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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 18 Apr 2008 03:52:57 -0600
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/Apr/18/t1208512502ewuzqobsbvi3w6h.htm/, Retrieved Sun, 12 May 2024 21:01:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10198, Retrieved Sun, 12 May 2024 21:01:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact302
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten hote...] [2008-04-18 09:52:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
65,05
65,84
66,6
67,55
68,07
69,06
69,06
69,11
69,29
69,38
69,28
69,75
69,9
70,21
70,48
71,55
72,18
72,64
72,77
72,74
73,13
73,44
73,34
73,34
73,81
74,26
74,72
75,11
75,26
75,89
75,91
76,43
76,56
76,76
76,76
76,56
76,82
77,09
77,51
77,76
77,86
77,89
77,94
77,99
78,17
78,91
78,87
78,88
79,08
79,41
79,51
79,73
80,38
80,56
80,46
80,45
80,58
80,68
80,52
81,49
81,66
81,95
82,3
82,4
83,14
83,17
83,11
83,21
83,33
83,88
83,8
83,73




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10198&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10198&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean76.19458333333330.598511192048271127.306864676288
Geometric Mean76.024561131931
Harmonic Mean75.8515426765101
Quadratic Mean76.3612980525985
Winsorized Mean ( 1 / 24 )76.20444444444440.595527109952959127.961335715622
Winsorized Mean ( 2 / 24 )76.22361111111110.590165831233111129.156259270123
Winsorized Mean ( 3 / 24 )76.24652777777780.578495605751095131.80139489354
Winsorized Mean ( 4 / 24 )76.268750.571371895200662133.483551852362
Winsorized Mean ( 5 / 24 )76.33472222222220.557623295005082136.892993721732
Winsorized Mean ( 6 / 24 )76.33222222222220.557192381365897136.994375327067
Winsorized Mean ( 7 / 24 )76.33416666666670.555799264815952137.341251597272
Winsorized Mean ( 8 / 24 )76.27416666666670.539254098171137141.443833111975
Winsorized Mean ( 9 / 24 )76.26291666666670.537036055094843142.007069996815
Winsorized Mean ( 10 / 24 )76.22680555555560.527183878175363144.592444327744
Winsorized Mean ( 11 / 24 )76.23902777777780.510246118760909149.416183630986
Winsorized Mean ( 12 / 24 )76.23569444444440.501572793394057151.993280832819
Winsorized Mean ( 13 / 24 )76.14541666666670.470890340455973161.705199968497
Winsorized Mean ( 14 / 24 )76.17847222222220.459007513538961165.963453702280
Winsorized Mean ( 15 / 24 )76.39722222222220.420803139911711181.550979487109
Winsorized Mean ( 16 / 24 )76.52833333333330.397394389076498192.575273926683
Winsorized Mean ( 17 / 24 )76.62277777777780.378966772476073202.188643814717
Winsorized Mean ( 18 / 24 )76.64527777777780.374925656283381204.427935227369
Winsorized Mean ( 19 / 24 )76.63472222222220.371131479145971206.489415553136
Winsorized Mean ( 20 / 24 )76.55416666666670.331469303936683230.954015220938
Winsorized Mean ( 21 / 24 )76.551250.314011972194586243.784494791692
Winsorized Mean ( 22 / 24 )76.52069444444440.309978628067678246.857968633042
Winsorized Mean ( 23 / 24 )76.44722222222220.291725562277829262.051846349401
Winsorized Mean ( 24 / 24 )76.51388888888890.266775986655778286.809505788146
Trimmed Mean ( 1 / 24 )76.2440.58408146287954130.536585811361
Trimmed Mean ( 2 / 24 )76.28588235294120.570396494851288133.741849821202
Trimmed Mean ( 3 / 24 )76.31984848484850.557424375479538136.915161665100
Trimmed Mean ( 4 / 24 )76.347343750.547110068172583139.546588870151
Trimmed Mean ( 5 / 24 )76.37016129032260.537158017432475142.174479039444
Trimmed Mean ( 6 / 24 )76.37866666666670.529249787056936144.314969102576
Trimmed Mean ( 7 / 24 )76.3882758620690.519518899898887147.036567633894
Trimmed Mean ( 8 / 24 )76.39821428571430.507773540071053150.457257530638
Trimmed Mean ( 9 / 24 )76.41888888888890.497167073525962153.708668490288
Trimmed Mean ( 10 / 24 )76.44288461538460.484284184838458157.847162902674
Trimmed Mean ( 11 / 24 )76.4740.470221658543357162.633937868578
Trimmed Mean ( 12 / 24 )76.50604166666670.456221544297057167.694933794822
Trimmed Mean ( 13 / 24 )76.54130434782610.440148592464926173.898782497925
Trimmed Mean ( 14 / 24 )76.59113636363640.426214992041232179.70070925198
Trimmed Mean ( 15 / 24 )76.64166666666670.410613392984046186.651648426978
Trimmed Mean ( 16 / 24 )76.6710.399536718892757191.899758831878
Trimmed Mean ( 17 / 24 )76.68789473684210.390159386385177196.555298713571
Trimmed Mean ( 18 / 24 )76.69555555555560.381528971719086201.021576972208
Trimmed Mean ( 19 / 24 )76.70147058823530.370079273762551207.256866369253
Trimmed Mean ( 20 / 24 )76.7093750.354518055838236216.376496871578
Trimmed Mean ( 21 / 24 )76.7280.343630180789501223.286557146159
Trimmed Mean ( 22 / 24 )76.74964285714290.332339583032914230.937410935915
Trimmed Mean ( 23 / 24 )76.77846153846150.315680311662919243.215869668949
Trimmed Mean ( 24 / 24 )76.82166666666670.295767036866210259.737080509809
Median76.79
Midrange74.465
Midmean - Weighted Average at Xnp76.5859459459459
Midmean - Weighted Average at X(n+1)p76.6955555555556
Midmean - Empirical Distribution Function76.5859459459459
Midmean - Empirical Distribution Function - Averaging76.6955555555556
Midmean - Empirical Distribution Function - Interpolation76.6955555555556
Midmean - Closest Observation76.5859459459459
Midmean - True Basic - Statistics Graphics Toolkit76.6955555555556
Midmean - MS Excel (old versions)76.6878947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 76.1945833333333 & 0.598511192048271 & 127.306864676288 \tabularnewline
Geometric Mean & 76.024561131931 &  &  \tabularnewline
Harmonic Mean & 75.8515426765101 &  &  \tabularnewline
Quadratic Mean & 76.3612980525985 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 76.2044444444444 & 0.595527109952959 & 127.961335715622 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 76.2236111111111 & 0.590165831233111 & 129.156259270123 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 76.2465277777778 & 0.578495605751095 & 131.80139489354 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 76.26875 & 0.571371895200662 & 133.483551852362 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 76.3347222222222 & 0.557623295005082 & 136.892993721732 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 76.3322222222222 & 0.557192381365897 & 136.994375327067 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 76.3341666666667 & 0.555799264815952 & 137.341251597272 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 76.2741666666667 & 0.539254098171137 & 141.443833111975 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 76.2629166666667 & 0.537036055094843 & 142.007069996815 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 76.2268055555556 & 0.527183878175363 & 144.592444327744 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 76.2390277777778 & 0.510246118760909 & 149.416183630986 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 76.2356944444444 & 0.501572793394057 & 151.993280832819 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 76.1454166666667 & 0.470890340455973 & 161.705199968497 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 76.1784722222222 & 0.459007513538961 & 165.963453702280 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 76.3972222222222 & 0.420803139911711 & 181.550979487109 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 76.5283333333333 & 0.397394389076498 & 192.575273926683 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 76.6227777777778 & 0.378966772476073 & 202.188643814717 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 76.6452777777778 & 0.374925656283381 & 204.427935227369 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 76.6347222222222 & 0.371131479145971 & 206.489415553136 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 76.5541666666667 & 0.331469303936683 & 230.954015220938 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 76.55125 & 0.314011972194586 & 243.784494791692 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 76.5206944444444 & 0.309978628067678 & 246.857968633042 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 76.4472222222222 & 0.291725562277829 & 262.051846349401 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 76.5138888888889 & 0.266775986655778 & 286.809505788146 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 76.244 & 0.58408146287954 & 130.536585811361 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 76.2858823529412 & 0.570396494851288 & 133.741849821202 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 76.3198484848485 & 0.557424375479538 & 136.915161665100 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 76.34734375 & 0.547110068172583 & 139.546588870151 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 76.3701612903226 & 0.537158017432475 & 142.174479039444 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 76.3786666666667 & 0.529249787056936 & 144.314969102576 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 76.388275862069 & 0.519518899898887 & 147.036567633894 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 76.3982142857143 & 0.507773540071053 & 150.457257530638 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 76.4188888888889 & 0.497167073525962 & 153.708668490288 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 76.4428846153846 & 0.484284184838458 & 157.847162902674 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 76.474 & 0.470221658543357 & 162.633937868578 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 76.5060416666667 & 0.456221544297057 & 167.694933794822 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 76.5413043478261 & 0.440148592464926 & 173.898782497925 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 76.5911363636364 & 0.426214992041232 & 179.70070925198 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 76.6416666666667 & 0.410613392984046 & 186.651648426978 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 76.671 & 0.399536718892757 & 191.899758831878 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 76.6878947368421 & 0.390159386385177 & 196.555298713571 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 76.6955555555556 & 0.381528971719086 & 201.021576972208 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 76.7014705882353 & 0.370079273762551 & 207.256866369253 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 76.709375 & 0.354518055838236 & 216.376496871578 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 76.728 & 0.343630180789501 & 223.286557146159 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 76.7496428571429 & 0.332339583032914 & 230.937410935915 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 76.7784615384615 & 0.315680311662919 & 243.215869668949 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 76.8216666666667 & 0.295767036866210 & 259.737080509809 \tabularnewline
Median & 76.79 &  &  \tabularnewline
Midrange & 74.465 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 76.5859459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 76.6955555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 76.5859459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 76.6955555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 76.6955555555556 &  &  \tabularnewline
Midmean - Closest Observation & 76.5859459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 76.6955555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 76.6878947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10198&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]76.1945833333333[/C][C]0.598511192048271[/C][C]127.306864676288[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]76.024561131931[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.8515426765101[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]76.3612980525985[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]76.2044444444444[/C][C]0.595527109952959[/C][C]127.961335715622[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]76.2236111111111[/C][C]0.590165831233111[/C][C]129.156259270123[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]76.2465277777778[/C][C]0.578495605751095[/C][C]131.80139489354[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]76.26875[/C][C]0.571371895200662[/C][C]133.483551852362[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]76.3347222222222[/C][C]0.557623295005082[/C][C]136.892993721732[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]76.3322222222222[/C][C]0.557192381365897[/C][C]136.994375327067[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]76.3341666666667[/C][C]0.555799264815952[/C][C]137.341251597272[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]76.2741666666667[/C][C]0.539254098171137[/C][C]141.443833111975[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]76.2629166666667[/C][C]0.537036055094843[/C][C]142.007069996815[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]76.2268055555556[/C][C]0.527183878175363[/C][C]144.592444327744[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]76.2390277777778[/C][C]0.510246118760909[/C][C]149.416183630986[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]76.2356944444444[/C][C]0.501572793394057[/C][C]151.993280832819[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]76.1454166666667[/C][C]0.470890340455973[/C][C]161.705199968497[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]76.1784722222222[/C][C]0.459007513538961[/C][C]165.963453702280[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]76.3972222222222[/C][C]0.420803139911711[/C][C]181.550979487109[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]76.5283333333333[/C][C]0.397394389076498[/C][C]192.575273926683[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]76.6227777777778[/C][C]0.378966772476073[/C][C]202.188643814717[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]76.6452777777778[/C][C]0.374925656283381[/C][C]204.427935227369[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]76.6347222222222[/C][C]0.371131479145971[/C][C]206.489415553136[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]76.5541666666667[/C][C]0.331469303936683[/C][C]230.954015220938[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]76.55125[/C][C]0.314011972194586[/C][C]243.784494791692[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]76.5206944444444[/C][C]0.309978628067678[/C][C]246.857968633042[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]76.4472222222222[/C][C]0.291725562277829[/C][C]262.051846349401[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]76.5138888888889[/C][C]0.266775986655778[/C][C]286.809505788146[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]76.244[/C][C]0.58408146287954[/C][C]130.536585811361[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]76.2858823529412[/C][C]0.570396494851288[/C][C]133.741849821202[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]76.3198484848485[/C][C]0.557424375479538[/C][C]136.915161665100[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]76.34734375[/C][C]0.547110068172583[/C][C]139.546588870151[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]76.3701612903226[/C][C]0.537158017432475[/C][C]142.174479039444[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]76.3786666666667[/C][C]0.529249787056936[/C][C]144.314969102576[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]76.388275862069[/C][C]0.519518899898887[/C][C]147.036567633894[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]76.3982142857143[/C][C]0.507773540071053[/C][C]150.457257530638[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]76.4188888888889[/C][C]0.497167073525962[/C][C]153.708668490288[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]76.4428846153846[/C][C]0.484284184838458[/C][C]157.847162902674[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]76.474[/C][C]0.470221658543357[/C][C]162.633937868578[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]76.5060416666667[/C][C]0.456221544297057[/C][C]167.694933794822[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]76.5413043478261[/C][C]0.440148592464926[/C][C]173.898782497925[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]76.5911363636364[/C][C]0.426214992041232[/C][C]179.70070925198[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]76.6416666666667[/C][C]0.410613392984046[/C][C]186.651648426978[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]76.671[/C][C]0.399536718892757[/C][C]191.899758831878[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]76.6878947368421[/C][C]0.390159386385177[/C][C]196.555298713571[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]76.6955555555556[/C][C]0.381528971719086[/C][C]201.021576972208[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]76.7014705882353[/C][C]0.370079273762551[/C][C]207.256866369253[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]76.709375[/C][C]0.354518055838236[/C][C]216.376496871578[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]76.728[/C][C]0.343630180789501[/C][C]223.286557146159[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]76.7496428571429[/C][C]0.332339583032914[/C][C]230.937410935915[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]76.7784615384615[/C][C]0.315680311662919[/C][C]243.215869668949[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]76.8216666666667[/C][C]0.295767036866210[/C][C]259.737080509809[/C][/ROW]
[ROW][C]Median[/C][C]76.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]74.465[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]76.6955555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]76.6955555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]76.6955555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]76.6955555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]76.6878947368421[/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=10198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10198&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 Mean76.19458333333330.598511192048271127.306864676288
Geometric Mean76.024561131931
Harmonic Mean75.8515426765101
Quadratic Mean76.3612980525985
Winsorized Mean ( 1 / 24 )76.20444444444440.595527109952959127.961335715622
Winsorized Mean ( 2 / 24 )76.22361111111110.590165831233111129.156259270123
Winsorized Mean ( 3 / 24 )76.24652777777780.578495605751095131.80139489354
Winsorized Mean ( 4 / 24 )76.268750.571371895200662133.483551852362
Winsorized Mean ( 5 / 24 )76.33472222222220.557623295005082136.892993721732
Winsorized Mean ( 6 / 24 )76.33222222222220.557192381365897136.994375327067
Winsorized Mean ( 7 / 24 )76.33416666666670.555799264815952137.341251597272
Winsorized Mean ( 8 / 24 )76.27416666666670.539254098171137141.443833111975
Winsorized Mean ( 9 / 24 )76.26291666666670.537036055094843142.007069996815
Winsorized Mean ( 10 / 24 )76.22680555555560.527183878175363144.592444327744
Winsorized Mean ( 11 / 24 )76.23902777777780.510246118760909149.416183630986
Winsorized Mean ( 12 / 24 )76.23569444444440.501572793394057151.993280832819
Winsorized Mean ( 13 / 24 )76.14541666666670.470890340455973161.705199968497
Winsorized Mean ( 14 / 24 )76.17847222222220.459007513538961165.963453702280
Winsorized Mean ( 15 / 24 )76.39722222222220.420803139911711181.550979487109
Winsorized Mean ( 16 / 24 )76.52833333333330.397394389076498192.575273926683
Winsorized Mean ( 17 / 24 )76.62277777777780.378966772476073202.188643814717
Winsorized Mean ( 18 / 24 )76.64527777777780.374925656283381204.427935227369
Winsorized Mean ( 19 / 24 )76.63472222222220.371131479145971206.489415553136
Winsorized Mean ( 20 / 24 )76.55416666666670.331469303936683230.954015220938
Winsorized Mean ( 21 / 24 )76.551250.314011972194586243.784494791692
Winsorized Mean ( 22 / 24 )76.52069444444440.309978628067678246.857968633042
Winsorized Mean ( 23 / 24 )76.44722222222220.291725562277829262.051846349401
Winsorized Mean ( 24 / 24 )76.51388888888890.266775986655778286.809505788146
Trimmed Mean ( 1 / 24 )76.2440.58408146287954130.536585811361
Trimmed Mean ( 2 / 24 )76.28588235294120.570396494851288133.741849821202
Trimmed Mean ( 3 / 24 )76.31984848484850.557424375479538136.915161665100
Trimmed Mean ( 4 / 24 )76.347343750.547110068172583139.546588870151
Trimmed Mean ( 5 / 24 )76.37016129032260.537158017432475142.174479039444
Trimmed Mean ( 6 / 24 )76.37866666666670.529249787056936144.314969102576
Trimmed Mean ( 7 / 24 )76.3882758620690.519518899898887147.036567633894
Trimmed Mean ( 8 / 24 )76.39821428571430.507773540071053150.457257530638
Trimmed Mean ( 9 / 24 )76.41888888888890.497167073525962153.708668490288
Trimmed Mean ( 10 / 24 )76.44288461538460.484284184838458157.847162902674
Trimmed Mean ( 11 / 24 )76.4740.470221658543357162.633937868578
Trimmed Mean ( 12 / 24 )76.50604166666670.456221544297057167.694933794822
Trimmed Mean ( 13 / 24 )76.54130434782610.440148592464926173.898782497925
Trimmed Mean ( 14 / 24 )76.59113636363640.426214992041232179.70070925198
Trimmed Mean ( 15 / 24 )76.64166666666670.410613392984046186.651648426978
Trimmed Mean ( 16 / 24 )76.6710.399536718892757191.899758831878
Trimmed Mean ( 17 / 24 )76.68789473684210.390159386385177196.555298713571
Trimmed Mean ( 18 / 24 )76.69555555555560.381528971719086201.021576972208
Trimmed Mean ( 19 / 24 )76.70147058823530.370079273762551207.256866369253
Trimmed Mean ( 20 / 24 )76.7093750.354518055838236216.376496871578
Trimmed Mean ( 21 / 24 )76.7280.343630180789501223.286557146159
Trimmed Mean ( 22 / 24 )76.74964285714290.332339583032914230.937410935915
Trimmed Mean ( 23 / 24 )76.77846153846150.315680311662919243.215869668949
Trimmed Mean ( 24 / 24 )76.82166666666670.295767036866210259.737080509809
Median76.79
Midrange74.465
Midmean - Weighted Average at Xnp76.5859459459459
Midmean - Weighted Average at X(n+1)p76.6955555555556
Midmean - Empirical Distribution Function76.5859459459459
Midmean - Empirical Distribution Function - Averaging76.6955555555556
Midmean - Empirical Distribution Function - Interpolation76.6955555555556
Midmean - Closest Observation76.5859459459459
Midmean - True Basic - Statistics Graphics Toolkit76.6955555555556
Midmean - MS Excel (old versions)76.6878947368421
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')