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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 22 May 2013 09:46:19 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/22/t1369230557jo6h8eev5zv4r1e.htm/, Retrieved Sun, 28 Apr 2024 09:51:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209643, Retrieved Sun, 28 Apr 2024 09:51:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid joggi...] [2013-05-22 13:46:19] [ed71d54cfbd47f943cb19691b5010a6e] [Current]
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Dataseries X:
85,3
85,65
85,15
84,94
85,15
85,15
85,15
85,14
85,37
85,61
85,59
85,54
85,54
85,5
85,78
86,16
86,38
86,49
86,49
86
85,9
85,66
85,64
85,6
85,6
85,57
85,81
86,29
86,37
86,41
86,41
86,38
86,62
87,08
87,19
87,21
87,21
87,24
87,16
87,05
87,04
86,98
86,98
86,94
86,96
86,98
86,86
86,82
86,82
86,84
86,91
86,85
86,61
86,65
86,65
86,36
86,33
86,43
86,36
86,29
86,29
86,44
86,51
86,72
86,93
86,79
86,79
86,8
86,41
86,26
86,19
86,28




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209643&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209643&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209643&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.29930555555560.07467386743994531155.68281802144
Geometric Mean86.2970067425888
Harmonic Mean86.2947029579209
Quadratic Mean86.3015993398217
Winsorized Mean ( 1 / 24 )86.30166666666670.07393717461667931167.2297070329
Winsorized Mean ( 2 / 24 )86.30194444444450.07387593724369341168.20100921037
Winsorized Mean ( 3 / 24 )86.30111111111110.07373305368963681170.45350480636
Winsorized Mean ( 4 / 24 )86.29944444444440.07345404301604181174.87671067469
Winsorized Mean ( 5 / 24 )86.29388888888890.0725716837229671189.08483945756
Winsorized Mean ( 6 / 24 )86.30388888888890.06953105709849791241.22791296889
Winsorized Mean ( 7 / 24 )86.30972222222220.06802977698350171268.70505900899
Winsorized Mean ( 8 / 24 )86.31750.06434111400563961341.56054544586
Winsorized Mean ( 9 / 24 )86.32250.06345945867361821360.27791292658
Winsorized Mean ( 10 / 24 )86.32250.06345945867361821360.27791292658
Winsorized Mean ( 11 / 24 )86.32402777777780.06222738973274391387.23523754612
Winsorized Mean ( 12 / 24 )86.32402777777780.06118504339540991410.8681303028
Winsorized Mean ( 13 / 24 )86.32402777777780.06062554058040241423.88879260043
Winsorized Mean ( 14 / 24 )86.32013888888890.06008291514494281436.68360099792
Winsorized Mean ( 15 / 24 )86.31180555555560.05832036287352711479.96002258646
Winsorized Mean ( 16 / 24 )86.316250.05690348110592011516.88874428141
Winsorized Mean ( 17 / 24 )86.316250.05619781094846171535.93616091487
Winsorized Mean ( 18 / 24 )86.313750.05512875720431231565.67559976209
Winsorized Mean ( 19 / 24 )86.34541666666670.04995417990503221728.4923269848
Winsorized Mean ( 20 / 24 )86.34819444444440.04788946518739381803.07284924899
Winsorized Mean ( 21 / 24 )86.37152777777780.04340895339476321989.71689071401
Winsorized Mean ( 22 / 24 )86.40208333333330.03883773952918882224.69392865662
Winsorized Mean ( 23 / 24 )86.43083333333330.02847297128676113035.53965137178
Winsorized Mean ( 24 / 24 )86.41750.02385545117705253622.54728944839
Trimmed Mean ( 1 / 24 )86.30528571428570.07304433590220561181.54658603282
Trimmed Mean ( 2 / 24 )86.30911764705880.07196133951760191199.38175450371
Trimmed Mean ( 3 / 24 )86.31303030303030.07068890764606831221.02651147462
Trimmed Mean ( 4 / 24 )86.31750.06921075760497031247.16883598744
Trimmed Mean ( 5 / 24 )86.32274193548390.06751468076043091278.57735477994
Trimmed Mean ( 6 / 24 )86.32966666666670.06571551711892071313.68770195389
Trimmed Mean ( 7 / 24 )86.3350.06438984882401071340.81693895523
Trimmed Mean ( 8 / 24 )86.33964285714290.06313609516005381367.51635713718
Trimmed Mean ( 9 / 24 )86.34333333333330.06244942048408491382.61224306057
Trimmed Mean ( 10 / 24 )86.34653846153850.06174430599194711398.45346181071
Trimmed Mean ( 11 / 24 )86.350.0608041351977221420.1336754352
Trimmed Mean ( 12 / 24 )86.35354166666670.05983464921556251443.20294008186
Trimmed Mean ( 13 / 24 )86.35739130434780.05876871459156481469.4449573131
Trimmed Mean ( 14 / 24 )86.36159090909090.05746121330096351502.95453137678
Trimmed Mean ( 15 / 24 )86.36666666666670.05581792478976481547.29268406094
Trimmed Mean ( 16 / 24 )86.373250.05399120001895841599.76533156646
Trimmed Mean ( 17 / 24 )86.380.05185602126733711665.76605549197
Trimmed Mean ( 18 / 24 )86.38750.0490729534662911760.38925513911
Trimmed Mean ( 19 / 24 )86.39617647058820.04542729339291261901.85613136413
Trimmed Mean ( 20 / 24 )86.40218750.04206066657078842054.22772733724
Trimmed Mean ( 21 / 24 )86.40866666666670.03782516748170672284.42257944942
Trimmed Mean ( 22 / 24 )86.41321428571430.03333354591768962592.37989558909
Trimmed Mean ( 23 / 24 )86.41461538461540.02848065885814593034.15085356775
Trimmed Mean ( 24 / 24 )86.41250.02585669817628913341.97736349961
Median86.395
Midrange86.09
Midmean - Weighted Average at Xnp86.3675675675676
Midmean - Weighted Average at X(n+1)p86.3875
Midmean - Empirical Distribution Function86.3675675675676
Midmean - Empirical Distribution Function - Averaging86.3875
Midmean - Empirical Distribution Function - Interpolation86.3875
Midmean - Closest Observation86.3675675675676
Midmean - True Basic - Statistics Graphics Toolkit86.3875
Midmean - MS Excel (old versions)86.38
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.2993055555556 & 0.0746738674399453 & 1155.68281802144 \tabularnewline
Geometric Mean & 86.2970067425888 &  &  \tabularnewline
Harmonic Mean & 86.2947029579209 &  &  \tabularnewline
Quadratic Mean & 86.3015993398217 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 86.3016666666667 & 0.0739371746166793 & 1167.2297070329 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 86.3019444444445 & 0.0738759372436934 & 1168.20100921037 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 86.3011111111111 & 0.0737330536896368 & 1170.45350480636 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 86.2994444444444 & 0.0734540430160418 & 1174.87671067469 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 86.2938888888889 & 0.072571683722967 & 1189.08483945756 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 86.3038888888889 & 0.0695310570984979 & 1241.22791296889 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 86.3097222222222 & 0.0680297769835017 & 1268.70505900899 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 86.3175 & 0.0643411140056396 & 1341.56054544586 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 86.3225 & 0.0634594586736182 & 1360.27791292658 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 86.3225 & 0.0634594586736182 & 1360.27791292658 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 86.3240277777778 & 0.0622273897327439 & 1387.23523754612 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 86.3240277777778 & 0.0611850433954099 & 1410.8681303028 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 86.3240277777778 & 0.0606255405804024 & 1423.88879260043 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 86.3201388888889 & 0.0600829151449428 & 1436.68360099792 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 86.3118055555556 & 0.0583203628735271 & 1479.96002258646 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 86.31625 & 0.0569034811059201 & 1516.88874428141 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 86.31625 & 0.0561978109484617 & 1535.93616091487 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 86.31375 & 0.0551287572043123 & 1565.67559976209 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 86.3454166666667 & 0.0499541799050322 & 1728.4923269848 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 86.3481944444444 & 0.0478894651873938 & 1803.07284924899 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 86.3715277777778 & 0.0434089533947632 & 1989.71689071401 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 86.4020833333333 & 0.0388377395291888 & 2224.69392865662 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 86.4308333333333 & 0.0284729712867611 & 3035.53965137178 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 86.4175 & 0.0238554511770525 & 3622.54728944839 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 86.3052857142857 & 0.0730443359022056 & 1181.54658603282 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 86.3091176470588 & 0.0719613395176019 & 1199.38175450371 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 86.3130303030303 & 0.0706889076460683 & 1221.02651147462 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 86.3175 & 0.0692107576049703 & 1247.16883598744 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 86.3227419354839 & 0.0675146807604309 & 1278.57735477994 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 86.3296666666667 & 0.0657155171189207 & 1313.68770195389 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 86.335 & 0.0643898488240107 & 1340.81693895523 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 86.3396428571429 & 0.0631360951600538 & 1367.51635713718 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 86.3433333333333 & 0.0624494204840849 & 1382.61224306057 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 86.3465384615385 & 0.0617443059919471 & 1398.45346181071 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 86.35 & 0.060804135197722 & 1420.1336754352 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 86.3535416666667 & 0.0598346492155625 & 1443.20294008186 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 86.3573913043478 & 0.0587687145915648 & 1469.4449573131 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 86.3615909090909 & 0.0574612133009635 & 1502.95453137678 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 86.3666666666667 & 0.0558179247897648 & 1547.29268406094 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 86.37325 & 0.0539912000189584 & 1599.76533156646 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 86.38 & 0.0518560212673371 & 1665.76605549197 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 86.3875 & 0.049072953466291 & 1760.38925513911 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 86.3961764705882 & 0.0454272933929126 & 1901.85613136413 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 86.4021875 & 0.0420606665707884 & 2054.22772733724 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 86.4086666666667 & 0.0378251674817067 & 2284.42257944942 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 86.4132142857143 & 0.0333335459176896 & 2592.37989558909 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 86.4146153846154 & 0.0284806588581459 & 3034.15085356775 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 86.4125 & 0.0258566981762891 & 3341.97736349961 \tabularnewline
Median & 86.395 &  &  \tabularnewline
Midrange & 86.09 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 86.3675675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 86.3875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 86.3675675675676 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 86.3875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 86.3875 &  &  \tabularnewline
Midmean - Closest Observation & 86.3675675675676 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 86.3875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.38 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209643&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]86.2993055555556[/C][C]0.0746738674399453[/C][C]1155.68281802144[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.2970067425888[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.2947029579209[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]86.3015993398217[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]86.3016666666667[/C][C]0.0739371746166793[/C][C]1167.2297070329[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]86.3019444444445[/C][C]0.0738759372436934[/C][C]1168.20100921037[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]86.3011111111111[/C][C]0.0737330536896368[/C][C]1170.45350480636[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]86.2994444444444[/C][C]0.0734540430160418[/C][C]1174.87671067469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]86.2938888888889[/C][C]0.072571683722967[/C][C]1189.08483945756[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]86.3038888888889[/C][C]0.0695310570984979[/C][C]1241.22791296889[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]86.3097222222222[/C][C]0.0680297769835017[/C][C]1268.70505900899[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]86.3175[/C][C]0.0643411140056396[/C][C]1341.56054544586[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]86.3225[/C][C]0.0634594586736182[/C][C]1360.27791292658[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]86.3225[/C][C]0.0634594586736182[/C][C]1360.27791292658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]86.3240277777778[/C][C]0.0622273897327439[/C][C]1387.23523754612[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]86.3240277777778[/C][C]0.0611850433954099[/C][C]1410.8681303028[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]86.3240277777778[/C][C]0.0606255405804024[/C][C]1423.88879260043[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]86.3201388888889[/C][C]0.0600829151449428[/C][C]1436.68360099792[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]86.3118055555556[/C][C]0.0583203628735271[/C][C]1479.96002258646[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]86.31625[/C][C]0.0569034811059201[/C][C]1516.88874428141[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]86.31625[/C][C]0.0561978109484617[/C][C]1535.93616091487[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]86.31375[/C][C]0.0551287572043123[/C][C]1565.67559976209[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]86.3454166666667[/C][C]0.0499541799050322[/C][C]1728.4923269848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]86.3481944444444[/C][C]0.0478894651873938[/C][C]1803.07284924899[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]86.3715277777778[/C][C]0.0434089533947632[/C][C]1989.71689071401[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]86.4020833333333[/C][C]0.0388377395291888[/C][C]2224.69392865662[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]86.4308333333333[/C][C]0.0284729712867611[/C][C]3035.53965137178[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]86.4175[/C][C]0.0238554511770525[/C][C]3622.54728944839[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]86.3052857142857[/C][C]0.0730443359022056[/C][C]1181.54658603282[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]86.3091176470588[/C][C]0.0719613395176019[/C][C]1199.38175450371[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]86.3130303030303[/C][C]0.0706889076460683[/C][C]1221.02651147462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]86.3175[/C][C]0.0692107576049703[/C][C]1247.16883598744[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]86.3227419354839[/C][C]0.0675146807604309[/C][C]1278.57735477994[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]86.3296666666667[/C][C]0.0657155171189207[/C][C]1313.68770195389[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]86.335[/C][C]0.0643898488240107[/C][C]1340.81693895523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]86.3396428571429[/C][C]0.0631360951600538[/C][C]1367.51635713718[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]86.3433333333333[/C][C]0.0624494204840849[/C][C]1382.61224306057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]86.3465384615385[/C][C]0.0617443059919471[/C][C]1398.45346181071[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]86.35[/C][C]0.060804135197722[/C][C]1420.1336754352[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]86.3535416666667[/C][C]0.0598346492155625[/C][C]1443.20294008186[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]86.3573913043478[/C][C]0.0587687145915648[/C][C]1469.4449573131[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]86.3615909090909[/C][C]0.0574612133009635[/C][C]1502.95453137678[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]86.3666666666667[/C][C]0.0558179247897648[/C][C]1547.29268406094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]86.37325[/C][C]0.0539912000189584[/C][C]1599.76533156646[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]86.38[/C][C]0.0518560212673371[/C][C]1665.76605549197[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]86.3875[/C][C]0.049072953466291[/C][C]1760.38925513911[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]86.3961764705882[/C][C]0.0454272933929126[/C][C]1901.85613136413[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]86.4021875[/C][C]0.0420606665707884[/C][C]2054.22772733724[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]86.4086666666667[/C][C]0.0378251674817067[/C][C]2284.42257944942[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]86.4132142857143[/C][C]0.0333335459176896[/C][C]2592.37989558909[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]86.4146153846154[/C][C]0.0284806588581459[/C][C]3034.15085356775[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]86.4125[/C][C]0.0258566981762891[/C][C]3341.97736349961[/C][/ROW]
[ROW][C]Median[/C][C]86.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]86.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]86.3675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]86.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]86.3675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]86.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]86.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.3675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]86.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.38[/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=209643&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209643&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 Mean86.29930555555560.07467386743994531155.68281802144
Geometric Mean86.2970067425888
Harmonic Mean86.2947029579209
Quadratic Mean86.3015993398217
Winsorized Mean ( 1 / 24 )86.30166666666670.07393717461667931167.2297070329
Winsorized Mean ( 2 / 24 )86.30194444444450.07387593724369341168.20100921037
Winsorized Mean ( 3 / 24 )86.30111111111110.07373305368963681170.45350480636
Winsorized Mean ( 4 / 24 )86.29944444444440.07345404301604181174.87671067469
Winsorized Mean ( 5 / 24 )86.29388888888890.0725716837229671189.08483945756
Winsorized Mean ( 6 / 24 )86.30388888888890.06953105709849791241.22791296889
Winsorized Mean ( 7 / 24 )86.30972222222220.06802977698350171268.70505900899
Winsorized Mean ( 8 / 24 )86.31750.06434111400563961341.56054544586
Winsorized Mean ( 9 / 24 )86.32250.06345945867361821360.27791292658
Winsorized Mean ( 10 / 24 )86.32250.06345945867361821360.27791292658
Winsorized Mean ( 11 / 24 )86.32402777777780.06222738973274391387.23523754612
Winsorized Mean ( 12 / 24 )86.32402777777780.06118504339540991410.8681303028
Winsorized Mean ( 13 / 24 )86.32402777777780.06062554058040241423.88879260043
Winsorized Mean ( 14 / 24 )86.32013888888890.06008291514494281436.68360099792
Winsorized Mean ( 15 / 24 )86.31180555555560.05832036287352711479.96002258646
Winsorized Mean ( 16 / 24 )86.316250.05690348110592011516.88874428141
Winsorized Mean ( 17 / 24 )86.316250.05619781094846171535.93616091487
Winsorized Mean ( 18 / 24 )86.313750.05512875720431231565.67559976209
Winsorized Mean ( 19 / 24 )86.34541666666670.04995417990503221728.4923269848
Winsorized Mean ( 20 / 24 )86.34819444444440.04788946518739381803.07284924899
Winsorized Mean ( 21 / 24 )86.37152777777780.04340895339476321989.71689071401
Winsorized Mean ( 22 / 24 )86.40208333333330.03883773952918882224.69392865662
Winsorized Mean ( 23 / 24 )86.43083333333330.02847297128676113035.53965137178
Winsorized Mean ( 24 / 24 )86.41750.02385545117705253622.54728944839
Trimmed Mean ( 1 / 24 )86.30528571428570.07304433590220561181.54658603282
Trimmed Mean ( 2 / 24 )86.30911764705880.07196133951760191199.38175450371
Trimmed Mean ( 3 / 24 )86.31303030303030.07068890764606831221.02651147462
Trimmed Mean ( 4 / 24 )86.31750.06921075760497031247.16883598744
Trimmed Mean ( 5 / 24 )86.32274193548390.06751468076043091278.57735477994
Trimmed Mean ( 6 / 24 )86.32966666666670.06571551711892071313.68770195389
Trimmed Mean ( 7 / 24 )86.3350.06438984882401071340.81693895523
Trimmed Mean ( 8 / 24 )86.33964285714290.06313609516005381367.51635713718
Trimmed Mean ( 9 / 24 )86.34333333333330.06244942048408491382.61224306057
Trimmed Mean ( 10 / 24 )86.34653846153850.06174430599194711398.45346181071
Trimmed Mean ( 11 / 24 )86.350.0608041351977221420.1336754352
Trimmed Mean ( 12 / 24 )86.35354166666670.05983464921556251443.20294008186
Trimmed Mean ( 13 / 24 )86.35739130434780.05876871459156481469.4449573131
Trimmed Mean ( 14 / 24 )86.36159090909090.05746121330096351502.95453137678
Trimmed Mean ( 15 / 24 )86.36666666666670.05581792478976481547.29268406094
Trimmed Mean ( 16 / 24 )86.373250.05399120001895841599.76533156646
Trimmed Mean ( 17 / 24 )86.380.05185602126733711665.76605549197
Trimmed Mean ( 18 / 24 )86.38750.0490729534662911760.38925513911
Trimmed Mean ( 19 / 24 )86.39617647058820.04542729339291261901.85613136413
Trimmed Mean ( 20 / 24 )86.40218750.04206066657078842054.22772733724
Trimmed Mean ( 21 / 24 )86.40866666666670.03782516748170672284.42257944942
Trimmed Mean ( 22 / 24 )86.41321428571430.03333354591768962592.37989558909
Trimmed Mean ( 23 / 24 )86.41461538461540.02848065885814593034.15085356775
Trimmed Mean ( 24 / 24 )86.41250.02585669817628913341.97736349961
Median86.395
Midrange86.09
Midmean - Weighted Average at Xnp86.3675675675676
Midmean - Weighted Average at X(n+1)p86.3875
Midmean - Empirical Distribution Function86.3675675675676
Midmean - Empirical Distribution Function - Averaging86.3875
Midmean - Empirical Distribution Function - Interpolation86.3875
Midmean - Closest Observation86.3675675675676
Midmean - True Basic - Statistics Graphics Toolkit86.3875
Midmean - MS Excel (old versions)86.38
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')