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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 26 Feb 2014 09:54:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/26/t1393426524oqx9wdht8h5t0z9.htm/, Retrieved Wed, 15 May 2024 00:24:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234056, Retrieved Wed, 15 May 2024 00:24:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-26 14:54:11] [c97636ecf0aef6cf672ffb6fe15d6b60] [Current]
-         [Central Tendency] [] [2014-05-19 08:49:23] [ccb4fa85fbb66dbee3adf4746bc114a3]
-         [Central Tendency] [] [2014-05-19 08:51:07] [ccb4fa85fbb66dbee3adf4746bc114a3]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234056&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]3 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=234056&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234056&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean107.1621621621622.3684982930167745.2447706963171
Geometric Mean105.667736979648
Harmonic Mean104.446119065561
Quadratic Mean109.056147205205
Winsorized Mean ( 1 / 24 )107.0270270270272.2906998499706846.7224141252714
Winsorized Mean ( 2 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 3 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 4 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 5 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 6 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 7 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 8 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 9 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 10 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 11 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 12 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 13 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 14 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 15 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 16 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 17 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 18 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 19 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 20 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 21 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 22 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 23 / 24 )104.8648648648650.584991962188687179.258642242748
Winsorized Mean ( 24 / 24 )104.8648648648650.584991962188687179.258642242748
Trimmed Mean ( 1 / 24 )105.9722222222221.9446540240284154.4941264167379
Trimmed Mean ( 2 / 24 )104.8571428571431.4495356169753972.3384383447843
Trimmed Mean ( 3 / 24 )104.8529411764711.4590194648786671.8653477218627
Trimmed Mean ( 4 / 24 )104.8484848484851.4682724454289171.4094207617283
Trimmed Mean ( 5 / 24 )104.843751.4772109388093870.9741224124045
Trimmed Mean ( 6 / 24 )104.8387096774191.4857321691577470.5636667588964
Trimmed Mean ( 7 / 24 )104.8333333333331.4937093453166470.1832211614843
Trimmed Mean ( 8 / 24 )104.8275862068971.500985345055269.8391803439238
Trimmed Mean ( 9 / 24 )104.8214285714291.5073644202255169.5395401171449
Trimmed Mean ( 10 / 24 )104.8148148148151.5126011754308569.2944158164885
Trimmed Mean ( 11 / 24 )104.8076923076921.5163857317433269.1167755760926
Trimmed Mean ( 12 / 24 )104.81.5183234577813169.0235005346898
Trimmed Mean ( 13 / 24 )104.7916666666671.517906807300869.0369567898644
Trimmed Mean ( 14 / 24 )104.7826086956521.5144754176942869.1873948374674
Trimmed Mean ( 15 / 24 )104.7727272727271.5071582672923569.5167385844315
Trimmed Mean ( 16 / 24 )104.7619047619051.4947875069171870.0848142475873
Trimmed Mean ( 17 / 24 )104.751.4757657725345970.9800985695003
Trimmed Mean ( 18 / 24 )104.7368421052631.4478532745376472.339403409997
Trimmed Mean ( 19 / 24 )104.7222222222221.4078076568157574.3867400601357
Trimmed Mean ( 20 / 24 )104.7058823529411.3507305818518877.5179623233133
Trimmed Mean ( 21 / 24 )104.68751.2687604282107682.5116370847357
Trimmed Mean ( 22 / 24 )104.6666666666671.1480451484306991.1694690838071
Trimmed Mean ( 23 / 24 )104.6428571428570.959792589083161109.026531703914
Trimmed Mean ( 24 / 24 )104.6153846153850.997037030524286104.926277974222
Median100
Midrange150
Midmean - Weighted Average at Xnp104.444444444444
Midmean - Weighted Average at X(n+1)p104.444444444444
Midmean - Empirical Distribution Function104.444444444444
Midmean - Empirical Distribution Function - Averaging104.444444444444
Midmean - Empirical Distribution Function - Interpolation104.444444444444
Midmean - Closest Observation104.444444444444
Midmean - True Basic - Statistics Graphics Toolkit104.444444444444
Midmean - MS Excel (old versions)104.444444444444
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.162162162162 & 2.36849829301677 & 45.2447706963171 \tabularnewline
Geometric Mean & 105.667736979648 &  &  \tabularnewline
Harmonic Mean & 104.446119065561 &  &  \tabularnewline
Quadratic Mean & 109.056147205205 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 107.027027027027 & 2.29069984997068 & 46.7224141252714 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 104.864864864865 & 1.4301358438187 & 73.3251077637901 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 104.864864864865 & 0.584991962188687 & 179.258642242748 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 104.864864864865 & 0.584991962188687 & 179.258642242748 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 105.972222222222 & 1.94465402402841 & 54.4941264167379 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 104.857142857143 & 1.44953561697539 & 72.3384383447843 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 104.852941176471 & 1.45901946487866 & 71.8653477218627 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 104.848484848485 & 1.46827244542891 & 71.4094207617283 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 104.84375 & 1.47721093880938 & 70.9741224124045 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 104.838709677419 & 1.48573216915774 & 70.5636667588964 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 104.833333333333 & 1.49370934531664 & 70.1832211614843 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 104.827586206897 & 1.5009853450552 & 69.8391803439238 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 104.821428571429 & 1.50736442022551 & 69.5395401171449 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 104.814814814815 & 1.51260117543085 & 69.2944158164885 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 104.807692307692 & 1.51638573174332 & 69.1167755760926 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 104.8 & 1.51832345778131 & 69.0235005346898 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 104.791666666667 & 1.5179068073008 & 69.0369567898644 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 104.782608695652 & 1.51447541769428 & 69.1873948374674 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 104.772727272727 & 1.50715826729235 & 69.5167385844315 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 104.761904761905 & 1.49478750691718 & 70.0848142475873 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 104.75 & 1.47576577253459 & 70.9800985695003 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 104.736842105263 & 1.44785327453764 & 72.339403409997 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 104.722222222222 & 1.40780765681575 & 74.3867400601357 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 104.705882352941 & 1.35073058185188 & 77.5179623233133 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 104.6875 & 1.26876042821076 & 82.5116370847357 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 104.666666666667 & 1.14804514843069 & 91.1694690838071 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 104.642857142857 & 0.959792589083161 & 109.026531703914 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 104.615384615385 & 0.997037030524286 & 104.926277974222 \tabularnewline
Median & 100 &  &  \tabularnewline
Midrange & 150 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.444444444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.444444444444 &  &  \tabularnewline
Midmean - Closest Observation & 104.444444444444 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.444444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.444444444444 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234056&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]107.162162162162[/C][C]2.36849829301677[/C][C]45.2447706963171[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.667736979648[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.446119065561[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.056147205205[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]107.027027027027[/C][C]2.29069984997068[/C][C]46.7224141252714[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]104.864864864865[/C][C]1.4301358438187[/C][C]73.3251077637901[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]104.864864864865[/C][C]0.584991962188687[/C][C]179.258642242748[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]104.864864864865[/C][C]0.584991962188687[/C][C]179.258642242748[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]105.972222222222[/C][C]1.94465402402841[/C][C]54.4941264167379[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]104.857142857143[/C][C]1.44953561697539[/C][C]72.3384383447843[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]104.852941176471[/C][C]1.45901946487866[/C][C]71.8653477218627[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]104.848484848485[/C][C]1.46827244542891[/C][C]71.4094207617283[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]104.84375[/C][C]1.47721093880938[/C][C]70.9741224124045[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]104.838709677419[/C][C]1.48573216915774[/C][C]70.5636667588964[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]104.833333333333[/C][C]1.49370934531664[/C][C]70.1832211614843[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]104.827586206897[/C][C]1.5009853450552[/C][C]69.8391803439238[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]104.821428571429[/C][C]1.50736442022551[/C][C]69.5395401171449[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]104.814814814815[/C][C]1.51260117543085[/C][C]69.2944158164885[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]104.807692307692[/C][C]1.51638573174332[/C][C]69.1167755760926[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]104.8[/C][C]1.51832345778131[/C][C]69.0235005346898[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]104.791666666667[/C][C]1.5179068073008[/C][C]69.0369567898644[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]104.782608695652[/C][C]1.51447541769428[/C][C]69.1873948374674[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]104.772727272727[/C][C]1.50715826729235[/C][C]69.5167385844315[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]104.761904761905[/C][C]1.49478750691718[/C][C]70.0848142475873[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]104.75[/C][C]1.47576577253459[/C][C]70.9800985695003[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]104.736842105263[/C][C]1.44785327453764[/C][C]72.339403409997[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]104.722222222222[/C][C]1.40780765681575[/C][C]74.3867400601357[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]104.705882352941[/C][C]1.35073058185188[/C][C]77.5179623233133[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]104.6875[/C][C]1.26876042821076[/C][C]82.5116370847357[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]104.666666666667[/C][C]1.14804514843069[/C][C]91.1694690838071[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]104.642857142857[/C][C]0.959792589083161[/C][C]109.026531703914[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]104.615384615385[/C][C]0.997037030524286[/C][C]104.926277974222[/C][/ROW]
[ROW][C]Median[/C][C]100[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]150[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234056&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234056&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean107.1621621621622.3684982930167745.2447706963171
Geometric Mean105.667736979648
Harmonic Mean104.446119065561
Quadratic Mean109.056147205205
Winsorized Mean ( 1 / 24 )107.0270270270272.2906998499706846.7224141252714
Winsorized Mean ( 2 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 3 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 4 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 5 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 6 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 7 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 8 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 9 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 10 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 11 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 12 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 13 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 14 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 15 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 16 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 17 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 18 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 19 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 20 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 21 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 22 / 24 )104.8648648648651.430135843818773.3251077637901
Winsorized Mean ( 23 / 24 )104.8648648648650.584991962188687179.258642242748
Winsorized Mean ( 24 / 24 )104.8648648648650.584991962188687179.258642242748
Trimmed Mean ( 1 / 24 )105.9722222222221.9446540240284154.4941264167379
Trimmed Mean ( 2 / 24 )104.8571428571431.4495356169753972.3384383447843
Trimmed Mean ( 3 / 24 )104.8529411764711.4590194648786671.8653477218627
Trimmed Mean ( 4 / 24 )104.8484848484851.4682724454289171.4094207617283
Trimmed Mean ( 5 / 24 )104.843751.4772109388093870.9741224124045
Trimmed Mean ( 6 / 24 )104.8387096774191.4857321691577470.5636667588964
Trimmed Mean ( 7 / 24 )104.8333333333331.4937093453166470.1832211614843
Trimmed Mean ( 8 / 24 )104.8275862068971.500985345055269.8391803439238
Trimmed Mean ( 9 / 24 )104.8214285714291.5073644202255169.5395401171449
Trimmed Mean ( 10 / 24 )104.8148148148151.5126011754308569.2944158164885
Trimmed Mean ( 11 / 24 )104.8076923076921.5163857317433269.1167755760926
Trimmed Mean ( 12 / 24 )104.81.5183234577813169.0235005346898
Trimmed Mean ( 13 / 24 )104.7916666666671.517906807300869.0369567898644
Trimmed Mean ( 14 / 24 )104.7826086956521.5144754176942869.1873948374674
Trimmed Mean ( 15 / 24 )104.7727272727271.5071582672923569.5167385844315
Trimmed Mean ( 16 / 24 )104.7619047619051.4947875069171870.0848142475873
Trimmed Mean ( 17 / 24 )104.751.4757657725345970.9800985695003
Trimmed Mean ( 18 / 24 )104.7368421052631.4478532745376472.339403409997
Trimmed Mean ( 19 / 24 )104.7222222222221.4078076568157574.3867400601357
Trimmed Mean ( 20 / 24 )104.7058823529411.3507305818518877.5179623233133
Trimmed Mean ( 21 / 24 )104.68751.2687604282107682.5116370847357
Trimmed Mean ( 22 / 24 )104.6666666666671.1480451484306991.1694690838071
Trimmed Mean ( 23 / 24 )104.6428571428570.959792589083161109.026531703914
Trimmed Mean ( 24 / 24 )104.6153846153850.997037030524286104.926277974222
Median100
Midrange150
Midmean - Weighted Average at Xnp104.444444444444
Midmean - Weighted Average at X(n+1)p104.444444444444
Midmean - Empirical Distribution Function104.444444444444
Midmean - Empirical Distribution Function - Averaging104.444444444444
Midmean - Empirical Distribution Function - Interpolation104.444444444444
Midmean - Closest Observation104.444444444444
Midmean - True Basic - Statistics Graphics Toolkit104.444444444444
Midmean - MS Excel (old versions)104.444444444444
Number of observations74


Figures (Output of Computation)

Input Parameters & R Code

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')