304347830.9770577679736153.910745884271
Trimmed Mean ( 14 / 24 )52.72727272727270.9503329984775855.4829442013916
Trimmed Mean ( 15 / 24 )52.80952380952380.92093858048937957.3431550467364
Trimmed Mean ( 16 / 24 )52.8750.89025169301893359.3933158618273
Trimmed Mean ( 17 / 24 )52.92105263157890.85788251917750361.6879950908862
Trimmed Mean ( 18 / 24 )52.94444444444440.84039337391943462.9995976735534
Trimmed Mean ( 19 / 24 )52.94117647058820.82403854900763264.2459949650947
Trimmed Mean ( 20 / 24 )52.968750.80882777459210265.4882926426612
Trimmed Mean ( 21 / 24 )53.03333333333330.79435267267277266.7629570061006
Trimmed Mean ( 22 / 24 )53.10714285714290.77038313445149968.9360144091866
Trimmed Mean ( 23 / 24 )53.19230769230770.7317402455668672.6928825010862
Trimmed Mean ( 24 / 24 )53.29166666666670.7031996404290375.784547662955
Median53.5
Midrange48
Midmean - Weighted Average at Xnp52.9210526315789
Midmean - Weighted Average at X(n+1)p53.1621621621622
Midmean - Empirical Distribution Function52.9210526315789
Midmean - Empirical Distribution Function - Averaging53.1621621621622
Midmean - Empirical Distribution Function - Interpolation53.1621621621622
Midmean - Closest Observation52.9210526315789
Midmean - True Basic - Statistics Graphics Toolkit53.1621621621622
Midmean - MS Excel (old versions)52.9210526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51.9583333333333 & 1.42268639572981 & 36.5212836007191 \tabularnewline
Geometric Mean & 50.3924882719918 &  &  \tabularnewline
Harmonic Mean & 48.6041484816367 &  &  \tabularnewline
Quadratic Mean & 53.3233063491003 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 52 & 1.39779616389728 & 37.2014184493222 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 52 & 1.39779616389728 & 37.2014184493222 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 51.9583333333333 & 1.37129604973727 & 37.8899460428608 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 52.0694444444444 & 1.34477578238385 & 38.7197963605071 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 52.4166666666667 & 1.27095117978955 & 41.2420771939848 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 52.4166666666667 & 1.23915483085677 & 42.300336779081 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 52.125 & 1.18759523133508 & 43.891216994364 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 52.125 & 1.14874523299496 & 45.375596348811 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 52.25 & 1.08459659102277 & 48.1745936069451 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 52.25 & 1.08459659102277 & 48.1745936069451 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 52.25 & 1.08459659102277 & 48.1745936069451 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 52.25 & 1.03134558171361 & 50.6619710467805 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 52.25 & 1.03134558171361 & 50.6619710467805 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 52.0555555555556 & 1.00349328987312 & 51.8743434369525 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 52.2638888888889 & 0.968799867322818 & 53.947043813409 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 52.4861111111111 & 0.93300485826914 & 56.2549172664337 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 52.7222222222222 & 0.8267870156561 & 63.7675982131677 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 52.9722222222222 & 0.790438811149509 & 67.0162212115907 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 52.7083333333333 & 0.753561574755744 & 69.945622360612 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 52.4305555555556 & 0.716676599147486 & 73.1579008131753 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 52.4305555555556 & 0.716676599147486 & 73.1579008131753 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 52.4305555555556 & 0.716676599147486 & 73.1579008131753 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 52.4305555555556 & 0.629798135955924 & 83.249778877124 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 52.7638888888889 & 0.582575985746787 & 90.5699688620918 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 52.0714285714286 & 1.36221130488629 & 38.2256617491331 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 52.1470588235294 & 1.31984659793879 & 39.5099391891208 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 52.2272727272727 & 1.26910490170685 & 41.1528413900468 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 52.328125 & 1.22049598937049 & 42.8744751770877 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 52.4032258064516 & 1.17200278249150 & 44.712543851688 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 52.4 & 1.13774482061496 & 46.0560215705289 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 52.3965517241379 & 1.10516021541571 & 47.410819710361 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 52.4464285714286 & 1.07869559360993 & 48.6202306583205 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 52.5 & 1.05533485500313 & 49.7472434944301 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 52.5384615384615 & 1.04081906575938 & 50.4779968650265 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 52.58 & 1.02183907834884 & 51.4562430759276 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 52.625 & 0.997170198238655 & 52.7743409228974 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 52.6739130434783 & 0.97705776797361 & 53.910745884271 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 52.7272727272727 & 0.95033299847758 & 55.4829442013916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 52.8095238095238 & 0.920938580489379 & 57.3431550467364 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 52.875 & 0.890251693018933 & 59.3933158618273 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 52.9210526315789 & 0.857882519177503 & 61.6879950908862 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 52.9444444444444 & 0.840393373919434 & 62.9995976735534 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 52.9411764705882 & 0.824038549007632 & 64.2459949650947 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 52.96875 & 0.808827774592102 & 65.4882926426612 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 53.0333333333333 & 0.794352672672772 & 66.7629570061006 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 53.1071428571429 & 0.770383134451499 & 68.9360144091866 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 53.1923076923077 & 0.73174024556686 & 72.6928825010862 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 53.2916666666667 & 0.70319964042903 & 75.784547662955 \tabularnewline
Median & 53.5 &  &  \tabularnewline
Midrange & 48 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.9210526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 53.1621621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.9210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 53.1621621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 53.1621621621622 &  &  \tabularnewline
Midmean - Closest Observation & 52.9210526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 53.1621621621622 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.9210526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35980&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]51.9583333333333[/C][C]1.42268639572981[/C][C]36.5212836007191[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50.3924882719918[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]48.6041484816367[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]53.3233063491003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]52[/C][C]1.39779616389728[/C][C]37.2014184493222[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]52[/C][C]1.39779616389728[/C][C]37.2014184493222[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]51.9583333333333[/C][C]1.37129604973727[/C][C]37.8899460428608[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]52.0694444444444[/C][C]1.34477578238385[/C][C]38.7197963605071[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]52.4166666666667[/C][C]1.27095117978955[/C][C]41.2420771939848[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]52.4166666666667[/C][C]1.23915483085677[/C][C]42.300336779081[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]52.125[/C][C]1.18759523133508[/C][C]43.891216994364[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]52.125[/C][C]1.14874523299496[/C][C]45.375596348811[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]52.25[/C][C]1.08459659102277[/C][C]48.1745936069451[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]52.25[/C][C]1.08459659102277[/C][C]48.1745936069451[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]52.25[/C][C]1.08459659102277[/C][C]48.1745936069451[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]52.25[/C][C]1.03134558171361[/C][C]50.6619710467805[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]52.25[/C][C]1.03134558171361[/C][C]50.6619710467805[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]52.0555555555556[/C][C]1.00349328987312[/C][C]51.8743434369525[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]52.2638888888889[/C][C]0.968799867322818[/C][C]53.947043813409[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]52.4861111111111[/C][C]0.93300485826914[/C][C]56.2549172664337[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]52.7222222222222[/C][C]0.8267870156561[/C][C]63.7675982131677[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]52.9722222222222[/C][C]0.790438811149509[/C][C]67.0162212115907[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]52.7083333333333[/C][C]0.753561574755744[/C][C]69.945622360612[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]52.4305555555556[/C][C]0.716676599147486[/C][C]73.1579008131753[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]52.4305555555556[/C][C]0.716676599147486[/C][C]73.1579008131753[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]52.4305555555556[/C][C]0.716676599147486[/C][C]73.1579008131753[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]52.4305555555556[/C][C]0.629798135955924[/C][C]83.249778877124[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]52.7638888888889[/C][C]0.582575985746787[/C][C]90.5699688620918[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]52.0714285714286[/C][C]1.36221130488629[/C][C]38.2256617491331[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]52.1470588235294[/C][C]1.31984659793879[/C][C]39.5099391891208[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]52.2272727272727[/C][C]1.26910490170685[/C][C]41.1528413900468[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]52.328125[/C][C]1.22049598937049[/C][C]42.8744751770877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]52.4032258064516[/C][C]1.17200278249150[/C][C]44.712543851688[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]52.4[/C][C]1.13774482061496[/C][C]46.0560215705289[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]52.3965517241379[/C][C]1.10516021541571[/C][C]47.410819710361[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]52.4464285714286[/C][C]1.07869559360993[/C][C]48.6202306583205[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]52.5[/C][C]1.05533485500313[/C][C]49.7472434944301[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]52.5384615384615[/C][C]1.04081906575938[/C][C]50.4779968650265[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]52.58[/C][C]1.02183907834884[/C][C]51.4562430759276[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]52.625[/C][C]0.997170198238655[/C][C]52.7743409228974[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]52.6739130434783[/C][C]0.97705776797361[/C][C]53.910745884271[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]52.7272727272727[/C][C]0.95033299847758[/C][C]55.4829442013916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]52.8095238095238[/C][C]0.920938580489379[/C][C]57.3431550467364[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]52.875[/C][C]0.890251693018933[/C][C]59.3933158618273[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]52.9210526315789[/C][C]0.857882519177503[/C][C]61.6879950908862[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]52.9444444444444[/C][C]0.840393373919434[/C][C]62.9995976735534[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]52.9411764705882[/C][C]0.824038549007632[/C][C]64.2459949650947[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]52.96875[/C][C]0.808827774592102[/C][C]65.4882926426612[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]53.0333333333333[/C][C]0.794352672672772[/C][C]66.7629570061006[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]53.1071428571429[/C][C]0.770383134451499[/C][C]68.9360144091866[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]53.1923076923077[/C][C]0.73174024556686[/C][C]72.6928825010862[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]53.2916666666667[/C][C]0.70319964042903[/C][C]75.784547662955[/C][/ROW]
[ROW][C]Median[/C][C]53.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.9210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]53.1621621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.9210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]53.1621621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]53.1621621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.9210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]53.1621621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.9210526315789[/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=35980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35980&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 Mean51.95833333333331.4226863957298136.5212836007191
Geometric Mean50.3924882719918
Harmonic Mean48.6041484816367
Quadratic Mean53.3233063491003
Winsorized Mean ( 1 / 24 )521.3977961638972837.2014184493222
Winsorized Mean ( 2 / 24 )521.3977961638972837.2014184493222
Winsorized Mean ( 3 / 24 )51.95833333333331.3712960497372737.8899460428608
Winsorized Mean ( 4 / 24 )52.06944444444441.3447757823838538.7197963605071
Winsorized Mean ( 5 / 24 )52.41666666666671.2709511797895541.2420771939848
Winsorized Mean ( 6 / 24 )52.41666666666671.2391548308567742.300336779081
Winsorized Mean ( 7 / 24 )52.1251.1875952313350843.891216994364
Winsorized Mean ( 8 / 24 )52.1251.1487452329949645.375596348811
Winsorized Mean ( 9 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 10 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 11 / 24 )52.251.0845965910227748.1745936069451
Winsorized Mean ( 12 / 24 )52.251.0313455817136150.6619710467805
Winsorized Mean ( 13 / 24 )52.251.0313455817136150.6619710467805
Winsorized Mean ( 14 / 24 )52.05555555555561.0034932898731251.8743434369525
Winsorized Mean ( 15 / 24 )52.26388888888890.96879986732281853.947043813409
Winsorized Mean ( 16 / 24 )52.48611111111110.9330048582691456.2549172664337
Winsorized Mean ( 17 / 24 )52.72222222222220.826787015656163.7675982131677
Winsorized Mean ( 18 / 24 )52.97222222222220.79043881114950967.0162212115907
Winsorized Mean ( 19 / 24 )52.70833333333330.75356157475574469.945622360612
Winsorized Mean ( 20 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 21 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 22 / 24 )52.43055555555560.71667659914748673.1579008131753
Winsorized Mean ( 23 / 24 )52.43055555555560.62979813595592483.249778877124
Winsorized Mean ( 24 / 24 )52.76388888888890.58257598574678790.5699688620918
Trimmed Mean ( 1 / 24 )52.07142857142861.3622113048862938.2256617491331
Trimmed Mean ( 2 / 24 )52.14705882352941.3198465979387939.5099391891208
Trimmed Mean ( 3 / 24 )52.22727272727271.2691049017068541.1528413900468
Trimmed Mean ( 4 / 24 )52.3281251.2204959893704942.8744751770877
Trimmed Mean ( 5 / 24 )52.40322580645161.1720027824915044.712543851688
Trimmed Mean ( 6 / 24 )52.41.1377448206149646.0560215705289
Trimmed Mean ( 7 / 24 )52.39655172413791.1051602154157147.410819710361
Trimmed Mean ( 8 / 24 )52.44642857142861.0786955936099348.6202306583205
Trimmed Mean ( 9 / 24 )52.51.0553348550031349.7472434944301
Trimmed Mean ( 10 / 24 )52.53846153846151.0408190657593850.4779968650265
Trimmed Mean ( 11 / 24 )52.581.0218390783488451.4562430759276
Trimmed Mean ( 12 / 24 )52.6250.99717019823865552.7743409228974
Trimmed Mean ( 13 / 24 )52.67391304347830.9770577679736153.910745884271
Trimmed Mean ( 14 / 24 )52.72727272727270.9503329984775855.4829442013916
Trimmed Mean ( 15 / 24 )52.80952380952380.92093858048937957.3431550467364
Trimmed Mean ( 16 / 24 )52.8750.89025169301893359.3933158618273
Trimmed Mean ( 17 / 24 )52.92105263157890.85788251917750361.6879950908862
Trimmed Mean ( 18 / 24 )52.94444444444440.84039337391943462.9995976735534
Trimmed Mean ( 19 / 24 )52.94117647058820.82403854900763264.2459949650947
Trimmed Mean ( 20 / 24 )52.968750.80882777459210265.4882926426612
Trimmed Mean ( 21 / 24 )53.03333333333330.79435267267277266.7629570061006
Trimmed Mean ( 22 / 24 )53.10714285714290.77038313445149968.9360144091866
Trimmed Mean ( 23 / 24 )53.19230769230770.7317402455668672.6928825010862
Trimmed Mean ( 24 / 24 )53.29166666666670.7031996404290375.784547662955
Median53.5
Midrange48
Midmean - Weighted Average at Xnp52.9210526315789
Midmean - Weighted Average at X(n+1)p53.1621621621622
Midmean - Empirical Distribution Function52.9210526315789
Midmean - Empirical Distribution Function - Averaging53.1621621621622
Midmean - Empirical Distribution Function - Interpolation53.1621621621622
Midmean - Closest Observation52.9210526315789
Midmean - True Basic - Statistics Graphics Toolkit53.1621621621622
Midmean - MS Excel (old versions)52.9210526315789
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')