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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Mar 2010 11:41:31 -0600
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/Mar/15/t1268674991p1v1gi9hynejah9.htm/, Retrieved Tue, 18 Jan 2022 13:56:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74443, Retrieved Tue, 18 Jan 2022 13:56:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-03-15 17:41:31] [4b0ce05bd143e68bee12076814fe6457] [Current]
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Dataseries X:
8027,7
8059,6
8059,5
7988,9
7950,2
8003,8
8037,5
8069
8157,6
8244,3
8329,4
8417
8432,5
8486,4
8531,1
8643,8
8727,9
8847,3
8904,3
9003,2
9025,3
9044,7
9120,7
9184,3
9247,2
9407,1
9488,9
9592,5
9666,2
9809,6
9932,7
10008,9
10103,4
10194,3
10328,8
10507,6
10601,2
10684
10819,9
11014,3
11043
11258,5
11267,9
11334,5
11297,2
11371,3
11340,1
11380,1
11477,9
11538,8
11596,4
11598,8
11645,8
11738,7
11935,5
12042,8
12127,6
12213,8
12303,5
12410,3
12534,1
12587,5
12683,2
12748,7
12915,9
12962,5
12965,9
13060,7
13099,9
13204
13321,1
13391,2
13366,9
13415,3
13324,6
13141,9
12925,4
12901,5
12973
13155




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74443&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74443&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10728.7925204.66595028236752.4209937471185
Geometric Mean10570.6613457301
Harmonic Mean10410.7145387657
Quadratic Mean10881.9186016644
Winsorized Mean ( 1 / 26 )10728.975204.53352249537752.4558266493576
Winsorized Mean ( 2 / 26 )10728.74204.37082460876352.4964364191344
Winsorized Mean ( 3 / 26 )10728.05203.96268296220152.5981019870589
Winsorized Mean ( 4 / 26 )10728.365203.85249963616252.6280767670159
Winsorized Mean ( 5 / 26 )10722.42125202.46619962239952.9590680814743
Winsorized Mean ( 6 / 26 )10718.75375201.89919388231453.0896312357141
Winsorized Mean ( 7 / 26 )10718.43201.58745675170453.1701236411843
Winsorized Mean ( 8 / 26 )10723.09199.49294418695553.7517256246959
Winsorized Mean ( 9 / 26 )10728.43375197.25898781839754.3875534831242
Winsorized Mean ( 10 / 26 )10728.10875193.95481750859055.3124118689389
Winsorized Mean ( 11 / 26 )10739.1775191.94641722461055.9488301750032
Winsorized Mean ( 12 / 26 )10740.9925191.51613061897156.0840095572401
Winsorized Mean ( 13 / 26 )10743.7225189.30449990284256.7536561757066
Winsorized Mean ( 14 / 26 )10749.8825187.88688108734757.2146519107018
Winsorized Mean ( 15 / 26 )10768.31375184.37131623218758.4055804886644
Winsorized Mean ( 16 / 26 )10754.57375177.51720023405060.5832772025497
Winsorized Mean ( 17 / 26 )10766.0275171.91884570754562.6227302521234
Winsorized Mean ( 18 / 26 )10757.32167.09992999907664.3765679618146
Winsorized Mean ( 19 / 26 )10768.12625162.07824672817866.437825355177
Winsorized Mean ( 20 / 26 )10742.70125157.10072390326468.3809786682772
Winsorized Mean ( 21 / 26 )10719.75875152.67003134390870.2152128720825
Winsorized Mean ( 22 / 26 )10715.99125146.56309349229473.1152092567113
Winsorized Mean ( 23 / 26 )10709.49375140.86786868659276.0250996188979
Winsorized Mean ( 24 / 26 )10702.92375135.06884179159679.2405088252258
Winsorized Mean ( 25 / 26 )10719.36125124.12858998968986.3569081940786
Winsorized Mean ( 26 / 26 )10681.98625112.80364547625894.6953992922881
Trimmed Mean ( 1 / 26 )10729.9730769231203.93853751843652.6137590643117
Trimmed Mean ( 2 / 26 )10731.0236842105203.13309690739152.8275492649179
Trimmed Mean ( 3 / 26 )10732.2581081081202.17885166357753.0829907272717
Trimmed Mean ( 4 / 26 )10733.8166666667201.12100846741153.3699425458377
Trimmed Mean ( 5 / 26 )10735.3742857143199.80028004885653.7305267194281
Trimmed Mean ( 6 / 26 )10738.4220588235198.52357033865554.0914211874448
Trimmed Mean ( 7 / 26 )10742.3954545455197.03058309141254.5214620288747
Trimmed Mean ( 8 / 26 )10746.675195.20318444955355.0537893646777
Trimmed Mean ( 9 / 26 )10750.4790322581193.35510489726255.5996648651726
Trimmed Mean ( 10 / 26 )10753.745191.46764507285856.1648157102886
Trimmed Mean ( 11 / 26 )10757.2810344828189.70208966134556.706181010903
Trimmed Mean ( 12 / 26 )10759.6321428571187.79082380986957.2958354650537
Trimmed Mean ( 13 / 26 )10761.9333333333185.37452903991858.055081186563
Trimmed Mean ( 14 / 26 )10764.0884615385182.66717766275958.9273267330554
Trimmed Mean ( 15 / 26 )10765.712179.42471742084860.0012760490998
Trimmed Mean ( 16 / 26 )10765.4229166667175.90861720431461.1989514087469
Trimmed Mean ( 17 / 26 )10766.6021739130172.68042453972262.349870882072
Trimmed Mean ( 18 / 26 )10766.6636363636169.51505081671163.5144996535152
Trimmed Mean ( 19 / 26 )10767.6523809524166.23067666864464.775362747371
Trimmed Mean ( 20 / 26 )10767.6025162.80744665320866.137039314521
Trimmed Mean ( 21 / 26 )10770.2236842105159.15727289962367.670320607988
Trimmed Mean ( 22 / 26 )10775.5638888889155.0372302011969.5030727452081
Trimmed Mean ( 23 / 26 )10781.9352941176150.68934304860471.5507485532006
Trimmed Mean ( 24 / 26 )10789.809375145.88553969715273.9607873227112
Trimmed Mean ( 25 / 26 )10799.4633333333140.44226043772776.8961087615213
Trimmed Mean ( 26 / 26 )10808.6178571429135.73386318518279.6309602003783
Median11028.65
Midrange10682.75
Midmean - Weighted Average at Xnp10724.5682926829
Midmean - Weighted Average at X(n+1)p10767.6025
Midmean - Empirical Distribution Function10724.5682926829
Midmean - Empirical Distribution Function - Averaging10767.6025
Midmean - Empirical Distribution Function - Interpolation10767.6025
Midmean - Closest Observation10724.5682926829
Midmean - True Basic - Statistics Graphics Toolkit10767.6025
Midmean - MS Excel (old versions)10767.6523809524
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10728.7925 & 204.665950282367 & 52.4209937471185 \tabularnewline
Geometric Mean & 10570.6613457301 &  &  \tabularnewline
Harmonic Mean & 10410.7145387657 &  &  \tabularnewline
Quadratic Mean & 10881.9186016644 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 10728.975 & 204.533522495377 & 52.4558266493576 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 10728.74 & 204.370824608763 & 52.4964364191344 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 10728.05 & 203.962682962201 & 52.5981019870589 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 10728.365 & 203.852499636162 & 52.6280767670159 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 10722.42125 & 202.466199622399 & 52.9590680814743 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 10718.75375 & 201.899193882314 & 53.0896312357141 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 10718.43 & 201.587456751704 & 53.1701236411843 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 10723.09 & 199.492944186955 & 53.7517256246959 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 10728.43375 & 197.258987818397 & 54.3875534831242 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 10728.10875 & 193.954817508590 & 55.3124118689389 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 10739.1775 & 191.946417224610 & 55.9488301750032 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 10740.9925 & 191.516130618971 & 56.0840095572401 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 10743.7225 & 189.304499902842 & 56.7536561757066 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 10749.8825 & 187.886881087347 & 57.2146519107018 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 10768.31375 & 184.371316232187 & 58.4055804886644 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 10754.57375 & 177.517200234050 & 60.5832772025497 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 10766.0275 & 171.918845707545 & 62.6227302521234 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 10757.32 & 167.099929999076 & 64.3765679618146 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 10768.12625 & 162.078246728178 & 66.437825355177 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 10742.70125 & 157.100723903264 & 68.3809786682772 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 10719.75875 & 152.670031343908 & 70.2152128720825 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 10715.99125 & 146.563093492294 & 73.1152092567113 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 10709.49375 & 140.867868686592 & 76.0250996188979 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 10702.92375 & 135.068841791596 & 79.2405088252258 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 10719.36125 & 124.128589989689 & 86.3569081940786 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 10681.98625 & 112.803645476258 & 94.6953992922881 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 10729.9730769231 & 203.938537518436 & 52.6137590643117 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 10731.0236842105 & 203.133096907391 & 52.8275492649179 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 10732.2581081081 & 202.178851663577 & 53.0829907272717 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 10733.8166666667 & 201.121008467411 & 53.3699425458377 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 10735.3742857143 & 199.800280048856 & 53.7305267194281 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 10738.4220588235 & 198.523570338655 & 54.0914211874448 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 10742.3954545455 & 197.030583091412 & 54.5214620288747 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 10746.675 & 195.203184449553 & 55.0537893646777 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 10750.4790322581 & 193.355104897262 & 55.5996648651726 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 10753.745 & 191.467645072858 & 56.1648157102886 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 10757.2810344828 & 189.702089661345 & 56.706181010903 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 10759.6321428571 & 187.790823809869 & 57.2958354650537 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 10761.9333333333 & 185.374529039918 & 58.055081186563 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 10764.0884615385 & 182.667177662759 & 58.9273267330554 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 10765.712 & 179.424717420848 & 60.0012760490998 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 10765.4229166667 & 175.908617204314 & 61.1989514087469 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 10766.6021739130 & 172.680424539722 & 62.349870882072 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 10766.6636363636 & 169.515050816711 & 63.5144996535152 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 10767.6523809524 & 166.230676668644 & 64.775362747371 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 10767.6025 & 162.807446653208 & 66.137039314521 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 10770.2236842105 & 159.157272899623 & 67.670320607988 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 10775.5638888889 & 155.03723020119 & 69.5030727452081 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 10781.9352941176 & 150.689343048604 & 71.5507485532006 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 10789.809375 & 145.885539697152 & 73.9607873227112 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 10799.4633333333 & 140.442260437727 & 76.8961087615213 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 10808.6178571429 & 135.733863185182 & 79.6309602003783 \tabularnewline
Median & 11028.65 &  &  \tabularnewline
Midrange & 10682.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10724.5682926829 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10767.6025 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10724.5682926829 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10767.6025 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10767.6025 &  &  \tabularnewline
Midmean - Closest Observation & 10724.5682926829 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10767.6025 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10767.6523809524 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74443&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]10728.7925[/C][C]204.665950282367[/C][C]52.4209937471185[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10570.6613457301[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10410.7145387657[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10881.9186016644[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]10728.975[/C][C]204.533522495377[/C][C]52.4558266493576[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]10728.74[/C][C]204.370824608763[/C][C]52.4964364191344[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]10728.05[/C][C]203.962682962201[/C][C]52.5981019870589[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]10728.365[/C][C]203.852499636162[/C][C]52.6280767670159[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]10722.42125[/C][C]202.466199622399[/C][C]52.9590680814743[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]10718.75375[/C][C]201.899193882314[/C][C]53.0896312357141[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]10718.43[/C][C]201.587456751704[/C][C]53.1701236411843[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]10723.09[/C][C]199.492944186955[/C][C]53.7517256246959[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]10728.43375[/C][C]197.258987818397[/C][C]54.3875534831242[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]10728.10875[/C][C]193.954817508590[/C][C]55.3124118689389[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]10739.1775[/C][C]191.946417224610[/C][C]55.9488301750032[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]10740.9925[/C][C]191.516130618971[/C][C]56.0840095572401[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]10743.7225[/C][C]189.304499902842[/C][C]56.7536561757066[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]10749.8825[/C][C]187.886881087347[/C][C]57.2146519107018[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]10768.31375[/C][C]184.371316232187[/C][C]58.4055804886644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]10754.57375[/C][C]177.517200234050[/C][C]60.5832772025497[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]10766.0275[/C][C]171.918845707545[/C][C]62.6227302521234[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]10757.32[/C][C]167.099929999076[/C][C]64.3765679618146[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]10768.12625[/C][C]162.078246728178[/C][C]66.437825355177[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]10742.70125[/C][C]157.100723903264[/C][C]68.3809786682772[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]10719.75875[/C][C]152.670031343908[/C][C]70.2152128720825[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]10715.99125[/C][C]146.563093492294[/C][C]73.1152092567113[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]10709.49375[/C][C]140.867868686592[/C][C]76.0250996188979[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]10702.92375[/C][C]135.068841791596[/C][C]79.2405088252258[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]10719.36125[/C][C]124.128589989689[/C][C]86.3569081940786[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]10681.98625[/C][C]112.803645476258[/C][C]94.6953992922881[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]10729.9730769231[/C][C]203.938537518436[/C][C]52.6137590643117[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]10731.0236842105[/C][C]203.133096907391[/C][C]52.8275492649179[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]10732.2581081081[/C][C]202.178851663577[/C][C]53.0829907272717[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]10733.8166666667[/C][C]201.121008467411[/C][C]53.3699425458377[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]10735.3742857143[/C][C]199.800280048856[/C][C]53.7305267194281[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]10738.4220588235[/C][C]198.523570338655[/C][C]54.0914211874448[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]10742.3954545455[/C][C]197.030583091412[/C][C]54.5214620288747[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]10746.675[/C][C]195.203184449553[/C][C]55.0537893646777[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]10750.4790322581[/C][C]193.355104897262[/C][C]55.5996648651726[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]10753.745[/C][C]191.467645072858[/C][C]56.1648157102886[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]10757.2810344828[/C][C]189.702089661345[/C][C]56.706181010903[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]10759.6321428571[/C][C]187.790823809869[/C][C]57.2958354650537[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]10761.9333333333[/C][C]185.374529039918[/C][C]58.055081186563[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]10764.0884615385[/C][C]182.667177662759[/C][C]58.9273267330554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]10765.712[/C][C]179.424717420848[/C][C]60.0012760490998[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]10765.4229166667[/C][C]175.908617204314[/C][C]61.1989514087469[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]10766.6021739130[/C][C]172.680424539722[/C][C]62.349870882072[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]10766.6636363636[/C][C]169.515050816711[/C][C]63.5144996535152[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]10767.6523809524[/C][C]166.230676668644[/C][C]64.775362747371[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]10767.6025[/C][C]162.807446653208[/C][C]66.137039314521[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]10770.2236842105[/C][C]159.157272899623[/C][C]67.670320607988[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]10775.5638888889[/C][C]155.03723020119[/C][C]69.5030727452081[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]10781.9352941176[/C][C]150.689343048604[/C][C]71.5507485532006[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]10789.809375[/C][C]145.885539697152[/C][C]73.9607873227112[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]10799.4633333333[/C][C]140.442260437727[/C][C]76.8961087615213[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]10808.6178571429[/C][C]135.733863185182[/C][C]79.6309602003783[/C][/ROW]
[ROW][C]Median[/C][C]11028.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10682.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10724.5682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10767.6025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10724.5682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10767.6025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10767.6025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10724.5682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10767.6025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10767.6523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74443&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 Mean10728.7925204.66595028236752.4209937471185
Geometric Mean10570.6613457301
Harmonic Mean10410.7145387657
Quadratic Mean10881.9186016644
Winsorized Mean ( 1 / 26 )10728.975204.53352249537752.4558266493576
Winsorized Mean ( 2 / 26 )10728.74204.37082460876352.4964364191344
Winsorized Mean ( 3 / 26 )10728.05203.96268296220152.5981019870589
Winsorized Mean ( 4 / 26 )10728.365203.85249963616252.6280767670159
Winsorized Mean ( 5 / 26 )10722.42125202.46619962239952.9590680814743
Winsorized Mean ( 6 / 26 )10718.75375201.89919388231453.0896312357141
Winsorized Mean ( 7 / 26 )10718.43201.58745675170453.1701236411843
Winsorized Mean ( 8 / 26 )10723.09199.49294418695553.7517256246959
Winsorized Mean ( 9 / 26 )10728.43375197.25898781839754.3875534831242
Winsorized Mean ( 10 / 26 )10728.10875193.95481750859055.3124118689389
Winsorized Mean ( 11 / 26 )10739.1775191.94641722461055.9488301750032
Winsorized Mean ( 12 / 26 )10740.9925191.51613061897156.0840095572401
Winsorized Mean ( 13 / 26 )10743.7225189.30449990284256.7536561757066
Winsorized Mean ( 14 / 26 )10749.8825187.88688108734757.2146519107018
Winsorized Mean ( 15 / 26 )10768.31375184.37131623218758.4055804886644
Winsorized Mean ( 16 / 26 )10754.57375177.51720023405060.5832772025497
Winsorized Mean ( 17 / 26 )10766.0275171.91884570754562.6227302521234
Winsorized Mean ( 18 / 26 )10757.32167.09992999907664.3765679618146
Winsorized Mean ( 19 / 26 )10768.12625162.07824672817866.437825355177
Winsorized Mean ( 20 / 26 )10742.70125157.10072390326468.3809786682772
Winsorized Mean ( 21 / 26 )10719.75875152.67003134390870.2152128720825
Winsorized Mean ( 22 / 26 )10715.99125146.56309349229473.1152092567113
Winsorized Mean ( 23 / 26 )10709.49375140.86786868659276.0250996188979
Winsorized Mean ( 24 / 26 )10702.92375135.06884179159679.2405088252258
Winsorized Mean ( 25 / 26 )10719.36125124.12858998968986.3569081940786
Winsorized Mean ( 26 / 26 )10681.98625112.80364547625894.6953992922881
Trimmed Mean ( 1 / 26 )10729.9730769231203.93853751843652.6137590643117
Trimmed Mean ( 2 / 26 )10731.0236842105203.13309690739152.8275492649179
Trimmed Mean ( 3 / 26 )10732.2581081081202.17885166357753.0829907272717
Trimmed Mean ( 4 / 26 )10733.8166666667201.12100846741153.3699425458377
Trimmed Mean ( 5 / 26 )10735.3742857143199.80028004885653.7305267194281
Trimmed Mean ( 6 / 26 )10738.4220588235198.52357033865554.0914211874448
Trimmed Mean ( 7 / 26 )10742.3954545455197.03058309141254.5214620288747
Trimmed Mean ( 8 / 26 )10746.675195.20318444955355.0537893646777
Trimmed Mean ( 9 / 26 )10750.4790322581193.35510489726255.5996648651726
Trimmed Mean ( 10 / 26 )10753.745191.46764507285856.1648157102886
Trimmed Mean ( 11 / 26 )10757.2810344828189.70208966134556.706181010903
Trimmed Mean ( 12 / 26 )10759.6321428571187.79082380986957.2958354650537
Trimmed Mean ( 13 / 26 )10761.9333333333185.37452903991858.055081186563
Trimmed Mean ( 14 / 26 )10764.0884615385182.66717766275958.9273267330554
Trimmed Mean ( 15 / 26 )10765.712179.42471742084860.0012760490998
Trimmed Mean ( 16 / 26 )10765.4229166667175.90861720431461.1989514087469
Trimmed Mean ( 17 / 26 )10766.6021739130172.68042453972262.349870882072
Trimmed Mean ( 18 / 26 )10766.6636363636169.51505081671163.5144996535152
Trimmed Mean ( 19 / 26 )10767.6523809524166.23067666864464.775362747371
Trimmed Mean ( 20 / 26 )10767.6025162.80744665320866.137039314521
Trimmed Mean ( 21 / 26 )10770.2236842105159.15727289962367.670320607988
Trimmed Mean ( 22 / 26 )10775.5638888889155.0372302011969.5030727452081
Trimmed Mean ( 23 / 26 )10781.9352941176150.68934304860471.5507485532006
Trimmed Mean ( 24 / 26 )10789.809375145.88553969715273.9607873227112
Trimmed Mean ( 25 / 26 )10799.4633333333140.44226043772776.8961087615213
Trimmed Mean ( 26 / 26 )10808.6178571429135.73386318518279.6309602003783
Median11028.65
Midrange10682.75
Midmean - Weighted Average at Xnp10724.5682926829
Midmean - Weighted Average at X(n+1)p10767.6025
Midmean - Empirical Distribution Function10724.5682926829
Midmean - Empirical Distribution Function - Averaging10767.6025
Midmean - Empirical Distribution Function - Interpolation10767.6025
Midmean - Closest Observation10724.5682926829
Midmean - True Basic - Statistics Graphics Toolkit10767.6025
Midmean - MS Excel (old versions)10767.6523809524
Number of observations80



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')