Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Mar 2017 14:53:17 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/11/t1489244046mr0ni9bwlfy8hh4.htm/, Retrieved Tue, 14 May 2024 02:45:35 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 02:45:35 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
99,5
101,8
102,3
102,6
102,5
104,3
105,3
105,8
104,8
104,5
102,8
101,4
103,6
106,8
108,2
108,3
108,4
108,8
109,4
109
109
109,8
110,5
110,5
111,1
110,8
111
111,7
111,9
112,6
112,2
112,3
112,8
114,3
114,3
114
113,9
113,7
113,8
113,8
113,2
112,2
112,2
113,2
113,6
113,2
112,2
110,5
109,2
109
109,1
109,4
108,8
109,6
109,6
109,8
110,5
109
107,5
105,6
103,4
101,9
101,4
101,3
100,8
100,3
100,3
100
99,2
98,1
96,9
96,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.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]'Sir Ronald Aylmer Fisher' @ fisher.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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean107.6597222222220.585795139707641183.783911686179
Geometric Mean107.544539387589
Harmonic Mean107.427370174235
Quadratic Mean107.772815965396
Winsorized Mean ( 1 / 24 )107.6666666666670.583953392785098184.37544502167
Winsorized Mean ( 2 / 24 )107.6916666666670.574390709370333187.488524639826
Winsorized Mean ( 3 / 24 )107.7333333333330.563464440114783191.19810526355
Winsorized Mean ( 4 / 24 )107.7444444444440.559104081875347192.709100035628
Winsorized Mean ( 5 / 24 )107.7791666666670.552051719796437195.233821038379
Winsorized Mean ( 6 / 24 )107.7958333333330.545878129545523197.472343182314
Winsorized Mean ( 7 / 24 )107.7861111111110.54440641734274197.988318428018
Winsorized Mean ( 8 / 24 )107.7972222222220.52727995218315204.440206338015
Winsorized Mean ( 9 / 24 )107.8597222222220.515839333519231209.095575334216
Winsorized Mean ( 10 / 24 )107.8736111111110.513362115281905210.131616455324
Winsorized Mean ( 11 / 24 )107.81250.504641746443475213.641659176677
Winsorized Mean ( 12 / 24 )107.8458333333330.488253801067284220.880683565783
Winsorized Mean ( 13 / 24 )107.8097222222220.477806181371747225.634841961877
Winsorized Mean ( 14 / 24 )107.8680555555560.461854067780322233.554412704366
Winsorized Mean ( 15 / 24 )107.9097222222220.454826144888816237.254879550957
Winsorized Mean ( 16 / 24 )107.9319444444440.451115060797792239.255910129819
Winsorized Mean ( 17 / 24 )107.9791666666670.443298815681196243.580995136972
Winsorized Mean ( 18 / 24 )108.0541666666670.408923055520795264.240827725038
Winsorized Mean ( 19 / 24 )108.0541666666670.393546023003946274.565515468525
Winsorized Mean ( 20 / 24 )108.0819444444440.341584075606143316.413885081301
Winsorized Mean ( 21 / 24 )108.1111111111110.328905780347015328.699334493445
Winsorized Mean ( 22 / 24 )108.1416666666670.307291094731703351.919299064249
Winsorized Mean ( 23 / 24 )108.2055555555560.271457038342073398.610241297932
Winsorized Mean ( 24 / 24 )108.3055555555560.256487719529646422.264098079117
Trimmed Mean ( 1 / 24 )107.7257142857140.572494761028352188.168908466883
Trimmed Mean ( 2 / 24 )107.7882352941180.558742196382448192.91228762028
Trimmed Mean ( 3 / 24 )107.8409090909090.548300945357001196.681968185726
Trimmed Mean ( 4 / 24 )107.881250.540575251174654199.567497338395
Trimmed Mean ( 5 / 24 )107.9209677419350.532612456733863202.625692241107
Trimmed Mean ( 6 / 24 )107.9550.52493973288735205.652179167712
Trimmed Mean ( 7 / 24 )107.9879310344830.517048007814358208.854747339545
Trimmed Mean ( 8 / 24 )108.0250.50745897409506212.874351454004
Trimmed Mean ( 9 / 24 )108.0629629629630.499505669657752216.339812593128
Trimmed Mean ( 10 / 24 )108.0942307692310.491982579655319219.71150044573
Trimmed Mean ( 11 / 24 )108.1260.482754088749212223.977388322382
Trimmed Mean ( 12 / 24 )108.168750.472564268678785228.897437172774
Trimmed Mean ( 13 / 24 )108.2108695652170.46288559599997233.774544942255
Trimmed Mean ( 14 / 24 )108.2613636363640.452187727731412239.416854985211
Trimmed Mean ( 15 / 24 )108.3095238095240.441539508228285245.299733752309
Trimmed Mean ( 16 / 24 )108.35750.428726311298945252.742827170324
Trimmed Mean ( 17 / 24 )108.4078947368420.412058316988671263.088718919906
Trimmed Mean ( 18 / 24 )108.4583333333330.391180042176011277.25937327992
Trimmed Mean ( 19 / 24 )108.5058823529410.372038302718034291.652449654296
Trimmed Mean ( 20 / 24 )108.5593750.349159687534506310.916119116047
Trimmed Mean ( 21 / 24 )108.6166666666670.332599767534472326.568678841332
Trimmed Mean ( 22 / 24 )108.6785714285710.311819932727137348.529904673132
Trimmed Mean ( 23 / 24 )108.7461538461540.287815687241827377.83261533894
Trimmed Mean ( 24 / 24 )108.8166666666670.265031216828735410.580564692441
Median109
Midrange105.35
Midmean - Weighted Average at Xnp108.305405405405
Midmean - Weighted Average at X(n+1)p108.458333333333
Midmean - Empirical Distribution Function108.305405405405
Midmean - Empirical Distribution Function - Averaging108.458333333333
Midmean - Empirical Distribution Function - Interpolation108.458333333333
Midmean - Closest Observation108.305405405405
Midmean - True Basic - Statistics Graphics Toolkit108.458333333333
Midmean - MS Excel (old versions)108.685365853659
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.659722222222 & 0.585795139707641 & 183.783911686179 \tabularnewline
Geometric Mean & 107.544539387589 &  &  \tabularnewline
Harmonic Mean & 107.427370174235 &  &  \tabularnewline
Quadratic Mean & 107.772815965396 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 107.666666666667 & 0.583953392785098 & 184.37544502167 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 107.691666666667 & 0.574390709370333 & 187.488524639826 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 107.733333333333 & 0.563464440114783 & 191.19810526355 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 107.744444444444 & 0.559104081875347 & 192.709100035628 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 107.779166666667 & 0.552051719796437 & 195.233821038379 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 107.795833333333 & 0.545878129545523 & 197.472343182314 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 107.786111111111 & 0.54440641734274 & 197.988318428018 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 107.797222222222 & 0.52727995218315 & 204.440206338015 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.859722222222 & 0.515839333519231 & 209.095575334216 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.873611111111 & 0.513362115281905 & 210.131616455324 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.8125 & 0.504641746443475 & 213.641659176677 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.845833333333 & 0.488253801067284 & 220.880683565783 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.809722222222 & 0.477806181371747 & 225.634841961877 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 107.868055555556 & 0.461854067780322 & 233.554412704366 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.909722222222 & 0.454826144888816 & 237.254879550957 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.931944444444 & 0.451115060797792 & 239.255910129819 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.979166666667 & 0.443298815681196 & 243.580995136972 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.054166666667 & 0.408923055520795 & 264.240827725038 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.054166666667 & 0.393546023003946 & 274.565515468525 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.081944444444 & 0.341584075606143 & 316.413885081301 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.111111111111 & 0.328905780347015 & 328.699334493445 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.141666666667 & 0.307291094731703 & 351.919299064249 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.205555555556 & 0.271457038342073 & 398.610241297932 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.305555555556 & 0.256487719529646 & 422.264098079117 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 107.725714285714 & 0.572494761028352 & 188.168908466883 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 107.788235294118 & 0.558742196382448 & 192.91228762028 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 107.840909090909 & 0.548300945357001 & 196.681968185726 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 107.88125 & 0.540575251174654 & 199.567497338395 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 107.920967741935 & 0.532612456733863 & 202.625692241107 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.955 & 0.52493973288735 & 205.652179167712 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.987931034483 & 0.517048007814358 & 208.854747339545 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.025 & 0.50745897409506 & 212.874351454004 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.062962962963 & 0.499505669657752 & 216.339812593128 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.094230769231 & 0.491982579655319 & 219.71150044573 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.126 & 0.482754088749212 & 223.977388322382 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.16875 & 0.472564268678785 & 228.897437172774 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.210869565217 & 0.46288559599997 & 233.774544942255 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.261363636364 & 0.452187727731412 & 239.416854985211 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.309523809524 & 0.441539508228285 & 245.299733752309 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.3575 & 0.428726311298945 & 252.742827170324 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.407894736842 & 0.412058316988671 & 263.088718919906 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.458333333333 & 0.391180042176011 & 277.25937327992 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.505882352941 & 0.372038302718034 & 291.652449654296 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.559375 & 0.349159687534506 & 310.916119116047 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.616666666667 & 0.332599767534472 & 326.568678841332 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 108.678571428571 & 0.311819932727137 & 348.529904673132 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.746153846154 & 0.287815687241827 & 377.83261533894 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.816666666667 & 0.265031216828735 & 410.580564692441 \tabularnewline
Median & 109 &  &  \tabularnewline
Midrange & 105.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.305405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.458333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.305405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.458333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.458333333333 &  &  \tabularnewline
Midmean - Closest Observation & 108.305405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.458333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.685365853659 &  &  \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]107.659722222222[/C][C]0.585795139707641[/C][C]183.783911686179[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.544539387589[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.427370174235[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.772815965396[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]107.666666666667[/C][C]0.583953392785098[/C][C]184.37544502167[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]107.691666666667[/C][C]0.574390709370333[/C][C]187.488524639826[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]107.733333333333[/C][C]0.563464440114783[/C][C]191.19810526355[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]107.744444444444[/C][C]0.559104081875347[/C][C]192.709100035628[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]107.779166666667[/C][C]0.552051719796437[/C][C]195.233821038379[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]107.795833333333[/C][C]0.545878129545523[/C][C]197.472343182314[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]107.786111111111[/C][C]0.54440641734274[/C][C]197.988318428018[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]107.797222222222[/C][C]0.52727995218315[/C][C]204.440206338015[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.859722222222[/C][C]0.515839333519231[/C][C]209.095575334216[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.873611111111[/C][C]0.513362115281905[/C][C]210.131616455324[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.8125[/C][C]0.504641746443475[/C][C]213.641659176677[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.845833333333[/C][C]0.488253801067284[/C][C]220.880683565783[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.809722222222[/C][C]0.477806181371747[/C][C]225.634841961877[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]107.868055555556[/C][C]0.461854067780322[/C][C]233.554412704366[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.909722222222[/C][C]0.454826144888816[/C][C]237.254879550957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.931944444444[/C][C]0.451115060797792[/C][C]239.255910129819[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.979166666667[/C][C]0.443298815681196[/C][C]243.580995136972[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.054166666667[/C][C]0.408923055520795[/C][C]264.240827725038[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.054166666667[/C][C]0.393546023003946[/C][C]274.565515468525[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.081944444444[/C][C]0.341584075606143[/C][C]316.413885081301[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.111111111111[/C][C]0.328905780347015[/C][C]328.699334493445[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.141666666667[/C][C]0.307291094731703[/C][C]351.919299064249[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.205555555556[/C][C]0.271457038342073[/C][C]398.610241297932[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.305555555556[/C][C]0.256487719529646[/C][C]422.264098079117[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]107.725714285714[/C][C]0.572494761028352[/C][C]188.168908466883[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]107.788235294118[/C][C]0.558742196382448[/C][C]192.91228762028[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]107.840909090909[/C][C]0.548300945357001[/C][C]196.681968185726[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]107.88125[/C][C]0.540575251174654[/C][C]199.567497338395[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]107.920967741935[/C][C]0.532612456733863[/C][C]202.625692241107[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.955[/C][C]0.52493973288735[/C][C]205.652179167712[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.987931034483[/C][C]0.517048007814358[/C][C]208.854747339545[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.025[/C][C]0.50745897409506[/C][C]212.874351454004[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.062962962963[/C][C]0.499505669657752[/C][C]216.339812593128[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.094230769231[/C][C]0.491982579655319[/C][C]219.71150044573[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.126[/C][C]0.482754088749212[/C][C]223.977388322382[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.16875[/C][C]0.472564268678785[/C][C]228.897437172774[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.210869565217[/C][C]0.46288559599997[/C][C]233.774544942255[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.261363636364[/C][C]0.452187727731412[/C][C]239.416854985211[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.309523809524[/C][C]0.441539508228285[/C][C]245.299733752309[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.3575[/C][C]0.428726311298945[/C][C]252.742827170324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.407894736842[/C][C]0.412058316988671[/C][C]263.088718919906[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.458333333333[/C][C]0.391180042176011[/C][C]277.25937327992[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.505882352941[/C][C]0.372038302718034[/C][C]291.652449654296[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.559375[/C][C]0.349159687534506[/C][C]310.916119116047[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.616666666667[/C][C]0.332599767534472[/C][C]326.568678841332[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]108.678571428571[/C][C]0.311819932727137[/C][C]348.529904673132[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.746153846154[/C][C]0.287815687241827[/C][C]377.83261533894[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.816666666667[/C][C]0.265031216828735[/C][C]410.580564692441[/C][/ROW]
[ROW][C]Median[/C][C]109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.305405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.458333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.305405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.458333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.458333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.305405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.458333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.685365853659[/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 Mean107.6597222222220.585795139707641183.783911686179
Geometric Mean107.544539387589
Harmonic Mean107.427370174235
Quadratic Mean107.772815965396
Winsorized Mean ( 1 / 24 )107.6666666666670.583953392785098184.37544502167
Winsorized Mean ( 2 / 24 )107.6916666666670.574390709370333187.488524639826
Winsorized Mean ( 3 / 24 )107.7333333333330.563464440114783191.19810526355
Winsorized Mean ( 4 / 24 )107.7444444444440.559104081875347192.709100035628
Winsorized Mean ( 5 / 24 )107.7791666666670.552051719796437195.233821038379
Winsorized Mean ( 6 / 24 )107.7958333333330.545878129545523197.472343182314
Winsorized Mean ( 7 / 24 )107.7861111111110.54440641734274197.988318428018
Winsorized Mean ( 8 / 24 )107.7972222222220.52727995218315204.440206338015
Winsorized Mean ( 9 / 24 )107.8597222222220.515839333519231209.095575334216
Winsorized Mean ( 10 / 24 )107.8736111111110.513362115281905210.131616455324
Winsorized Mean ( 11 / 24 )107.81250.504641746443475213.641659176677
Winsorized Mean ( 12 / 24 )107.8458333333330.488253801067284220.880683565783
Winsorized Mean ( 13 / 24 )107.8097222222220.477806181371747225.634841961877
Winsorized Mean ( 14 / 24 )107.8680555555560.461854067780322233.554412704366
Winsorized Mean ( 15 / 24 )107.9097222222220.454826144888816237.254879550957
Winsorized Mean ( 16 / 24 )107.9319444444440.451115060797792239.255910129819
Winsorized Mean ( 17 / 24 )107.9791666666670.443298815681196243.580995136972
Winsorized Mean ( 18 / 24 )108.0541666666670.408923055520795264.240827725038
Winsorized Mean ( 19 / 24 )108.0541666666670.393546023003946274.565515468525
Winsorized Mean ( 20 / 24 )108.0819444444440.341584075606143316.413885081301
Winsorized Mean ( 21 / 24 )108.1111111111110.328905780347015328.699334493445
Winsorized Mean ( 22 / 24 )108.1416666666670.307291094731703351.919299064249
Winsorized Mean ( 23 / 24 )108.2055555555560.271457038342073398.610241297932
Winsorized Mean ( 24 / 24 )108.3055555555560.256487719529646422.264098079117
Trimmed Mean ( 1 / 24 )107.7257142857140.572494761028352188.168908466883
Trimmed Mean ( 2 / 24 )107.7882352941180.558742196382448192.91228762028
Trimmed Mean ( 3 / 24 )107.8409090909090.548300945357001196.681968185726
Trimmed Mean ( 4 / 24 )107.881250.540575251174654199.567497338395
Trimmed Mean ( 5 / 24 )107.9209677419350.532612456733863202.625692241107
Trimmed Mean ( 6 / 24 )107.9550.52493973288735205.652179167712
Trimmed Mean ( 7 / 24 )107.9879310344830.517048007814358208.854747339545
Trimmed Mean ( 8 / 24 )108.0250.50745897409506212.874351454004
Trimmed Mean ( 9 / 24 )108.0629629629630.499505669657752216.339812593128
Trimmed Mean ( 10 / 24 )108.0942307692310.491982579655319219.71150044573
Trimmed Mean ( 11 / 24 )108.1260.482754088749212223.977388322382
Trimmed Mean ( 12 / 24 )108.168750.472564268678785228.897437172774
Trimmed Mean ( 13 / 24 )108.2108695652170.46288559599997233.774544942255
Trimmed Mean ( 14 / 24 )108.2613636363640.452187727731412239.416854985211
Trimmed Mean ( 15 / 24 )108.3095238095240.441539508228285245.299733752309
Trimmed Mean ( 16 / 24 )108.35750.428726311298945252.742827170324
Trimmed Mean ( 17 / 24 )108.4078947368420.412058316988671263.088718919906
Trimmed Mean ( 18 / 24 )108.4583333333330.391180042176011277.25937327992
Trimmed Mean ( 19 / 24 )108.5058823529410.372038302718034291.652449654296
Trimmed Mean ( 20 / 24 )108.5593750.349159687534506310.916119116047
Trimmed Mean ( 21 / 24 )108.6166666666670.332599767534472326.568678841332
Trimmed Mean ( 22 / 24 )108.6785714285710.311819932727137348.529904673132
Trimmed Mean ( 23 / 24 )108.7461538461540.287815687241827377.83261533894
Trimmed Mean ( 24 / 24 )108.8166666666670.265031216828735410.580564692441
Median109
Midrange105.35
Midmean - Weighted Average at Xnp108.305405405405
Midmean - Weighted Average at X(n+1)p108.458333333333
Midmean - Empirical Distribution Function108.305405405405
Midmean - Empirical Distribution Function - Averaging108.458333333333
Midmean - Empirical Distribution Function - Interpolation108.458333333333
Midmean - Closest Observation108.305405405405
Midmean - True Basic - Statistics Graphics Toolkit108.458333333333
Midmean - MS Excel (old versions)108.685365853659
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')