Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 21:09:29 +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/13/t14763893914djwvwp9aif7i49.htm/, Retrieved Tue, 30 Apr 2024 18:31:29 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 18:31:29 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
37729
48191
52498
57319
44377
48081
52597
53331
39587
46278
50365
57176
39251
47946
50427
54317
41210
50592
55728
59099
47519
53203
53882
55163
45255
50423
52161
54562
40971
48014
48440
44967
27218
30269
33234
36811
27745
31891
32398
34093
28358
29532
30769
32080
23951
34628
22978
35704
23090
22111
28925
35968
28963
34074
39160
51314
34527
40722
50609
52435




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]'Gwilym Jenkins' @ jenkins.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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean41903.61357.7898084588830.8616250755052
Geometric Mean40495.9334362053
Harmonic Mean39002.8416312904
Quadratic Mean43181.9833916106
Winsorized Mean ( 1 / 20 )41888.38333333331348.2244029573731.0692962102228
Winsorized Mean ( 2 / 20 )41887.351346.4179052609731.1102146193466
Winsorized Mean ( 3 / 20 )418581322.9808461232731.6391579837732
Winsorized Mean ( 4 / 20 )42038.13333333331269.7366906333333.1077566265846
Winsorized Mean ( 5 / 20 )42031.96666666671252.5125584283433.5581199436503
Winsorized Mean ( 6 / 20 )42068.76666666671236.6928714920534.0171498004282
Winsorized Mean ( 7 / 20 )42084.16666666671215.9767105278534.6093525495221
Winsorized Mean ( 8 / 20 )42015.76666666671203.1492234463234.9214925695719
Winsorized Mean ( 9 / 20 )42081.91666666671184.5799432595135.5247587181609
Winsorized Mean ( 10 / 20 )42103.751146.9358686490736.7097683060453
Winsorized Mean ( 11 / 20 )42177.26666666671128.2494890445137.3829255640841
Winsorized Mean ( 12 / 20 )42389.06666666671088.7052367744238.9353015259261
Winsorized Mean ( 13 / 20 )42370.651072.7957653432539.495541806546
Winsorized Mean ( 14 / 20 )42247.21666666671030.7260750847940.987821777179
Winsorized Mean ( 15 / 20 )42279.9666666667971.33729470980543.5275850077374
Winsorized Mean ( 16 / 20 )42499.4333333333935.89650737864245.4103984770391
Winsorized Mean ( 17 / 20 )42458.0666666667928.24757524144445.740024320153
Winsorized Mean ( 18 / 20 )42587.0666666667908.33664236167146.8846732373809
Winsorized Mean ( 19 / 20 )42600.6833333333900.84843733973347.2895123836104
Winsorized Mean ( 20 / 20 )42317.6833333333756.19378382518955.961427134815
Trimmed Mean ( 1 / 20 )41948.37931034481328.9524259392931.5649969792532
Trimmed Mean ( 2 / 20 )42012.66071428571304.6385819070832.20252819204
Trimmed Mean ( 3 / 20 )42082.27777777781275.2216308698432.9999717375191
Trimmed Mean ( 4 / 20 )42168.53846153851249.2562612332333.7549146401003
Trimmed Mean ( 5 / 20 )42207.661236.580096883434.1325726545151
Trimmed Mean ( 6 / 20 )42251.58333333331224.8314523768934.4958347136992
Trimmed Mean ( 7 / 20 )42291.32608695651213.0131513576134.864688844984
Trimmed Mean ( 8 / 20 )42331.68181818181201.8145683219135.2231391880107
Trimmed Mean ( 9 / 20 )42388.09523809521188.6233615884135.6615027164283
Trimmed Mean ( 10 / 20 )42439.1251174.1172331430436.1455600872097
Trimmed Mean ( 11 / 20 )42492.07894736841162.2129859560436.5613527475897
Trimmed Mean ( 12 / 20 )42539.77777777781148.3280206602637.0449706115492
Trimmed Mean ( 13 / 20 )42561.94117647061136.8795574894437.4375112087155
Trimmed Mean ( 14 / 20 )42589.531251121.6986299807837.9687824444698
Trimmed Mean ( 15 / 20 )42638.43333333331108.0098900792438.4819970607699
Trimmed Mean ( 16 / 20 )42689.64285714291100.7693440112938.7816422117812
Trimmed Mean ( 17 / 20 )42717.07692307691094.9843004467539.0115884818153
Trimmed Mean ( 18 / 20 )42755.16666666671081.3734769349439.5378355199284
Trimmed Mean ( 19 / 20 )42780.63636363641059.87298010840.3639277220532
Trimmed Mean ( 20 / 20 )42809.051019.5130428813941.989703122396
Median42793.5
Midrange40605
Midmean - Weighted Average at Xnp42308.0967741935
Midmean - Weighted Average at X(n+1)p42638.4333333333
Midmean - Empirical Distribution Function42308.0967741935
Midmean - Empirical Distribution Function - Averaging42638.4333333333
Midmean - Empirical Distribution Function - Interpolation42638.4333333333
Midmean - Closest Observation42308.0967741935
Midmean - True Basic - Statistics Graphics Toolkit42638.4333333333
Midmean - MS Excel (old versions)42589.53125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 41903.6 & 1357.78980845888 & 30.8616250755052 \tabularnewline
Geometric Mean & 40495.9334362053 &  &  \tabularnewline
Harmonic Mean & 39002.8416312904 &  &  \tabularnewline
Quadratic Mean & 43181.9833916106 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 41888.3833333333 & 1348.22440295737 & 31.0692962102228 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 41887.35 & 1346.41790526097 & 31.1102146193466 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 41858 & 1322.98084612327 & 31.6391579837732 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 42038.1333333333 & 1269.73669063333 & 33.1077566265846 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 42031.9666666667 & 1252.51255842834 & 33.5581199436503 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 42068.7666666667 & 1236.69287149205 & 34.0171498004282 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 42084.1666666667 & 1215.97671052785 & 34.6093525495221 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 42015.7666666667 & 1203.14922344632 & 34.9214925695719 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 42081.9166666667 & 1184.57994325951 & 35.5247587181609 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 42103.75 & 1146.93586864907 & 36.7097683060453 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 42177.2666666667 & 1128.24948904451 & 37.3829255640841 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 42389.0666666667 & 1088.70523677442 & 38.9353015259261 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 42370.65 & 1072.79576534325 & 39.495541806546 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 42247.2166666667 & 1030.72607508479 & 40.987821777179 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 42279.9666666667 & 971.337294709805 & 43.5275850077374 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 42499.4333333333 & 935.896507378642 & 45.4103984770391 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 42458.0666666667 & 928.247575241444 & 45.740024320153 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 42587.0666666667 & 908.336642361671 & 46.8846732373809 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 42600.6833333333 & 900.848437339733 & 47.2895123836104 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 42317.6833333333 & 756.193783825189 & 55.961427134815 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 41948.3793103448 & 1328.95242593929 & 31.5649969792532 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 42012.6607142857 & 1304.63858190708 & 32.20252819204 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 42082.2777777778 & 1275.22163086984 & 32.9999717375191 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 42168.5384615385 & 1249.25626123323 & 33.7549146401003 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 42207.66 & 1236.5800968834 & 34.1325726545151 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 42251.5833333333 & 1224.83145237689 & 34.4958347136992 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 42291.3260869565 & 1213.01315135761 & 34.864688844984 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 42331.6818181818 & 1201.81456832191 & 35.2231391880107 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 42388.0952380952 & 1188.62336158841 & 35.6615027164283 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 42439.125 & 1174.11723314304 & 36.1455600872097 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 42492.0789473684 & 1162.21298595604 & 36.5613527475897 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 42539.7777777778 & 1148.32802066026 & 37.0449706115492 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 42561.9411764706 & 1136.87955748944 & 37.4375112087155 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 42589.53125 & 1121.69862998078 & 37.9687824444698 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 42638.4333333333 & 1108.00989007924 & 38.4819970607699 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 42689.6428571429 & 1100.76934401129 & 38.7816422117812 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 42717.0769230769 & 1094.98430044675 & 39.0115884818153 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 42755.1666666667 & 1081.37347693494 & 39.5378355199284 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 42780.6363636364 & 1059.872980108 & 40.3639277220532 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 42809.05 & 1019.51304288139 & 41.989703122396 \tabularnewline
Median & 42793.5 &  &  \tabularnewline
Midrange & 40605 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 42308.0967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 42638.4333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 42308.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 42638.4333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 42638.4333333333 &  &  \tabularnewline
Midmean - Closest Observation & 42308.0967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 42638.4333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 42589.53125 &  &  \tabularnewline
Number of observations & 60 &  &  \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]41903.6[/C][C]1357.78980845888[/C][C]30.8616250755052[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40495.9334362053[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]39002.8416312904[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]43181.9833916106[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]41888.3833333333[/C][C]1348.22440295737[/C][C]31.0692962102228[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]41887.35[/C][C]1346.41790526097[/C][C]31.1102146193466[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]41858[/C][C]1322.98084612327[/C][C]31.6391579837732[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]42038.1333333333[/C][C]1269.73669063333[/C][C]33.1077566265846[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]42031.9666666667[/C][C]1252.51255842834[/C][C]33.5581199436503[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]42068.7666666667[/C][C]1236.69287149205[/C][C]34.0171498004282[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]42084.1666666667[/C][C]1215.97671052785[/C][C]34.6093525495221[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]42015.7666666667[/C][C]1203.14922344632[/C][C]34.9214925695719[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]42081.9166666667[/C][C]1184.57994325951[/C][C]35.5247587181609[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]42103.75[/C][C]1146.93586864907[/C][C]36.7097683060453[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]42177.2666666667[/C][C]1128.24948904451[/C][C]37.3829255640841[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]42389.0666666667[/C][C]1088.70523677442[/C][C]38.9353015259261[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]42370.65[/C][C]1072.79576534325[/C][C]39.495541806546[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]42247.2166666667[/C][C]1030.72607508479[/C][C]40.987821777179[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]42279.9666666667[/C][C]971.337294709805[/C][C]43.5275850077374[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]42499.4333333333[/C][C]935.896507378642[/C][C]45.4103984770391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]42458.0666666667[/C][C]928.247575241444[/C][C]45.740024320153[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]42587.0666666667[/C][C]908.336642361671[/C][C]46.8846732373809[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]42600.6833333333[/C][C]900.848437339733[/C][C]47.2895123836104[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]42317.6833333333[/C][C]756.193783825189[/C][C]55.961427134815[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]41948.3793103448[/C][C]1328.95242593929[/C][C]31.5649969792532[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]42012.6607142857[/C][C]1304.63858190708[/C][C]32.20252819204[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]42082.2777777778[/C][C]1275.22163086984[/C][C]32.9999717375191[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]42168.5384615385[/C][C]1249.25626123323[/C][C]33.7549146401003[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]42207.66[/C][C]1236.5800968834[/C][C]34.1325726545151[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]42251.5833333333[/C][C]1224.83145237689[/C][C]34.4958347136992[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]42291.3260869565[/C][C]1213.01315135761[/C][C]34.864688844984[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]42331.6818181818[/C][C]1201.81456832191[/C][C]35.2231391880107[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]42388.0952380952[/C][C]1188.62336158841[/C][C]35.6615027164283[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]42439.125[/C][C]1174.11723314304[/C][C]36.1455600872097[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]42492.0789473684[/C][C]1162.21298595604[/C][C]36.5613527475897[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]42539.7777777778[/C][C]1148.32802066026[/C][C]37.0449706115492[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]42561.9411764706[/C][C]1136.87955748944[/C][C]37.4375112087155[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]42589.53125[/C][C]1121.69862998078[/C][C]37.9687824444698[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]42638.4333333333[/C][C]1108.00989007924[/C][C]38.4819970607699[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]42689.6428571429[/C][C]1100.76934401129[/C][C]38.7816422117812[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]42717.0769230769[/C][C]1094.98430044675[/C][C]39.0115884818153[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]42755.1666666667[/C][C]1081.37347693494[/C][C]39.5378355199284[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]42780.6363636364[/C][C]1059.872980108[/C][C]40.3639277220532[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]42809.05[/C][C]1019.51304288139[/C][C]41.989703122396[/C][/ROW]
[ROW][C]Median[/C][C]42793.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]40605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]42308.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]42638.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]42308.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]42638.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]42638.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]42308.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]42638.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]42589.53125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/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 Mean41903.61357.7898084588830.8616250755052
Geometric Mean40495.9334362053
Harmonic Mean39002.8416312904
Quadratic Mean43181.9833916106
Winsorized Mean ( 1 / 20 )41888.38333333331348.2244029573731.0692962102228
Winsorized Mean ( 2 / 20 )41887.351346.4179052609731.1102146193466
Winsorized Mean ( 3 / 20 )418581322.9808461232731.6391579837732
Winsorized Mean ( 4 / 20 )42038.13333333331269.7366906333333.1077566265846
Winsorized Mean ( 5 / 20 )42031.96666666671252.5125584283433.5581199436503
Winsorized Mean ( 6 / 20 )42068.76666666671236.6928714920534.0171498004282
Winsorized Mean ( 7 / 20 )42084.16666666671215.9767105278534.6093525495221
Winsorized Mean ( 8 / 20 )42015.76666666671203.1492234463234.9214925695719
Winsorized Mean ( 9 / 20 )42081.91666666671184.5799432595135.5247587181609
Winsorized Mean ( 10 / 20 )42103.751146.9358686490736.7097683060453
Winsorized Mean ( 11 / 20 )42177.26666666671128.2494890445137.3829255640841
Winsorized Mean ( 12 / 20 )42389.06666666671088.7052367744238.9353015259261
Winsorized Mean ( 13 / 20 )42370.651072.7957653432539.495541806546
Winsorized Mean ( 14 / 20 )42247.21666666671030.7260750847940.987821777179
Winsorized Mean ( 15 / 20 )42279.9666666667971.33729470980543.5275850077374
Winsorized Mean ( 16 / 20 )42499.4333333333935.89650737864245.4103984770391
Winsorized Mean ( 17 / 20 )42458.0666666667928.24757524144445.740024320153
Winsorized Mean ( 18 / 20 )42587.0666666667908.33664236167146.8846732373809
Winsorized Mean ( 19 / 20 )42600.6833333333900.84843733973347.2895123836104
Winsorized Mean ( 20 / 20 )42317.6833333333756.19378382518955.961427134815
Trimmed Mean ( 1 / 20 )41948.37931034481328.9524259392931.5649969792532
Trimmed Mean ( 2 / 20 )42012.66071428571304.6385819070832.20252819204
Trimmed Mean ( 3 / 20 )42082.27777777781275.2216308698432.9999717375191
Trimmed Mean ( 4 / 20 )42168.53846153851249.2562612332333.7549146401003
Trimmed Mean ( 5 / 20 )42207.661236.580096883434.1325726545151
Trimmed Mean ( 6 / 20 )42251.58333333331224.8314523768934.4958347136992
Trimmed Mean ( 7 / 20 )42291.32608695651213.0131513576134.864688844984
Trimmed Mean ( 8 / 20 )42331.68181818181201.8145683219135.2231391880107
Trimmed Mean ( 9 / 20 )42388.09523809521188.6233615884135.6615027164283
Trimmed Mean ( 10 / 20 )42439.1251174.1172331430436.1455600872097
Trimmed Mean ( 11 / 20 )42492.07894736841162.2129859560436.5613527475897
Trimmed Mean ( 12 / 20 )42539.77777777781148.3280206602637.0449706115492
Trimmed Mean ( 13 / 20 )42561.94117647061136.8795574894437.4375112087155
Trimmed Mean ( 14 / 20 )42589.531251121.6986299807837.9687824444698
Trimmed Mean ( 15 / 20 )42638.43333333331108.0098900792438.4819970607699
Trimmed Mean ( 16 / 20 )42689.64285714291100.7693440112938.7816422117812
Trimmed Mean ( 17 / 20 )42717.07692307691094.9843004467539.0115884818153
Trimmed Mean ( 18 / 20 )42755.16666666671081.3734769349439.5378355199284
Trimmed Mean ( 19 / 20 )42780.63636363641059.87298010840.3639277220532
Trimmed Mean ( 20 / 20 )42809.051019.5130428813941.989703122396
Median42793.5
Midrange40605
Midmean - Weighted Average at Xnp42308.0967741935
Midmean - Weighted Average at X(n+1)p42638.4333333333
Midmean - Empirical Distribution Function42308.0967741935
Midmean - Empirical Distribution Function - Averaging42638.4333333333
Midmean - Empirical Distribution Function - Interpolation42638.4333333333
Midmean - Closest Observation42308.0967741935
Midmean - True Basic - Statistics Graphics Toolkit42638.4333333333
Midmean - MS Excel (old versions)42589.53125
Number of observations60



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')