Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:08:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476274211vkejefjnnnq16st.htm/, Retrieved Sun, 05 May 2024 10:45:51 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 10:45:51 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
98,36
95,05
93,72
91,33
91,33
90,4
90,59
91,84
91,28
91,11
90,62
91,13
90,97
90,27
91,07
90,46
92,41
94,64
95,56
96,21
96,7
96,12
96,23
96,43
96,36
96,06
96,14
96,19
95,87
95,58
95,29
96,06
94,83
94,88
97,41
97,87
97,89
98,87
98,72
98,17
98,03
98,65
99,28
100,09
101,29
101,95
103,29
103,78
105,79
106,14
106,5
106,89
106,59
106,01
105,91
105,65
104,72
103,42
102,47
99,32
97,71
98,44
96,4
97,44
98,21
97,42
97,44
96,66
94,78
113,29
114,16
115,05




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.09430555555560.67403921729165145.532044781767
Geometric Mean97.9350326103733
Harmonic Mean97.7806591945479
Quadratic Mean98.2585880823882
Winsorized Mean ( 1 / 24 )98.083750.669465177821324146.510607645343
Winsorized Mean ( 2 / 24 )98.061250.661187843015853148.310727482097
Winsorized Mean ( 3 / 24 )97.80.587112739878018166.577887613748
Winsorized Mean ( 4 / 24 )97.7850.583235135933328167.659652129014
Winsorized Mean ( 5 / 24 )97.80305555555560.577780737435239169.273652129183
Winsorized Mean ( 6 / 24 )97.78138888888890.570117781037315171.510856425102
Winsorized Mean ( 7 / 24 )97.77263888888890.566875168526824172.476489211862
Winsorized Mean ( 8 / 24 )97.763750.564240506242663173.266096493176
Winsorized Mean ( 9 / 24 )97.76750.558109574320632175.176174175132
Winsorized Mean ( 10 / 24 )97.7550.553049802917461176.756233316277
Winsorized Mean ( 11 / 24 )97.61291666666670.525206920900083185.856112671518
Winsorized Mean ( 12 / 24 )97.541250.481712067060441202.488699515516
Winsorized Mean ( 13 / 24 )97.57916666666670.453023996486722215.395138940563
Winsorized Mean ( 14 / 24 )97.80861111111110.409861197617944238.638377283727
Winsorized Mean ( 15 / 24 )97.82944444444440.35211422074083277.834403389378
Winsorized Mean ( 16 / 24 )97.7450.326942072752708298.967334418082
Winsorized Mean ( 17 / 24 )97.60097222222220.297676458347897327.876019366487
Winsorized Mean ( 18 / 24 )97.31347222222220.245714772852379396.042415734956
Winsorized Mean ( 19 / 24 )97.15513888888890.208245802556255466.540682675435
Winsorized Mean ( 20 / 24 )97.21069444444440.19729056032964492.72856380975
Winsorized Mean ( 21 / 24 )97.16986111111110.169289282681024573.987080411932
Winsorized Mean ( 22 / 24 )97.13013888888890.162058777791077599.351298416599
Winsorized Mean ( 23 / 24 )97.20041666666670.14679004593661662.173078879218
Winsorized Mean ( 24 / 24 )97.193750.129195088119517752.302207573769
Trimmed Mean ( 1 / 24 )97.96385714285710.639070018321206153.291273779674
Trimmed Mean ( 2 / 24 )97.83691176470590.602161721010882162.476139467088
Trimmed Mean ( 3 / 24 )97.71454545454550.562585364952428173.688388539592
Trimmed Mean ( 4 / 24 )97.68250.550698735446362177.379197939913
Trimmed Mean ( 5 / 24 )97.65274193548390.537711534966772181.608047410622
Trimmed Mean ( 6 / 24 )97.61666666666670.523593767290071186.435883627673
Trimmed Mean ( 7 / 24 )97.58258620689660.508523571377365191.893929208805
Trimmed Mean ( 8 / 24 )97.54767857142860.490803475301749198.750993992974
Trimmed Mean ( 9 / 24 )97.51166666666670.469454889293701207.712538287489
Trimmed Mean ( 10 / 24 )97.47230769230770.444212457099731219.427227072166
Trimmed Mean ( 11 / 24 )97.43160.413358406525013235.707314674158
Trimmed Mean ( 12 / 24 )97.4068750.381439992335177255.366183298387
Trimmed Mean ( 13 / 24 )97.3893478260870.352094547328341276.599988739013
Trimmed Mean ( 14 / 24 )97.36545454545450.321393052410903302.94822434734
Trimmed Mean ( 15 / 24 )97.31119047619050.292092892957454333.151517282431
Trimmed Mean ( 16 / 24 )97.2490.269156755394248361.309898603713
Trimmed Mean ( 17 / 24 )97.19026315789470.245425136074292396.007779449594
Trimmed Mean ( 18 / 24 )97.14194444444440.222228189404011437.127012126443
Trimmed Mean ( 19 / 24 )97.12176470588240.207704314113332467.596280416635
Trimmed Mean ( 20 / 24 )97.11781250.198987727765838488.059306925123
Trimmed Mean ( 21 / 24 )97.10666666666670.189553821752546512.290734994702
Trimmed Mean ( 22 / 24 )97.09892857142860.184578985606264526.056247695258
Trimmed Mean ( 23 / 24 )97.0950.178975933061919542.503108316852
Trimmed Mean ( 24 / 24 )97.081250.174963052517887554.867148251631
Median97.055
Midrange102.66
Midmean - Weighted Average at Xnp97.0794594594595
Midmean - Weighted Average at X(n+1)p97.1419444444445
Midmean - Empirical Distribution Function97.0794594594595
Midmean - Empirical Distribution Function - Averaging97.1419444444445
Midmean - Empirical Distribution Function - Interpolation97.1419444444445
Midmean - Closest Observation97.0794594594595
Midmean - True Basic - Statistics Graphics Toolkit97.1419444444445
Midmean - MS Excel (old versions)97.1902631578948
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.0943055555556 & 0.67403921729165 & 145.532044781767 \tabularnewline
Geometric Mean & 97.9350326103733 &  &  \tabularnewline
Harmonic Mean & 97.7806591945479 &  &  \tabularnewline
Quadratic Mean & 98.2585880823882 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.08375 & 0.669465177821324 & 146.510607645343 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.06125 & 0.661187843015853 & 148.310727482097 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.8 & 0.587112739878018 & 166.577887613748 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.785 & 0.583235135933328 & 167.659652129014 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.8030555555556 & 0.577780737435239 & 169.273652129183 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.7813888888889 & 0.570117781037315 & 171.510856425102 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.7726388888889 & 0.566875168526824 & 172.476489211862 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.76375 & 0.564240506242663 & 173.266096493176 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.7675 & 0.558109574320632 & 175.176174175132 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.755 & 0.553049802917461 & 176.756233316277 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.6129166666667 & 0.525206920900083 & 185.856112671518 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.54125 & 0.481712067060441 & 202.488699515516 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.5791666666667 & 0.453023996486722 & 215.395138940563 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.8086111111111 & 0.409861197617944 & 238.638377283727 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.8294444444444 & 0.35211422074083 & 277.834403389378 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.745 & 0.326942072752708 & 298.967334418082 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.6009722222222 & 0.297676458347897 & 327.876019366487 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.3134722222222 & 0.245714772852379 & 396.042415734956 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.1551388888889 & 0.208245802556255 & 466.540682675435 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.2106944444444 & 0.19729056032964 & 492.72856380975 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.1698611111111 & 0.169289282681024 & 573.987080411932 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.1301388888889 & 0.162058777791077 & 599.351298416599 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.2004166666667 & 0.14679004593661 & 662.173078879218 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.19375 & 0.129195088119517 & 752.302207573769 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.9638571428571 & 0.639070018321206 & 153.291273779674 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.8369117647059 & 0.602161721010882 & 162.476139467088 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.7145454545455 & 0.562585364952428 & 173.688388539592 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.6825 & 0.550698735446362 & 177.379197939913 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.6527419354839 & 0.537711534966772 & 181.608047410622 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.6166666666667 & 0.523593767290071 & 186.435883627673 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.5825862068966 & 0.508523571377365 & 191.893929208805 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.5476785714286 & 0.490803475301749 & 198.750993992974 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.5116666666667 & 0.469454889293701 & 207.712538287489 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.4723076923077 & 0.444212457099731 & 219.427227072166 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.4316 & 0.413358406525013 & 235.707314674158 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.406875 & 0.381439992335177 & 255.366183298387 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.389347826087 & 0.352094547328341 & 276.599988739013 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.3654545454545 & 0.321393052410903 & 302.94822434734 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.3111904761905 & 0.292092892957454 & 333.151517282431 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.249 & 0.269156755394248 & 361.309898603713 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.1902631578947 & 0.245425136074292 & 396.007779449594 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.1419444444444 & 0.222228189404011 & 437.127012126443 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.1217647058824 & 0.207704314113332 & 467.596280416635 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.1178125 & 0.198987727765838 & 488.059306925123 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.1066666666667 & 0.189553821752546 & 512.290734994702 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.0989285714286 & 0.184578985606264 & 526.056247695258 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.095 & 0.178975933061919 & 542.503108316852 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.08125 & 0.174963052517887 & 554.867148251631 \tabularnewline
Median & 97.055 &  &  \tabularnewline
Midrange & 102.66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.0794594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.1419444444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.0794594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.1419444444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.1419444444445 &  &  \tabularnewline
Midmean - Closest Observation & 97.0794594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.1419444444445 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.1902631578948 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]98.0943055555556[/C][C]0.67403921729165[/C][C]145.532044781767[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.9350326103733[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.7806591945479[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.2585880823882[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.08375[/C][C]0.669465177821324[/C][C]146.510607645343[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.06125[/C][C]0.661187843015853[/C][C]148.310727482097[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.8[/C][C]0.587112739878018[/C][C]166.577887613748[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.785[/C][C]0.583235135933328[/C][C]167.659652129014[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.8030555555556[/C][C]0.577780737435239[/C][C]169.273652129183[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.7813888888889[/C][C]0.570117781037315[/C][C]171.510856425102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.7726388888889[/C][C]0.566875168526824[/C][C]172.476489211862[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.76375[/C][C]0.564240506242663[/C][C]173.266096493176[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.7675[/C][C]0.558109574320632[/C][C]175.176174175132[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.755[/C][C]0.553049802917461[/C][C]176.756233316277[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.6129166666667[/C][C]0.525206920900083[/C][C]185.856112671518[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.54125[/C][C]0.481712067060441[/C][C]202.488699515516[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.5791666666667[/C][C]0.453023996486722[/C][C]215.395138940563[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.8086111111111[/C][C]0.409861197617944[/C][C]238.638377283727[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.8294444444444[/C][C]0.35211422074083[/C][C]277.834403389378[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.745[/C][C]0.326942072752708[/C][C]298.967334418082[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.6009722222222[/C][C]0.297676458347897[/C][C]327.876019366487[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.3134722222222[/C][C]0.245714772852379[/C][C]396.042415734956[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.1551388888889[/C][C]0.208245802556255[/C][C]466.540682675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.2106944444444[/C][C]0.19729056032964[/C][C]492.72856380975[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.1698611111111[/C][C]0.169289282681024[/C][C]573.987080411932[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.1301388888889[/C][C]0.162058777791077[/C][C]599.351298416599[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.2004166666667[/C][C]0.14679004593661[/C][C]662.173078879218[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.19375[/C][C]0.129195088119517[/C][C]752.302207573769[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.9638571428571[/C][C]0.639070018321206[/C][C]153.291273779674[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.8369117647059[/C][C]0.602161721010882[/C][C]162.476139467088[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.7145454545455[/C][C]0.562585364952428[/C][C]173.688388539592[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.6825[/C][C]0.550698735446362[/C][C]177.379197939913[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.6527419354839[/C][C]0.537711534966772[/C][C]181.608047410622[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.6166666666667[/C][C]0.523593767290071[/C][C]186.435883627673[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.5825862068966[/C][C]0.508523571377365[/C][C]191.893929208805[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.5476785714286[/C][C]0.490803475301749[/C][C]198.750993992974[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.5116666666667[/C][C]0.469454889293701[/C][C]207.712538287489[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.4723076923077[/C][C]0.444212457099731[/C][C]219.427227072166[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.4316[/C][C]0.413358406525013[/C][C]235.707314674158[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.406875[/C][C]0.381439992335177[/C][C]255.366183298387[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.389347826087[/C][C]0.352094547328341[/C][C]276.599988739013[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.3654545454545[/C][C]0.321393052410903[/C][C]302.94822434734[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.3111904761905[/C][C]0.292092892957454[/C][C]333.151517282431[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.249[/C][C]0.269156755394248[/C][C]361.309898603713[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.1902631578947[/C][C]0.245425136074292[/C][C]396.007779449594[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.1419444444444[/C][C]0.222228189404011[/C][C]437.127012126443[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.1217647058824[/C][C]0.207704314113332[/C][C]467.596280416635[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.1178125[/C][C]0.198987727765838[/C][C]488.059306925123[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.1066666666667[/C][C]0.189553821752546[/C][C]512.290734994702[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.0989285714286[/C][C]0.184578985606264[/C][C]526.056247695258[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.095[/C][C]0.178975933061919[/C][C]542.503108316852[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.08125[/C][C]0.174963052517887[/C][C]554.867148251631[/C][/ROW]
[ROW][C]Median[/C][C]97.055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.0794594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.1419444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.0794594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.1419444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.1419444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.0794594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.1419444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.1902631578948[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean98.09430555555560.67403921729165145.532044781767
Geometric Mean97.9350326103733
Harmonic Mean97.7806591945479
Quadratic Mean98.2585880823882
Winsorized Mean ( 1 / 24 )98.083750.669465177821324146.510607645343
Winsorized Mean ( 2 / 24 )98.061250.661187843015853148.310727482097
Winsorized Mean ( 3 / 24 )97.80.587112739878018166.577887613748
Winsorized Mean ( 4 / 24 )97.7850.583235135933328167.659652129014
Winsorized Mean ( 5 / 24 )97.80305555555560.577780737435239169.273652129183
Winsorized Mean ( 6 / 24 )97.78138888888890.570117781037315171.510856425102
Winsorized Mean ( 7 / 24 )97.77263888888890.566875168526824172.476489211862
Winsorized Mean ( 8 / 24 )97.763750.564240506242663173.266096493176
Winsorized Mean ( 9 / 24 )97.76750.558109574320632175.176174175132
Winsorized Mean ( 10 / 24 )97.7550.553049802917461176.756233316277
Winsorized Mean ( 11 / 24 )97.61291666666670.525206920900083185.856112671518
Winsorized Mean ( 12 / 24 )97.541250.481712067060441202.488699515516
Winsorized Mean ( 13 / 24 )97.57916666666670.453023996486722215.395138940563
Winsorized Mean ( 14 / 24 )97.80861111111110.409861197617944238.638377283727
Winsorized Mean ( 15 / 24 )97.82944444444440.35211422074083277.834403389378
Winsorized Mean ( 16 / 24 )97.7450.326942072752708298.967334418082
Winsorized Mean ( 17 / 24 )97.60097222222220.297676458347897327.876019366487
Winsorized Mean ( 18 / 24 )97.31347222222220.245714772852379396.042415734956
Winsorized Mean ( 19 / 24 )97.15513888888890.208245802556255466.540682675435
Winsorized Mean ( 20 / 24 )97.21069444444440.19729056032964492.72856380975
Winsorized Mean ( 21 / 24 )97.16986111111110.169289282681024573.987080411932
Winsorized Mean ( 22 / 24 )97.13013888888890.162058777791077599.351298416599
Winsorized Mean ( 23 / 24 )97.20041666666670.14679004593661662.173078879218
Winsorized Mean ( 24 / 24 )97.193750.129195088119517752.302207573769
Trimmed Mean ( 1 / 24 )97.96385714285710.639070018321206153.291273779674
Trimmed Mean ( 2 / 24 )97.83691176470590.602161721010882162.476139467088
Trimmed Mean ( 3 / 24 )97.71454545454550.562585364952428173.688388539592
Trimmed Mean ( 4 / 24 )97.68250.550698735446362177.379197939913
Trimmed Mean ( 5 / 24 )97.65274193548390.537711534966772181.608047410622
Trimmed Mean ( 6 / 24 )97.61666666666670.523593767290071186.435883627673
Trimmed Mean ( 7 / 24 )97.58258620689660.508523571377365191.893929208805
Trimmed Mean ( 8 / 24 )97.54767857142860.490803475301749198.750993992974
Trimmed Mean ( 9 / 24 )97.51166666666670.469454889293701207.712538287489
Trimmed Mean ( 10 / 24 )97.47230769230770.444212457099731219.427227072166
Trimmed Mean ( 11 / 24 )97.43160.413358406525013235.707314674158
Trimmed Mean ( 12 / 24 )97.4068750.381439992335177255.366183298387
Trimmed Mean ( 13 / 24 )97.3893478260870.352094547328341276.599988739013
Trimmed Mean ( 14 / 24 )97.36545454545450.321393052410903302.94822434734
Trimmed Mean ( 15 / 24 )97.31119047619050.292092892957454333.151517282431
Trimmed Mean ( 16 / 24 )97.2490.269156755394248361.309898603713
Trimmed Mean ( 17 / 24 )97.19026315789470.245425136074292396.007779449594
Trimmed Mean ( 18 / 24 )97.14194444444440.222228189404011437.127012126443
Trimmed Mean ( 19 / 24 )97.12176470588240.207704314113332467.596280416635
Trimmed Mean ( 20 / 24 )97.11781250.198987727765838488.059306925123
Trimmed Mean ( 21 / 24 )97.10666666666670.189553821752546512.290734994702
Trimmed Mean ( 22 / 24 )97.09892857142860.184578985606264526.056247695258
Trimmed Mean ( 23 / 24 )97.0950.178975933061919542.503108316852
Trimmed Mean ( 24 / 24 )97.081250.174963052517887554.867148251631
Median97.055
Midrange102.66
Midmean - Weighted Average at Xnp97.0794594594595
Midmean - Weighted Average at X(n+1)p97.1419444444445
Midmean - Empirical Distribution Function97.0794594594595
Midmean - Empirical Distribution Function - Averaging97.1419444444445
Midmean - Empirical Distribution Function - Interpolation97.1419444444445
Midmean - Closest Observation97.0794594594595
Midmean - True Basic - Statistics Graphics Toolkit97.1419444444445
Midmean - MS Excel (old versions)97.1902631578948
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')