Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 16:31:53 +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/11/t1476199983m9295ps78f2yvam.htm/, Retrieved Mon, 29 Apr 2024 05:21:27 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 05:21:27 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
102,59
102,91
101,94
101,8
102,25
102,6
102,49
102,13
100,76
100,86
101,12
100,74
99,99
99,39
99,52
99,21
99,38
99,37
99,38
99,26
99,36
99,2
98,53
98,65
99,15
100,17
99,98
100,07
99,94
100,05
99,13
98,74
98,64
98,44
98,81
98,88
99,63
100,08
100,07
100,55
99,98
99,89
99,86
99,61
100,12
100,24
100,1
99,86
97,99
97,57
98,28
97,97
97,99
97,84
97,33
96,7
96,79
96,76
96,23
96,29
96,46
97,23
97,59
97,13
97,37
96,12
96,96
96,7
97
97,15
96,51
96,68




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 Mean99.11194444444440.207003609821715478.793314424835
Geometric Mean99.0966253666063
Harmonic Mean99.0813358039077
Quadratic Mean99.1272914825512
Winsorized Mean ( 1 / 24 )99.10916666666670.205626238217562481.986965893938
Winsorized Mean ( 2 / 24 )99.11055555555550.205234215689935482.91438745911
Winsorized Mean ( 3 / 24 )99.11347222222220.202910373582629488.459364951399
Winsorized Mean ( 4 / 24 )99.10291666666670.199354635355477497.118697490793
Winsorized Mean ( 5 / 24 )99.10638888888890.195405791969013507.182452936732
Winsorized Mean ( 6 / 24 )99.09222222222220.191731487530683516.828109448451
Winsorized Mean ( 7 / 24 )99.07861111111110.188926763095115524.4286700727
Winsorized Mean ( 8 / 24 )99.00972222222220.173542665694076570.520925365744
Winsorized Mean ( 9 / 24 )98.98097222222220.167500514997249590.929360568522
Winsorized Mean ( 10 / 24 )98.99069444444440.161055342696683614.637756108933
Winsorized Mean ( 11 / 24 )98.993750.159502777569626620.639662257839
Winsorized Mean ( 12 / 24 )98.983750.1509622808215655.685310670682
Winsorized Mean ( 13 / 24 )98.93138888888890.142612598014699693.70721988174
Winsorized Mean ( 14 / 24 )98.93333333333330.138155465716544716.1014790129
Winsorized Mean ( 15 / 24 )98.943750.133265158260152742.457753337509
Winsorized Mean ( 16 / 24 )98.94819444444450.131203101225098754.160484931563
Winsorized Mean ( 17 / 24 )98.99069444444440.122762498031292806.359401543065
Winsorized Mean ( 18 / 24 )98.99319444444440.121636729609833813.842946632809
Winsorized Mean ( 19 / 24 )99.05916666666670.111170284517151891.057957591033
Winsorized Mean ( 20 / 24 )99.08972222222220.104952476804556944.138959261995
Winsorized Mean ( 21 / 24 )99.07805555555560.10184384601248972.842831793824
Winsorized Mean ( 22 / 24 )99.0750.101459228071558976.500628706966
Winsorized Mean ( 23 / 24 )99.16763888888890.08786426370424651128.64587612877
Winsorized Mean ( 24 / 24 )99.20763888888890.07865519060070551261.29805460034
Trimmed Mean ( 1 / 24 )99.10042857142860.201272086551037492.370453695772
Trimmed Mean ( 2 / 24 )99.09117647058820.196083976362918505.350708959448
Trimmed Mean ( 3 / 24 )99.08060606060610.190127901839025521.126068831782
Trimmed Mean ( 4 / 24 )99.068281250.184046442482465538.278707883412
Trimmed Mean ( 5 / 24 )99.05822580645160.178054223226988556.337412340789
Trimmed Mean ( 6 / 24 )99.04666666666670.172061391400122575.6472492794
Trimmed Mean ( 7 / 24 )99.03724137931030.16583466739153597.20469149847
Trimmed Mean ( 8 / 24 )99.02964285714290.158953551225269623.009942802712
Trimmed Mean ( 9 / 24 )99.0329629629630.154479498373939641.075120034636
Trimmed Mean ( 10 / 24 )99.04096153846150.150321741320672658.859860645065
Trimmed Mean ( 11 / 24 )99.04820.14657746854723675.739600237977
Trimmed Mean ( 12 / 24 )99.0556250.142137590122069696.899566926176
Trimmed Mean ( 13 / 24 )99.0650.138370346017508715.940971828354
Trimmed Mean ( 14 / 24 )99.08181818181820.13517793173068732.973325699512
Trimmed Mean ( 15 / 24 )99.10.131870752899888751.493396532237
Trimmed Mean ( 16 / 24 )99.118750.128497324874878771.368198493743
Trimmed Mean ( 17 / 24 )99.13894736842110.12429476132101797.611631534328
Trimmed Mean ( 18 / 24 )99.15638888888890.120723449398068821.351521873229
Trimmed Mean ( 19 / 24 )99.17558823529410.115865487792539855.954522134076
Trimmed Mean ( 20 / 24 )99.1893750.112131059461541884.584302300468
Trimmed Mean ( 21 / 24 )99.20133333333330.108495175308094914.338661158257
Trimmed Mean ( 22 / 24 )99.21642857142860.103798510410393955.855996190618
Trimmed Mean ( 23 / 24 )99.23423076923080.09647506346109591028.5997978042
Trimmed Mean ( 24 / 24 )99.24291666666670.0911013115900641089.36869222298
Median99.31
Midrange99.515
Midmean - Weighted Average at Xnp99.1135135135135
Midmean - Weighted Average at X(n+1)p99.1563888888889
Midmean - Empirical Distribution Function99.1135135135135
Midmean - Empirical Distribution Function - Averaging99.1563888888889
Midmean - Empirical Distribution Function - Interpolation99.1563888888889
Midmean - Closest Observation99.1135135135135
Midmean - True Basic - Statistics Graphics Toolkit99.1563888888889
Midmean - MS Excel (old versions)99.1389473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.1119444444444 & 0.207003609821715 & 478.793314424835 \tabularnewline
Geometric Mean & 99.0966253666063 &  &  \tabularnewline
Harmonic Mean & 99.0813358039077 &  &  \tabularnewline
Quadratic Mean & 99.1272914825512 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.1091666666667 & 0.205626238217562 & 481.986965893938 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.1105555555555 & 0.205234215689935 & 482.91438745911 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.1134722222222 & 0.202910373582629 & 488.459364951399 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.1029166666667 & 0.199354635355477 & 497.118697490793 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.1063888888889 & 0.195405791969013 & 507.182452936732 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.0922222222222 & 0.191731487530683 & 516.828109448451 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.0786111111111 & 0.188926763095115 & 524.4286700727 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.0097222222222 & 0.173542665694076 & 570.520925365744 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.9809722222222 & 0.167500514997249 & 590.929360568522 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.9906944444444 & 0.161055342696683 & 614.637756108933 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.99375 & 0.159502777569626 & 620.639662257839 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.98375 & 0.1509622808215 & 655.685310670682 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.9313888888889 & 0.142612598014699 & 693.70721988174 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.9333333333333 & 0.138155465716544 & 716.1014790129 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.94375 & 0.133265158260152 & 742.457753337509 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.9481944444445 & 0.131203101225098 & 754.160484931563 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.9906944444444 & 0.122762498031292 & 806.359401543065 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.9931944444444 & 0.121636729609833 & 813.842946632809 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.0591666666667 & 0.111170284517151 & 891.057957591033 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.0897222222222 & 0.104952476804556 & 944.138959261995 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.0780555555556 & 0.10184384601248 & 972.842831793824 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.075 & 0.101459228071558 & 976.500628706966 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.1676388888889 & 0.0878642637042465 & 1128.64587612877 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.2076388888889 & 0.0786551906007055 & 1261.29805460034 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.1004285714286 & 0.201272086551037 & 492.370453695772 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.0911764705882 & 0.196083976362918 & 505.350708959448 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.0806060606061 & 0.190127901839025 & 521.126068831782 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.06828125 & 0.184046442482465 & 538.278707883412 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.0582258064516 & 0.178054223226988 & 556.337412340789 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.0466666666667 & 0.172061391400122 & 575.6472492794 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.0372413793103 & 0.16583466739153 & 597.20469149847 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.0296428571429 & 0.158953551225269 & 623.009942802712 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.032962962963 & 0.154479498373939 & 641.075120034636 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.0409615384615 & 0.150321741320672 & 658.859860645065 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.0482 & 0.14657746854723 & 675.739600237977 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.055625 & 0.142137590122069 & 696.899566926176 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.065 & 0.138370346017508 & 715.940971828354 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.0818181818182 & 0.13517793173068 & 732.973325699512 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.1 & 0.131870752899888 & 751.493396532237 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.11875 & 0.128497324874878 & 771.368198493743 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.1389473684211 & 0.12429476132101 & 797.611631534328 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.1563888888889 & 0.120723449398068 & 821.351521873229 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.1755882352941 & 0.115865487792539 & 855.954522134076 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.189375 & 0.112131059461541 & 884.584302300468 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.2013333333333 & 0.108495175308094 & 914.338661158257 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.2164285714286 & 0.103798510410393 & 955.855996190618 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.2342307692308 & 0.0964750634610959 & 1028.5997978042 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.2429166666667 & 0.091101311590064 & 1089.36869222298 \tabularnewline
Median & 99.31 &  &  \tabularnewline
Midrange & 99.515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.1135135135135 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.1563888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.1135135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.1563888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.1563888888889 &  &  \tabularnewline
Midmean - Closest Observation & 99.1135135135135 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.1563888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.1389473684211 &  &  \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]99.1119444444444[/C][C]0.207003609821715[/C][C]478.793314424835[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.0966253666063[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.0813358039077[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.1272914825512[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.1091666666667[/C][C]0.205626238217562[/C][C]481.986965893938[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.1105555555555[/C][C]0.205234215689935[/C][C]482.91438745911[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.1134722222222[/C][C]0.202910373582629[/C][C]488.459364951399[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.1029166666667[/C][C]0.199354635355477[/C][C]497.118697490793[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.1063888888889[/C][C]0.195405791969013[/C][C]507.182452936732[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.0922222222222[/C][C]0.191731487530683[/C][C]516.828109448451[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.0786111111111[/C][C]0.188926763095115[/C][C]524.4286700727[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.0097222222222[/C][C]0.173542665694076[/C][C]570.520925365744[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.9809722222222[/C][C]0.167500514997249[/C][C]590.929360568522[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.9906944444444[/C][C]0.161055342696683[/C][C]614.637756108933[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.99375[/C][C]0.159502777569626[/C][C]620.639662257839[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.98375[/C][C]0.1509622808215[/C][C]655.685310670682[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.9313888888889[/C][C]0.142612598014699[/C][C]693.70721988174[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.9333333333333[/C][C]0.138155465716544[/C][C]716.1014790129[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.94375[/C][C]0.133265158260152[/C][C]742.457753337509[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.9481944444445[/C][C]0.131203101225098[/C][C]754.160484931563[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.9906944444444[/C][C]0.122762498031292[/C][C]806.359401543065[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.9931944444444[/C][C]0.121636729609833[/C][C]813.842946632809[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.0591666666667[/C][C]0.111170284517151[/C][C]891.057957591033[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.0897222222222[/C][C]0.104952476804556[/C][C]944.138959261995[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.0780555555556[/C][C]0.10184384601248[/C][C]972.842831793824[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.075[/C][C]0.101459228071558[/C][C]976.500628706966[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.1676388888889[/C][C]0.0878642637042465[/C][C]1128.64587612877[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.2076388888889[/C][C]0.0786551906007055[/C][C]1261.29805460034[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.1004285714286[/C][C]0.201272086551037[/C][C]492.370453695772[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.0911764705882[/C][C]0.196083976362918[/C][C]505.350708959448[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.0806060606061[/C][C]0.190127901839025[/C][C]521.126068831782[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.06828125[/C][C]0.184046442482465[/C][C]538.278707883412[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.0582258064516[/C][C]0.178054223226988[/C][C]556.337412340789[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.0466666666667[/C][C]0.172061391400122[/C][C]575.6472492794[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.0372413793103[/C][C]0.16583466739153[/C][C]597.20469149847[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.0296428571429[/C][C]0.158953551225269[/C][C]623.009942802712[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.032962962963[/C][C]0.154479498373939[/C][C]641.075120034636[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.0409615384615[/C][C]0.150321741320672[/C][C]658.859860645065[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.0482[/C][C]0.14657746854723[/C][C]675.739600237977[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.055625[/C][C]0.142137590122069[/C][C]696.899566926176[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.065[/C][C]0.138370346017508[/C][C]715.940971828354[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.0818181818182[/C][C]0.13517793173068[/C][C]732.973325699512[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.1[/C][C]0.131870752899888[/C][C]751.493396532237[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.11875[/C][C]0.128497324874878[/C][C]771.368198493743[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.1389473684211[/C][C]0.12429476132101[/C][C]797.611631534328[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.1563888888889[/C][C]0.120723449398068[/C][C]821.351521873229[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.1755882352941[/C][C]0.115865487792539[/C][C]855.954522134076[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.189375[/C][C]0.112131059461541[/C][C]884.584302300468[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.2013333333333[/C][C]0.108495175308094[/C][C]914.338661158257[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.2164285714286[/C][C]0.103798510410393[/C][C]955.855996190618[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.2342307692308[/C][C]0.0964750634610959[/C][C]1028.5997978042[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.2429166666667[/C][C]0.091101311590064[/C][C]1089.36869222298[/C][/ROW]
[ROW][C]Median[/C][C]99.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.1135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.1563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.1135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.1563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.1563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.1135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.1563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.1389473684211[/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 Mean99.11194444444440.207003609821715478.793314424835
Geometric Mean99.0966253666063
Harmonic Mean99.0813358039077
Quadratic Mean99.1272914825512
Winsorized Mean ( 1 / 24 )99.10916666666670.205626238217562481.986965893938
Winsorized Mean ( 2 / 24 )99.11055555555550.205234215689935482.91438745911
Winsorized Mean ( 3 / 24 )99.11347222222220.202910373582629488.459364951399
Winsorized Mean ( 4 / 24 )99.10291666666670.199354635355477497.118697490793
Winsorized Mean ( 5 / 24 )99.10638888888890.195405791969013507.182452936732
Winsorized Mean ( 6 / 24 )99.09222222222220.191731487530683516.828109448451
Winsorized Mean ( 7 / 24 )99.07861111111110.188926763095115524.4286700727
Winsorized Mean ( 8 / 24 )99.00972222222220.173542665694076570.520925365744
Winsorized Mean ( 9 / 24 )98.98097222222220.167500514997249590.929360568522
Winsorized Mean ( 10 / 24 )98.99069444444440.161055342696683614.637756108933
Winsorized Mean ( 11 / 24 )98.993750.159502777569626620.639662257839
Winsorized Mean ( 12 / 24 )98.983750.1509622808215655.685310670682
Winsorized Mean ( 13 / 24 )98.93138888888890.142612598014699693.70721988174
Winsorized Mean ( 14 / 24 )98.93333333333330.138155465716544716.1014790129
Winsorized Mean ( 15 / 24 )98.943750.133265158260152742.457753337509
Winsorized Mean ( 16 / 24 )98.94819444444450.131203101225098754.160484931563
Winsorized Mean ( 17 / 24 )98.99069444444440.122762498031292806.359401543065
Winsorized Mean ( 18 / 24 )98.99319444444440.121636729609833813.842946632809
Winsorized Mean ( 19 / 24 )99.05916666666670.111170284517151891.057957591033
Winsorized Mean ( 20 / 24 )99.08972222222220.104952476804556944.138959261995
Winsorized Mean ( 21 / 24 )99.07805555555560.10184384601248972.842831793824
Winsorized Mean ( 22 / 24 )99.0750.101459228071558976.500628706966
Winsorized Mean ( 23 / 24 )99.16763888888890.08786426370424651128.64587612877
Winsorized Mean ( 24 / 24 )99.20763888888890.07865519060070551261.29805460034
Trimmed Mean ( 1 / 24 )99.10042857142860.201272086551037492.370453695772
Trimmed Mean ( 2 / 24 )99.09117647058820.196083976362918505.350708959448
Trimmed Mean ( 3 / 24 )99.08060606060610.190127901839025521.126068831782
Trimmed Mean ( 4 / 24 )99.068281250.184046442482465538.278707883412
Trimmed Mean ( 5 / 24 )99.05822580645160.178054223226988556.337412340789
Trimmed Mean ( 6 / 24 )99.04666666666670.172061391400122575.6472492794
Trimmed Mean ( 7 / 24 )99.03724137931030.16583466739153597.20469149847
Trimmed Mean ( 8 / 24 )99.02964285714290.158953551225269623.009942802712
Trimmed Mean ( 9 / 24 )99.0329629629630.154479498373939641.075120034636
Trimmed Mean ( 10 / 24 )99.04096153846150.150321741320672658.859860645065
Trimmed Mean ( 11 / 24 )99.04820.14657746854723675.739600237977
Trimmed Mean ( 12 / 24 )99.0556250.142137590122069696.899566926176
Trimmed Mean ( 13 / 24 )99.0650.138370346017508715.940971828354
Trimmed Mean ( 14 / 24 )99.08181818181820.13517793173068732.973325699512
Trimmed Mean ( 15 / 24 )99.10.131870752899888751.493396532237
Trimmed Mean ( 16 / 24 )99.118750.128497324874878771.368198493743
Trimmed Mean ( 17 / 24 )99.13894736842110.12429476132101797.611631534328
Trimmed Mean ( 18 / 24 )99.15638888888890.120723449398068821.351521873229
Trimmed Mean ( 19 / 24 )99.17558823529410.115865487792539855.954522134076
Trimmed Mean ( 20 / 24 )99.1893750.112131059461541884.584302300468
Trimmed Mean ( 21 / 24 )99.20133333333330.108495175308094914.338661158257
Trimmed Mean ( 22 / 24 )99.21642857142860.103798510410393955.855996190618
Trimmed Mean ( 23 / 24 )99.23423076923080.09647506346109591028.5997978042
Trimmed Mean ( 24 / 24 )99.24291666666670.0911013115900641089.36869222298
Median99.31
Midrange99.515
Midmean - Weighted Average at Xnp99.1135135135135
Midmean - Weighted Average at X(n+1)p99.1563888888889
Midmean - Empirical Distribution Function99.1135135135135
Midmean - Empirical Distribution Function - Averaging99.1563888888889
Midmean - Empirical Distribution Function - Interpolation99.1563888888889
Midmean - Closest Observation99.1135135135135
Midmean - True Basic - Statistics Graphics Toolkit99.1563888888889
Midmean - MS Excel (old versions)99.1389473684211
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')