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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 20 Oct 2010 14:47:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t1287585990dkgeip4mmi4bzva.htm/, Retrieved Fri, 03 May 2024 16:43:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87224, Retrieved Fri, 03 May 2024 16:43:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [KDGP1W52] [2010-10-20 14:47:13] [d83d17ce80f1d5ae1d2c83db1cba10f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
75,9
76,9
77,9
78,9
79,9
80,9
81,9
82,9
83,9
84,9
85,9
86,9
87,9
88,9
89,9
90,9
91,9
92,9
93,9
94,9
95,9
96,9
97,9
98,9
99,9
100,9
101,9
102,9
103,9
104,9
105,9
106,9
107,9
108,9
109,9
110,9
111,9
112,9
113,9
114,9
115,9
116,9
117,9
118,9
119,9
120,9
121,9
122,9
123,9
124,9
125,9
126,9
127,9
128,9
129,9
130,9
131,9
132,9
133,9
134,9
135,9
136,9
137,9
138,9
139,9
140,9
141,9
142,9
143,9
144,9
145,9
146,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87224&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87224&T=0

As an alternative you can also use a QR Code:  
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'RServer@AstonUniversity' @ vre.aston.ac.uk






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.42.4664414311581245.1662863722216
Geometric Mean109.415384433464
Harmonic Mean107.408614555839
Quadratic Mean113.322004335728
Winsorized Mean ( 1 / 24 )111.42.4608833356870645.2682979255893
Winsorized Mean ( 2 / 24 )111.42.4500487044438745.4684838705222
Winsorized Mean ( 3 / 24 )111.42.434188543522245.76473761511
Winsorized Mean ( 4 / 24 )111.42.4135279925644246.1564980158509
Winsorized Mean ( 5 / 24 )111.42.3882701094737946.6446402180802
Winsorized Mean ( 6 / 24 )111.42.358598958149447.2314293259108
Winsorized Mean ( 7 / 24 )111.42.3246821513599147.9205296667471
Winsorized Mean ( 8 / 24 )111.42.2866729629390948.7170670251055
Winsorized Mean ( 9 / 24 )111.42.2447120960974549.6277452211688
Winsorized Mean ( 10 / 24 )111.42.1989291745908950.6610223227066
Winsorized Mean ( 11 / 24 )111.42.1494440086138351.8273560760681
Winsorized Mean ( 12 / 24 )111.42.0963676761221653.1395333313222
Winsorized Mean ( 13 / 24 )111.42.0398034518221954.6131049540506
Winsorized Mean ( 14 / 24 )111.41.9798476095701256.2669568412835
Winsorized Mean ( 15 / 24 )111.41.9165901189041658.1240604870146
Winsorized Mean ( 16 / 24 )111.41.8501152525111360.2124650606488
Winsorized Mean ( 17 / 24 )111.41.7805021183439362.5666203102384
Winsorized Mean ( 18 / 24 )111.41.7078251276599365.22916087588
Winsorized Mean ( 19 / 24 )111.41.6321544082958568.2533462727428
Winsorized Mean ( 20 / 24 )111.41.5535561709229771.7064513565784
Winsorized Mean ( 21 / 24 )111.41.4720930347547375.6745649697069
Winsorized Mean ( 22 / 24 )111.41.3878243181426780.2695258641144
Winsorized Mean ( 23 / 24 )111.41.3008062986486885.6391917195714
Winsorized Mean ( 24 / 24 )111.41.2110924464829391.9830689420207
Trimmed Mean ( 1 / 24 )111.42.4324199198877445.7980133648722
Trimmed Mean ( 2 / 24 )111.42.3979157616563646.4570114519163
Trimmed Mean ( 3 / 24 )111.42.362907813126347.1453009639887
Trimmed Mean ( 4 / 24 )111.42.3273733406281647.8651181807957
Trimmed Mean ( 5 / 24 )111.42.2912878474779248.6189459445791
Trimmed Mean ( 6 / 24 )111.42.2546248764114549.4095497506037
Trimmed Mean ( 7 / 24 )111.42.2173557826083550.2400205117091
Trimmed Mean ( 8 / 24 )111.42.1794494717703451.1138255063612
Trimmed Mean ( 9 / 24 )111.42.1408720964441952.0348694277562
Trimmed Mean ( 10 / 24 )111.42.1015867021530853.0075679894008
Trimmed Mean ( 11 / 24 )111.42.0615528128088354.036937258095
Trimmed Mean ( 12 / 24 )111.42.0207259421636955.1287028466208
Trimmed Mean ( 13 / 24 )111.41.9790570145063256.2894344040861
Trimmed Mean ( 14 / 24 )111.41.9364916731037157.5267126356675
Trimmed Mean ( 15 / 24 )111.41.8929694486000958.8493385788047
Trimmed Mean ( 16 / 24 )111.41.8484227510682460.2675983811712
Trimmed Mean ( 17 / 24 )111.41.8027756377319961.7936018594905
Trimmed Mean ( 18 / 24 )111.41.7559422921421263.441720436097
Trimmed Mean ( 19 / 24 )111.41.7078251276599365.22916087588
Trimmed Mean ( 20 / 24 )111.41.658312395177767.1767275719257
Trimmed Mean ( 21 / 24 )111.41.6072751268321669.3098512757816
Trimmed Mean ( 22 / 24 )111.41.554563175514871.6600018285582
Trimmed Mean ( 23 / 24 )111.41.574.2666666666667
Trimmed Mean ( 24 / 24 )111.41.4433756729740677.1801839852692
Median111.4
Midrange111.4
Midmean - Weighted Average at Xnp110.9
Midmean - Weighted Average at X(n+1)p111.4
Midmean - Empirical Distribution Function110.9
Midmean - Empirical Distribution Function - Averaging111.4
Midmean - Empirical Distribution Function - Interpolation111.4
Midmean - Closest Observation110.9
Midmean - True Basic - Statistics Graphics Toolkit111.4
Midmean - MS Excel (old versions)111.4
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.4 & 2.46644143115812 & 45.1662863722216 \tabularnewline
Geometric Mean & 109.415384433464 &  &  \tabularnewline
Harmonic Mean & 107.408614555839 &  &  \tabularnewline
Quadratic Mean & 113.322004335728 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 111.4 & 2.46088333568706 & 45.2682979255893 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 111.4 & 2.45004870444387 & 45.4684838705222 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.4 & 2.4341885435222 & 45.76473761511 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 111.4 & 2.41352799256442 & 46.1564980158509 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 111.4 & 2.38827010947379 & 46.6446402180802 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 111.4 & 2.3585989581494 & 47.2314293259108 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 111.4 & 2.32468215135991 & 47.9205296667471 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 111.4 & 2.28667296293909 & 48.7170670251055 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.4 & 2.24471209609745 & 49.6277452211688 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.4 & 2.19892917459089 & 50.6610223227066 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.4 & 2.14944400861383 & 51.8273560760681 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.4 & 2.09636767612216 & 53.1395333313222 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.4 & 2.03980345182219 & 54.6131049540506 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 111.4 & 1.97984760957012 & 56.2669568412835 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.4 & 1.91659011890416 & 58.1240604870146 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.4 & 1.85011525251113 & 60.2124650606488 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.4 & 1.78050211834393 & 62.5666203102384 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.4 & 1.70782512765993 & 65.22916087588 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.4 & 1.63215440829585 & 68.2533462727428 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.4 & 1.55355617092297 & 71.7064513565784 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.4 & 1.47209303475473 & 75.6745649697069 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.4 & 1.38782431814267 & 80.2695258641144 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.4 & 1.30080629864868 & 85.6391917195714 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.4 & 1.21109244648293 & 91.9830689420207 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 111.4 & 2.43241991988774 & 45.7980133648722 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 111.4 & 2.39791576165636 & 46.4570114519163 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 111.4 & 2.3629078131263 & 47.1453009639887 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 111.4 & 2.32737334062816 & 47.8651181807957 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 111.4 & 2.29128784747792 & 48.6189459445791 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 111.4 & 2.25462487641145 & 49.4095497506037 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 111.4 & 2.21735578260835 & 50.2400205117091 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 111.4 & 2.17944947177034 & 51.1138255063612 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 111.4 & 2.14087209644419 & 52.0348694277562 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 111.4 & 2.10158670215308 & 53.0075679894008 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 111.4 & 2.06155281280883 & 54.036937258095 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 111.4 & 2.02072594216369 & 55.1287028466208 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 111.4 & 1.97905701450632 & 56.2894344040861 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 111.4 & 1.93649167310371 & 57.5267126356675 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 111.4 & 1.89296944860009 & 58.8493385788047 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 111.4 & 1.84842275106824 & 60.2675983811712 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.4 & 1.80277563773199 & 61.7936018594905 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.4 & 1.75594229214212 & 63.441720436097 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.4 & 1.70782512765993 & 65.22916087588 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.4 & 1.6583123951777 & 67.1767275719257 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.4 & 1.60727512683216 & 69.3098512757816 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.4 & 1.5545631755148 & 71.6600018285582 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.4 & 1.5 & 74.2666666666667 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.4 & 1.44337567297406 & 77.1801839852692 \tabularnewline
Median & 111.4 &  &  \tabularnewline
Midrange & 111.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.9 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.4 &  &  \tabularnewline
Midmean - Closest Observation & 110.9 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.4 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87224&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]111.4[/C][C]2.46644143115812[/C][C]45.1662863722216[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.415384433464[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.408614555839[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.322004335728[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]111.4[/C][C]2.46088333568706[/C][C]45.2682979255893[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]111.4[/C][C]2.45004870444387[/C][C]45.4684838705222[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.4[/C][C]2.4341885435222[/C][C]45.76473761511[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]111.4[/C][C]2.41352799256442[/C][C]46.1564980158509[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]111.4[/C][C]2.38827010947379[/C][C]46.6446402180802[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]111.4[/C][C]2.3585989581494[/C][C]47.2314293259108[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]111.4[/C][C]2.32468215135991[/C][C]47.9205296667471[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]111.4[/C][C]2.28667296293909[/C][C]48.7170670251055[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.4[/C][C]2.24471209609745[/C][C]49.6277452211688[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.4[/C][C]2.19892917459089[/C][C]50.6610223227066[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.4[/C][C]2.14944400861383[/C][C]51.8273560760681[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.4[/C][C]2.09636767612216[/C][C]53.1395333313222[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.4[/C][C]2.03980345182219[/C][C]54.6131049540506[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]111.4[/C][C]1.97984760957012[/C][C]56.2669568412835[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.4[/C][C]1.91659011890416[/C][C]58.1240604870146[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.4[/C][C]1.85011525251113[/C][C]60.2124650606488[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.4[/C][C]1.78050211834393[/C][C]62.5666203102384[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.4[/C][C]1.70782512765993[/C][C]65.22916087588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.4[/C][C]1.63215440829585[/C][C]68.2533462727428[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.4[/C][C]1.55355617092297[/C][C]71.7064513565784[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.4[/C][C]1.47209303475473[/C][C]75.6745649697069[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.4[/C][C]1.38782431814267[/C][C]80.2695258641144[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.4[/C][C]1.30080629864868[/C][C]85.6391917195714[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.4[/C][C]1.21109244648293[/C][C]91.9830689420207[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]111.4[/C][C]2.43241991988774[/C][C]45.7980133648722[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]111.4[/C][C]2.39791576165636[/C][C]46.4570114519163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]111.4[/C][C]2.3629078131263[/C][C]47.1453009639887[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]111.4[/C][C]2.32737334062816[/C][C]47.8651181807957[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]111.4[/C][C]2.29128784747792[/C][C]48.6189459445791[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]111.4[/C][C]2.25462487641145[/C][C]49.4095497506037[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]111.4[/C][C]2.21735578260835[/C][C]50.2400205117091[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]111.4[/C][C]2.17944947177034[/C][C]51.1138255063612[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]111.4[/C][C]2.14087209644419[/C][C]52.0348694277562[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]111.4[/C][C]2.10158670215308[/C][C]53.0075679894008[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]111.4[/C][C]2.06155281280883[/C][C]54.036937258095[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]111.4[/C][C]2.02072594216369[/C][C]55.1287028466208[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]111.4[/C][C]1.97905701450632[/C][C]56.2894344040861[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]111.4[/C][C]1.93649167310371[/C][C]57.5267126356675[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]111.4[/C][C]1.89296944860009[/C][C]58.8493385788047[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]111.4[/C][C]1.84842275106824[/C][C]60.2675983811712[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.4[/C][C]1.80277563773199[/C][C]61.7936018594905[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.4[/C][C]1.75594229214212[/C][C]63.441720436097[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.4[/C][C]1.70782512765993[/C][C]65.22916087588[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.4[/C][C]1.6583123951777[/C][C]67.1767275719257[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.4[/C][C]1.60727512683216[/C][C]69.3098512757816[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.4[/C][C]1.5545631755148[/C][C]71.6600018285582[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.4[/C][C]1.5[/C][C]74.2666666666667[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.4[/C][C]1.44337567297406[/C][C]77.1801839852692[/C][/ROW]
[ROW][C]Median[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.4[/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=87224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87224&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.42.4664414311581245.1662863722216
Geometric Mean109.415384433464
Harmonic Mean107.408614555839
Quadratic Mean113.322004335728
Winsorized Mean ( 1 / 24 )111.42.4608833356870645.2682979255893
Winsorized Mean ( 2 / 24 )111.42.4500487044438745.4684838705222
Winsorized Mean ( 3 / 24 )111.42.434188543522245.76473761511
Winsorized Mean ( 4 / 24 )111.42.4135279925644246.1564980158509
Winsorized Mean ( 5 / 24 )111.42.3882701094737946.6446402180802
Winsorized Mean ( 6 / 24 )111.42.358598958149447.2314293259108
Winsorized Mean ( 7 / 24 )111.42.3246821513599147.9205296667471
Winsorized Mean ( 8 / 24 )111.42.2866729629390948.7170670251055
Winsorized Mean ( 9 / 24 )111.42.2447120960974549.6277452211688
Winsorized Mean ( 10 / 24 )111.42.1989291745908950.6610223227066
Winsorized Mean ( 11 / 24 )111.42.1494440086138351.8273560760681
Winsorized Mean ( 12 / 24 )111.42.0963676761221653.1395333313222
Winsorized Mean ( 13 / 24 )111.42.0398034518221954.6131049540506
Winsorized Mean ( 14 / 24 )111.41.9798476095701256.2669568412835
Winsorized Mean ( 15 / 24 )111.41.9165901189041658.1240604870146
Winsorized Mean ( 16 / 24 )111.41.8501152525111360.2124650606488
Winsorized Mean ( 17 / 24 )111.41.7805021183439362.5666203102384
Winsorized Mean ( 18 / 24 )111.41.7078251276599365.22916087588
Winsorized Mean ( 19 / 24 )111.41.6321544082958568.2533462727428
Winsorized Mean ( 20 / 24 )111.41.5535561709229771.7064513565784
Winsorized Mean ( 21 / 24 )111.41.4720930347547375.6745649697069
Winsorized Mean ( 22 / 24 )111.41.3878243181426780.2695258641144
Winsorized Mean ( 23 / 24 )111.41.3008062986486885.6391917195714
Winsorized Mean ( 24 / 24 )111.41.2110924464829391.9830689420207
Trimmed Mean ( 1 / 24 )111.42.4324199198877445.7980133648722
Trimmed Mean ( 2 / 24 )111.42.3979157616563646.4570114519163
Trimmed Mean ( 3 / 24 )111.42.362907813126347.1453009639887
Trimmed Mean ( 4 / 24 )111.42.3273733406281647.8651181807957
Trimmed Mean ( 5 / 24 )111.42.2912878474779248.6189459445791
Trimmed Mean ( 6 / 24 )111.42.2546248764114549.4095497506037
Trimmed Mean ( 7 / 24 )111.42.2173557826083550.2400205117091
Trimmed Mean ( 8 / 24 )111.42.1794494717703451.1138255063612
Trimmed Mean ( 9 / 24 )111.42.1408720964441952.0348694277562
Trimmed Mean ( 10 / 24 )111.42.1015867021530853.0075679894008
Trimmed Mean ( 11 / 24 )111.42.0615528128088354.036937258095
Trimmed Mean ( 12 / 24 )111.42.0207259421636955.1287028466208
Trimmed Mean ( 13 / 24 )111.41.9790570145063256.2894344040861
Trimmed Mean ( 14 / 24 )111.41.9364916731037157.5267126356675
Trimmed Mean ( 15 / 24 )111.41.8929694486000958.8493385788047
Trimmed Mean ( 16 / 24 )111.41.8484227510682460.2675983811712
Trimmed Mean ( 17 / 24 )111.41.8027756377319961.7936018594905
Trimmed Mean ( 18 / 24 )111.41.7559422921421263.441720436097
Trimmed Mean ( 19 / 24 )111.41.7078251276599365.22916087588
Trimmed Mean ( 20 / 24 )111.41.658312395177767.1767275719257
Trimmed Mean ( 21 / 24 )111.41.6072751268321669.3098512757816
Trimmed Mean ( 22 / 24 )111.41.554563175514871.6600018285582
Trimmed Mean ( 23 / 24 )111.41.574.2666666666667
Trimmed Mean ( 24 / 24 )111.41.4433756729740677.1801839852692
Median111.4
Midrange111.4
Midmean - Weighted Average at Xnp110.9
Midmean - Weighted Average at X(n+1)p111.4
Midmean - Empirical Distribution Function110.9
Midmean - Empirical Distribution Function - Averaging111.4
Midmean - Empirical Distribution Function - Interpolation111.4
Midmean - Closest Observation110.9
Midmean - True Basic - Statistics Graphics Toolkit111.4
Midmean - MS Excel (old versions)111.4
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')