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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 10 Dec 2008 05:16:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t12289115162r867tl3rsbcijr.htm/, Retrieved Sat, 25 May 2024 20:23:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31917, Retrieved Sat, 25 May 2024 20:23:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-10 12:16:30] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]
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Dataseries X:
97,7
101,5
119,6
108,1
117,8
125,5
89,2
92,3
104,6
122,8
96,0
94,6
93,3
101,1
114,2
104,7
113,3
118,2
83,6
73,9
99,5
97,7
103,0
106,3
92,2
101,8
122,8
111,8
106,3
121,5
81,9
85,4
110,9
117,3
106,3
105,5
101,3
105,9
126,3
111,9
108,9
127,2
94,2
85,7
116,2
107,2
110,6
112,0
104,5
112,0
132,8
110,8
128,7
136,8
94,9
88,8
123,2
125,3
122,7
125,7
116,3
118,7
142,0
127,9
131,9
152,3
110,8
99,1
135,0
133,2
131,0
133,9
119,9
136,9
148,9
145,1
142,4
159,6
120,7
109,0
142,0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31917&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31917&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.7333333333331.9545562471969958.1888259784987
Geometric Mean112.388228869872
Harmonic Mean111.038385072555
Quadratic Mean115.069084992398
Winsorized Mean ( 1 / 27 )113.7419753086421.9070118052337959.644085577487
Winsorized Mean ( 2 / 27 )113.71.8779758278200960.543910265331
Winsorized Mean ( 3 / 27 )113.6259259259261.8332733809875761.9798045966918
Winsorized Mean ( 4 / 27 )113.5074074074071.8027489107240162.9635146260171
Winsorized Mean ( 5 / 27 )113.6740740740741.7624502250022364.4977500422345
Winsorized Mean ( 6 / 27 )113.7037037037041.7572543156204864.7053205065286
Winsorized Mean ( 7 / 27 )113.5222222222221.6293394101844669.6737717829891
Winsorized Mean ( 8 / 27 )113.5222222222221.6259565086130869.818732309793
Winsorized Mean ( 9 / 27 )113.4333333333331.5729542857900272.1148315358455
Winsorized Mean ( 10 / 27 )113.4086419753091.5323670440894174.008797313114
Winsorized Mean ( 11 / 27 )113.3679012345681.5081269831844275.1713234353722
Winsorized Mean ( 12 / 27 )113.3530864197531.491533809953375.9976647282988
Winsorized Mean ( 13 / 27 )113.3851851851851.4411951820666378.6744131510308
Winsorized Mean ( 14 / 27 )113.5234567901231.3729859228920382.6836276303546
Winsorized Mean ( 15 / 27 )113.0975308641981.3072777946687886.5137703137169
Winsorized Mean ( 16 / 27 )113.2160493827161.2438359831810491.0216868731942
Winsorized Mean ( 17 / 27 )113.1530864197531.2104650244305393.4790218106354
Winsorized Mean ( 18 / 27 )113.3086419753091.13255855533747100.046608134575
Winsorized Mean ( 19 / 27 )113.2148148148151.10621994429578102.343856118855
Winsorized Mean ( 20 / 27 )113.2148148148151.09263261069212103.616543847341
Winsorized Mean ( 21 / 27 )113.2407407407411.07496738075371105.343420431364
Winsorized Mean ( 22 / 27 )112.9962962962960.95367295887157118.485373046541
Winsorized Mean ( 23 / 27 )113.3086419753090.883974605681816128.180879006035
Winsorized Mean ( 24 / 27 )113.3382716049380.88029100109495128.750914713387
Winsorized Mean ( 25 / 27 )113.3382716049380.872322301231622129.927059579833
Winsorized Mean ( 26 / 27 )113.2098765432100.789607663434924143.374845237353
Winsorized Mean ( 27 / 27 )113.0765432098770.738663857973957153.082544907542
Trimmed Mean ( 1 / 27 )113.6569620253161.8489088017100561.472454412135
Trimmed Mean ( 2 / 27 )113.5675324675321.7809929507141963.7664132370602
Trimmed Mean ( 3 / 27 )113.4961.7198024608961665.9936257684262
Trimmed Mean ( 4 / 27 )113.4479452054791.6682060352095668.0059553862172
Trimmed Mean ( 5 / 27 )113.4309859154931.6184792916507170.0849164401744
Trimmed Mean ( 6 / 27 )113.3739130434781.5720608540891772.1180180452784
Trimmed Mean ( 7 / 27 )113.3074626865671.5181374622500174.6358386536589
Trimmed Mean ( 8 / 27 )113.2692307692311.4862622890041976.2107950980322
Trimmed Mean ( 9 / 27 )113.2285714285711.4485394034459478.1674086042886
Trimmed Mean ( 10 / 27 )113.1983606557381.4146607305398680.018027087342
Trimmed Mean ( 11 / 27 )113.1694915254241.3819286496548781.8924273360187
Trimmed Mean ( 12 / 27 )113.1438596491231.3466984076444284.0157373075305
Trimmed Mean ( 13 / 27 )113.1181818181821.3065184695106086.5798566632998
Trimmed Mean ( 14 / 27 )113.0867924528301.2669633814694189.2581380857857
Trimmed Mean ( 15 / 27 )113.0372549019611.2313167216019591.8019327755888
Trimmed Mean ( 16 / 27 )113.0306122448981.1997739444166094.2099241035447
Trimmed Mean ( 17 / 27 )113.0106382978721.1721452381117596.4135114176847
Trimmed Mean ( 18 / 27 )112.9955555555561.142949204645498.863147282746
Trimmed Mean ( 19 / 27 )112.9627906976741.12062622530026100.80327244475
Trimmed Mean ( 20 / 27 )112.9365853658541.09591679015602103.052153576163
Trimmed Mean ( 21 / 27 )112.9076923076921.06503365602535106.013262274788
Trimmed Mean ( 22 / 27 )112.8729729729731.02668340229024109.939415326268
Trimmed Mean ( 23 / 27 )112.861.00415272198786112.393262029483
Trimmed Mean ( 24 / 27 )112.8121212121210.988156739573791114.164197534876
Trimmed Mean ( 25 / 27 )112.7548387096770.963772144463968116.993253392263
Trimmed Mean ( 26 / 27 )112.6896551724140.928428207585301121.376811100454
Trimmed Mean ( 27 / 27 )112.6296296296300.901499460219112124.935881383950
Median111.9
Midrange116.75
Midmean - Weighted Average at Xnp112.6225
Midmean - Weighted Average at X(n+1)p112.936585365854
Midmean - Empirical Distribution Function112.936585365854
Midmean - Empirical Distribution Function - Averaging112.936585365854
Midmean - Empirical Distribution Function - Interpolation112.936585365854
Midmean - Closest Observation112.659523809524
Midmean - True Basic - Statistics Graphics Toolkit112.936585365854
Midmean - MS Excel (old versions)112.936585365854
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.733333333333 & 1.95455624719699 & 58.1888259784987 \tabularnewline
Geometric Mean & 112.388228869872 &  &  \tabularnewline
Harmonic Mean & 111.038385072555 &  &  \tabularnewline
Quadratic Mean & 115.069084992398 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 113.741975308642 & 1.90701180523379 & 59.644085577487 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 113.7 & 1.87797582782009 & 60.543910265331 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 113.625925925926 & 1.83327338098757 & 61.9798045966918 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 113.507407407407 & 1.80274891072401 & 62.9635146260171 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 113.674074074074 & 1.76245022500223 & 64.4977500422345 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 113.703703703704 & 1.75725431562048 & 64.7053205065286 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 113.522222222222 & 1.62933941018446 & 69.6737717829891 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 113.522222222222 & 1.62595650861308 & 69.818732309793 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 113.433333333333 & 1.57295428579002 & 72.1148315358455 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 113.408641975309 & 1.53236704408941 & 74.008797313114 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 113.367901234568 & 1.50812698318442 & 75.1713234353722 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 113.353086419753 & 1.4915338099533 & 75.9976647282988 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 113.385185185185 & 1.44119518206663 & 78.6744131510308 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 113.523456790123 & 1.37298592289203 & 82.6836276303546 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 113.097530864198 & 1.30727779466878 & 86.5137703137169 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 113.216049382716 & 1.24383598318104 & 91.0216868731942 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 113.153086419753 & 1.21046502443053 & 93.4790218106354 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 113.308641975309 & 1.13255855533747 & 100.046608134575 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 113.214814814815 & 1.10621994429578 & 102.343856118855 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 113.214814814815 & 1.09263261069212 & 103.616543847341 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 113.240740740741 & 1.07496738075371 & 105.343420431364 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 112.996296296296 & 0.95367295887157 & 118.485373046541 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 113.308641975309 & 0.883974605681816 & 128.180879006035 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 113.338271604938 & 0.88029100109495 & 128.750914713387 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 113.338271604938 & 0.872322301231622 & 129.927059579833 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 113.209876543210 & 0.789607663434924 & 143.374845237353 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 113.076543209877 & 0.738663857973957 & 153.082544907542 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 113.656962025316 & 1.84890880171005 & 61.472454412135 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 113.567532467532 & 1.78099295071419 & 63.7664132370602 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 113.496 & 1.71980246089616 & 65.9936257684262 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 113.447945205479 & 1.66820603520956 & 68.0059553862172 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 113.430985915493 & 1.61847929165071 & 70.0849164401744 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 113.373913043478 & 1.57206085408917 & 72.1180180452784 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 113.307462686567 & 1.51813746225001 & 74.6358386536589 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 113.269230769231 & 1.48626228900419 & 76.2107950980322 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 113.228571428571 & 1.44853940344594 & 78.1674086042886 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 113.198360655738 & 1.41466073053986 & 80.018027087342 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 113.169491525424 & 1.38192864965487 & 81.8924273360187 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 113.143859649123 & 1.34669840764442 & 84.0157373075305 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 113.118181818182 & 1.30651846951060 & 86.5798566632998 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 113.086792452830 & 1.26696338146941 & 89.2581380857857 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 113.037254901961 & 1.23131672160195 & 91.8019327755888 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 113.030612244898 & 1.19977394441660 & 94.2099241035447 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 113.010638297872 & 1.17214523811175 & 96.4135114176847 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 112.995555555556 & 1.1429492046454 & 98.863147282746 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 112.962790697674 & 1.12062622530026 & 100.80327244475 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 112.936585365854 & 1.09591679015602 & 103.052153576163 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 112.907692307692 & 1.06503365602535 & 106.013262274788 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 112.872972972973 & 1.02668340229024 & 109.939415326268 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 112.86 & 1.00415272198786 & 112.393262029483 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 112.812121212121 & 0.988156739573791 & 114.164197534876 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 112.754838709677 & 0.963772144463968 & 116.993253392263 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 112.689655172414 & 0.928428207585301 & 121.376811100454 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 112.629629629630 & 0.901499460219112 & 124.935881383950 \tabularnewline
Median & 111.9 &  &  \tabularnewline
Midrange & 116.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.6225 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.936585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.936585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.936585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.936585365854 &  &  \tabularnewline
Midmean - Closest Observation & 112.659523809524 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.936585365854 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.936585365854 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31917&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]113.733333333333[/C][C]1.95455624719699[/C][C]58.1888259784987[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.388228869872[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.038385072555[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.069084992398[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]113.741975308642[/C][C]1.90701180523379[/C][C]59.644085577487[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]113.7[/C][C]1.87797582782009[/C][C]60.543910265331[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]113.625925925926[/C][C]1.83327338098757[/C][C]61.9798045966918[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]113.507407407407[/C][C]1.80274891072401[/C][C]62.9635146260171[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]113.674074074074[/C][C]1.76245022500223[/C][C]64.4977500422345[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]113.703703703704[/C][C]1.75725431562048[/C][C]64.7053205065286[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]113.522222222222[/C][C]1.62933941018446[/C][C]69.6737717829891[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]113.522222222222[/C][C]1.62595650861308[/C][C]69.818732309793[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]113.433333333333[/C][C]1.57295428579002[/C][C]72.1148315358455[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]113.408641975309[/C][C]1.53236704408941[/C][C]74.008797313114[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]113.367901234568[/C][C]1.50812698318442[/C][C]75.1713234353722[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]113.353086419753[/C][C]1.4915338099533[/C][C]75.9976647282988[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]113.385185185185[/C][C]1.44119518206663[/C][C]78.6744131510308[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]113.523456790123[/C][C]1.37298592289203[/C][C]82.6836276303546[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]113.097530864198[/C][C]1.30727779466878[/C][C]86.5137703137169[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]113.216049382716[/C][C]1.24383598318104[/C][C]91.0216868731942[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]113.153086419753[/C][C]1.21046502443053[/C][C]93.4790218106354[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]113.308641975309[/C][C]1.13255855533747[/C][C]100.046608134575[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]113.214814814815[/C][C]1.10621994429578[/C][C]102.343856118855[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]113.214814814815[/C][C]1.09263261069212[/C][C]103.616543847341[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]113.240740740741[/C][C]1.07496738075371[/C][C]105.343420431364[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]112.996296296296[/C][C]0.95367295887157[/C][C]118.485373046541[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]113.308641975309[/C][C]0.883974605681816[/C][C]128.180879006035[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]113.338271604938[/C][C]0.88029100109495[/C][C]128.750914713387[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]113.338271604938[/C][C]0.872322301231622[/C][C]129.927059579833[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]113.209876543210[/C][C]0.789607663434924[/C][C]143.374845237353[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]113.076543209877[/C][C]0.738663857973957[/C][C]153.082544907542[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]113.656962025316[/C][C]1.84890880171005[/C][C]61.472454412135[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]113.567532467532[/C][C]1.78099295071419[/C][C]63.7664132370602[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]113.496[/C][C]1.71980246089616[/C][C]65.9936257684262[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]113.447945205479[/C][C]1.66820603520956[/C][C]68.0059553862172[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]113.430985915493[/C][C]1.61847929165071[/C][C]70.0849164401744[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]113.373913043478[/C][C]1.57206085408917[/C][C]72.1180180452784[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]113.307462686567[/C][C]1.51813746225001[/C][C]74.6358386536589[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]113.269230769231[/C][C]1.48626228900419[/C][C]76.2107950980322[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]113.228571428571[/C][C]1.44853940344594[/C][C]78.1674086042886[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]113.198360655738[/C][C]1.41466073053986[/C][C]80.018027087342[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]113.169491525424[/C][C]1.38192864965487[/C][C]81.8924273360187[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]113.143859649123[/C][C]1.34669840764442[/C][C]84.0157373075305[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]113.118181818182[/C][C]1.30651846951060[/C][C]86.5798566632998[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]113.086792452830[/C][C]1.26696338146941[/C][C]89.2581380857857[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]113.037254901961[/C][C]1.23131672160195[/C][C]91.8019327755888[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]113.030612244898[/C][C]1.19977394441660[/C][C]94.2099241035447[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]113.010638297872[/C][C]1.17214523811175[/C][C]96.4135114176847[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]112.995555555556[/C][C]1.1429492046454[/C][C]98.863147282746[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]112.962790697674[/C][C]1.12062622530026[/C][C]100.80327244475[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]112.936585365854[/C][C]1.09591679015602[/C][C]103.052153576163[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]112.907692307692[/C][C]1.06503365602535[/C][C]106.013262274788[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]112.872972972973[/C][C]1.02668340229024[/C][C]109.939415326268[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]112.86[/C][C]1.00415272198786[/C][C]112.393262029483[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]112.812121212121[/C][C]0.988156739573791[/C][C]114.164197534876[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]112.754838709677[/C][C]0.963772144463968[/C][C]116.993253392263[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]112.689655172414[/C][C]0.928428207585301[/C][C]121.376811100454[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]112.629629629630[/C][C]0.901499460219112[/C][C]124.935881383950[/C][/ROW]
[ROW][C]Median[/C][C]111.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]116.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.6225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.659523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.936585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31917&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 Mean113.7333333333331.9545562471969958.1888259784987
Geometric Mean112.388228869872
Harmonic Mean111.038385072555
Quadratic Mean115.069084992398
Winsorized Mean ( 1 / 27 )113.7419753086421.9070118052337959.644085577487
Winsorized Mean ( 2 / 27 )113.71.8779758278200960.543910265331
Winsorized Mean ( 3 / 27 )113.6259259259261.8332733809875761.9798045966918
Winsorized Mean ( 4 / 27 )113.5074074074071.8027489107240162.9635146260171
Winsorized Mean ( 5 / 27 )113.6740740740741.7624502250022364.4977500422345
Winsorized Mean ( 6 / 27 )113.7037037037041.7572543156204864.7053205065286
Winsorized Mean ( 7 / 27 )113.5222222222221.6293394101844669.6737717829891
Winsorized Mean ( 8 / 27 )113.5222222222221.6259565086130869.818732309793
Winsorized Mean ( 9 / 27 )113.4333333333331.5729542857900272.1148315358455
Winsorized Mean ( 10 / 27 )113.4086419753091.5323670440894174.008797313114
Winsorized Mean ( 11 / 27 )113.3679012345681.5081269831844275.1713234353722
Winsorized Mean ( 12 / 27 )113.3530864197531.491533809953375.9976647282988
Winsorized Mean ( 13 / 27 )113.3851851851851.4411951820666378.6744131510308
Winsorized Mean ( 14 / 27 )113.5234567901231.3729859228920382.6836276303546
Winsorized Mean ( 15 / 27 )113.0975308641981.3072777946687886.5137703137169
Winsorized Mean ( 16 / 27 )113.2160493827161.2438359831810491.0216868731942
Winsorized Mean ( 17 / 27 )113.1530864197531.2104650244305393.4790218106354
Winsorized Mean ( 18 / 27 )113.3086419753091.13255855533747100.046608134575
Winsorized Mean ( 19 / 27 )113.2148148148151.10621994429578102.343856118855
Winsorized Mean ( 20 / 27 )113.2148148148151.09263261069212103.616543847341
Winsorized Mean ( 21 / 27 )113.2407407407411.07496738075371105.343420431364
Winsorized Mean ( 22 / 27 )112.9962962962960.95367295887157118.485373046541
Winsorized Mean ( 23 / 27 )113.3086419753090.883974605681816128.180879006035
Winsorized Mean ( 24 / 27 )113.3382716049380.88029100109495128.750914713387
Winsorized Mean ( 25 / 27 )113.3382716049380.872322301231622129.927059579833
Winsorized Mean ( 26 / 27 )113.2098765432100.789607663434924143.374845237353
Winsorized Mean ( 27 / 27 )113.0765432098770.738663857973957153.082544907542
Trimmed Mean ( 1 / 27 )113.6569620253161.8489088017100561.472454412135
Trimmed Mean ( 2 / 27 )113.5675324675321.7809929507141963.7664132370602
Trimmed Mean ( 3 / 27 )113.4961.7198024608961665.9936257684262
Trimmed Mean ( 4 / 27 )113.4479452054791.6682060352095668.0059553862172
Trimmed Mean ( 5 / 27 )113.4309859154931.6184792916507170.0849164401744
Trimmed Mean ( 6 / 27 )113.3739130434781.5720608540891772.1180180452784
Trimmed Mean ( 7 / 27 )113.3074626865671.5181374622500174.6358386536589
Trimmed Mean ( 8 / 27 )113.2692307692311.4862622890041976.2107950980322
Trimmed Mean ( 9 / 27 )113.2285714285711.4485394034459478.1674086042886
Trimmed Mean ( 10 / 27 )113.1983606557381.4146607305398680.018027087342
Trimmed Mean ( 11 / 27 )113.1694915254241.3819286496548781.8924273360187
Trimmed Mean ( 12 / 27 )113.1438596491231.3466984076444284.0157373075305
Trimmed Mean ( 13 / 27 )113.1181818181821.3065184695106086.5798566632998
Trimmed Mean ( 14 / 27 )113.0867924528301.2669633814694189.2581380857857
Trimmed Mean ( 15 / 27 )113.0372549019611.2313167216019591.8019327755888
Trimmed Mean ( 16 / 27 )113.0306122448981.1997739444166094.2099241035447
Trimmed Mean ( 17 / 27 )113.0106382978721.1721452381117596.4135114176847
Trimmed Mean ( 18 / 27 )112.9955555555561.142949204645498.863147282746
Trimmed Mean ( 19 / 27 )112.9627906976741.12062622530026100.80327244475
Trimmed Mean ( 20 / 27 )112.9365853658541.09591679015602103.052153576163
Trimmed Mean ( 21 / 27 )112.9076923076921.06503365602535106.013262274788
Trimmed Mean ( 22 / 27 )112.8729729729731.02668340229024109.939415326268
Trimmed Mean ( 23 / 27 )112.861.00415272198786112.393262029483
Trimmed Mean ( 24 / 27 )112.8121212121210.988156739573791114.164197534876
Trimmed Mean ( 25 / 27 )112.7548387096770.963772144463968116.993253392263
Trimmed Mean ( 26 / 27 )112.6896551724140.928428207585301121.376811100454
Trimmed Mean ( 27 / 27 )112.6296296296300.901499460219112124.935881383950
Median111.9
Midrange116.75
Midmean - Weighted Average at Xnp112.6225
Midmean - Weighted Average at X(n+1)p112.936585365854
Midmean - Empirical Distribution Function112.936585365854
Midmean - Empirical Distribution Function - Averaging112.936585365854
Midmean - Empirical Distribution Function - Interpolation112.936585365854
Midmean - Closest Observation112.659523809524
Midmean - True Basic - Statistics Graphics Toolkit112.936585365854
Midmean - MS Excel (old versions)112.936585365854
Number of observations81



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')