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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 03 Apr 2011 17:04:28 +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/2011/Apr/03/t1301850311heq904fincoh56h.htm/, Retrieved Thu, 09 May 2024 19:11:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120023, Retrieved Thu, 09 May 2024 19:11:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-04-03 17:04:28] [cbd72b4390db0347015264c7aa42331b] [Current]
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Dataseries X:
30790
30800
31025
30835
31110
31270
31090
30755
31460
32135
32680
32700
32515
32275
32200
31835
31985
31875
31795
32260
33255
33160
32195
33130
33950
34210
33855
33735
34175
34265
33915
33660
33720
33810
33590
33545
33660
33165
33800
33880
33975
33930
33905
33890
33640
34395
34245
33940
34295
33745
33535
33715
33600
34120
34330
34130
33755
32910
32910
32850
32780
32565
31905
31975
31380
31355
31440
30310
31410
31300
31070
31075
31815




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120023&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120023&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120023&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32770.6849315068138.409793300726236.765651837261
Geometric Mean32749.4449682093
Harmonic Mean32728.0204939476
Quadratic Mean32791.7232603528
Winsorized Mean ( 1 / 24 )32775.8904109589136.888752843744239.434502324468
Winsorized Mean ( 2 / 24 )32775.8904109589136.543906556363240.039202316433
Winsorized Mean ( 3 / 24 )32775.0684931507136.272174446767240.511818544099
Winsorized Mean ( 4 / 24 )32775.8904109589135.723102262245241.490872700722
Winsorized Mean ( 5 / 24 )32786.5068493151132.87308853663246.750543773779
Winsorized Mean ( 6 / 24 )32787.3287671233131.773412100194248.815965562107
Winsorized Mean ( 7 / 24 )32783.4931506849131.063175541363250.135043770083
Winsorized Mean ( 8 / 24 )32784.0410958904130.610273507859251.006603197396
Winsorized Mean ( 9 / 24 )32768.6301369863127.722343968176256.561452905618
Winsorized Mean ( 10 / 24 )32787.1232876712123.424312280646265.645582153368
Winsorized Mean ( 11 / 24 )32790.1369863014122.459571987391267.762956003778
Winsorized Mean ( 12 / 24 )32797.5342465753120.731027517371271.657873878828
Winsorized Mean ( 13 / 24 )32799.3150684932119.647873895947274.132034281005
Winsorized Mean ( 14 / 24 )32803.1506849315118.455926706967276.922831949801
Winsorized Mean ( 15 / 24 )32806.2328767123117.05552371361280.262151122202
Winsorized Mean ( 16 / 24 )32808.4246575342116.065102574786282.672602959138
Winsorized Mean ( 17 / 24 )32880.6164383562103.287612565539318.340366493536
Winsorized Mean ( 18 / 24 )32874.4520547945101.128975325279325.074509546394
Winsorized Mean ( 19 / 24 )32877.0547945205100.039748360634328.639918965028
Winsorized Mean ( 20 / 24 )32875.684931506896.8938891374149339.295751508979
Winsorized Mean ( 21 / 24 )32881.438356164495.29851159057345.036221524976
Winsorized Mean ( 22 / 24 )32899.520547945291.9440678316587357.821024496994
Winsorized Mean ( 23 / 24 )32897.945205479590.909326617581361.876458989383
Winsorized Mean ( 24 / 24 )32945.616438356283.9502816145196392.442000250039
Trimmed Mean ( 1 / 24 )32782.4647887324136.046058053387240.965929169869
Trimmed Mean ( 2 / 24 )32789.4202898551134.973851159881242.931649412707
Trimmed Mean ( 3 / 24 )32796.7910447761133.838779421812245.046997488017
Trimmed Mean ( 4 / 24 )32804.9230769231132.526643380195247.534550338016
Trimmed Mean ( 5 / 24 )32813.3333333333131.071932580918250.345994655079
Trimmed Mean ( 6 / 24 )32819.7540983607130.104173594631252.257504056849
Trimmed Mean ( 7 / 24 )32826.4406779661129.120799078377254.230464125616
Trimmed Mean ( 8 / 24 )32834.298245614127.98059446443256.556850536741
Trimmed Mean ( 9 / 24 )32842.6363636364126.574185706633259.473416165262
Trimmed Mean ( 10 / 24 )32853.9622641509125.331733866486262.136022941721
Trimmed Mean ( 11 / 24 )32863.5294117647124.580023429123263.794535489565
Trimmed Mean ( 12 / 24 )32873.4693877551123.663278216641265.830486315956
Trimmed Mean ( 13 / 24 )32883.2978723404122.685159635981268.029955455968
Trimmed Mean ( 14 / 24 )32893.7777777778121.464979734523270.808737215215
Trimmed Mean ( 15 / 24 )32904.7674418605119.94611117983274.329589498134
Trimmed Mean ( 16 / 24 )32916.4634146341118.066775739879278.795310605878
Trimmed Mean ( 17 / 24 )32929.1025641026115.602317492097284.848117913845
Trimmed Mean ( 18 / 24 )32934.7297297297115.146620520058286.024284351383
Trimmed Mean ( 19 / 24 )32941.7142857143114.638808536067287.352203903535
Trimmed Mean ( 20 / 24 )32949.2424242424113.800172337562289.535962445699
Trimmed Mean ( 21 / 24 )32957.9032258065112.976059456886291.724666130561
Trimmed Mean ( 22 / 24 )32967.0689655172111.745972597273295.017960820198
Trimmed Mean ( 23 / 24 )32975.3703703704110.449717171273298.555498510114
Trimmed Mean ( 24 / 24 )32985.2108.213323270905304.816440369582
Median32910
Midrange32352.5
Midmean - Weighted Average at Xnp32910.4166666667
Midmean - Weighted Average at X(n+1)p32934.7297297297
Midmean - Empirical Distribution Function32934.7297297297
Midmean - Empirical Distribution Function - Averaging32934.7297297297
Midmean - Empirical Distribution Function - Interpolation32934.7297297297
Midmean - Closest Observation32904.7368421053
Midmean - True Basic - Statistics Graphics Toolkit32934.7297297297
Midmean - MS Excel (old versions)32934.7297297297
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32770.6849315068 & 138.409793300726 & 236.765651837261 \tabularnewline
Geometric Mean & 32749.4449682093 &  &  \tabularnewline
Harmonic Mean & 32728.0204939476 &  &  \tabularnewline
Quadratic Mean & 32791.7232603528 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 32775.8904109589 & 136.888752843744 & 239.434502324468 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 32775.8904109589 & 136.543906556363 & 240.039202316433 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 32775.0684931507 & 136.272174446767 & 240.511818544099 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 32775.8904109589 & 135.723102262245 & 241.490872700722 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 32786.5068493151 & 132.87308853663 & 246.750543773779 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 32787.3287671233 & 131.773412100194 & 248.815965562107 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 32783.4931506849 & 131.063175541363 & 250.135043770083 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 32784.0410958904 & 130.610273507859 & 251.006603197396 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 32768.6301369863 & 127.722343968176 & 256.561452905618 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 32787.1232876712 & 123.424312280646 & 265.645582153368 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 32790.1369863014 & 122.459571987391 & 267.762956003778 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 32797.5342465753 & 120.731027517371 & 271.657873878828 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 32799.3150684932 & 119.647873895947 & 274.132034281005 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 32803.1506849315 & 118.455926706967 & 276.922831949801 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 32806.2328767123 & 117.05552371361 & 280.262151122202 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 32808.4246575342 & 116.065102574786 & 282.672602959138 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 32880.6164383562 & 103.287612565539 & 318.340366493536 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 32874.4520547945 & 101.128975325279 & 325.074509546394 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 32877.0547945205 & 100.039748360634 & 328.639918965028 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 32875.6849315068 & 96.8938891374149 & 339.295751508979 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 32881.4383561644 & 95.29851159057 & 345.036221524976 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 32899.5205479452 & 91.9440678316587 & 357.821024496994 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 32897.9452054795 & 90.909326617581 & 361.876458989383 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 32945.6164383562 & 83.9502816145196 & 392.442000250039 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 32782.4647887324 & 136.046058053387 & 240.965929169869 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 32789.4202898551 & 134.973851159881 & 242.931649412707 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 32796.7910447761 & 133.838779421812 & 245.046997488017 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 32804.9230769231 & 132.526643380195 & 247.534550338016 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 32813.3333333333 & 131.071932580918 & 250.345994655079 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 32819.7540983607 & 130.104173594631 & 252.257504056849 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 32826.4406779661 & 129.120799078377 & 254.230464125616 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 32834.298245614 & 127.98059446443 & 256.556850536741 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 32842.6363636364 & 126.574185706633 & 259.473416165262 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 32853.9622641509 & 125.331733866486 & 262.136022941721 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 32863.5294117647 & 124.580023429123 & 263.794535489565 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 32873.4693877551 & 123.663278216641 & 265.830486315956 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 32883.2978723404 & 122.685159635981 & 268.029955455968 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 32893.7777777778 & 121.464979734523 & 270.808737215215 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 32904.7674418605 & 119.94611117983 & 274.329589498134 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 32916.4634146341 & 118.066775739879 & 278.795310605878 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 32929.1025641026 & 115.602317492097 & 284.848117913845 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 32934.7297297297 & 115.146620520058 & 286.024284351383 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 32941.7142857143 & 114.638808536067 & 287.352203903535 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 32949.2424242424 & 113.800172337562 & 289.535962445699 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 32957.9032258065 & 112.976059456886 & 291.724666130561 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 32967.0689655172 & 111.745972597273 & 295.017960820198 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 32975.3703703704 & 110.449717171273 & 298.555498510114 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 32985.2 & 108.213323270905 & 304.816440369582 \tabularnewline
Median & 32910 &  &  \tabularnewline
Midrange & 32352.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32910.4166666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32934.7297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32934.7297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32934.7297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32934.7297297297 &  &  \tabularnewline
Midmean - Closest Observation & 32904.7368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32934.7297297297 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32934.7297297297 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120023&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]32770.6849315068[/C][C]138.409793300726[/C][C]236.765651837261[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]32749.4449682093[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32728.0204939476[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32791.7232603528[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]32775.8904109589[/C][C]136.888752843744[/C][C]239.434502324468[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]32775.8904109589[/C][C]136.543906556363[/C][C]240.039202316433[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]32775.0684931507[/C][C]136.272174446767[/C][C]240.511818544099[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]32775.8904109589[/C][C]135.723102262245[/C][C]241.490872700722[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]32786.5068493151[/C][C]132.87308853663[/C][C]246.750543773779[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]32787.3287671233[/C][C]131.773412100194[/C][C]248.815965562107[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]32783.4931506849[/C][C]131.063175541363[/C][C]250.135043770083[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]32784.0410958904[/C][C]130.610273507859[/C][C]251.006603197396[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]32768.6301369863[/C][C]127.722343968176[/C][C]256.561452905618[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]32787.1232876712[/C][C]123.424312280646[/C][C]265.645582153368[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]32790.1369863014[/C][C]122.459571987391[/C][C]267.762956003778[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]32797.5342465753[/C][C]120.731027517371[/C][C]271.657873878828[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]32799.3150684932[/C][C]119.647873895947[/C][C]274.132034281005[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]32803.1506849315[/C][C]118.455926706967[/C][C]276.922831949801[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]32806.2328767123[/C][C]117.05552371361[/C][C]280.262151122202[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]32808.4246575342[/C][C]116.065102574786[/C][C]282.672602959138[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]32880.6164383562[/C][C]103.287612565539[/C][C]318.340366493536[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]32874.4520547945[/C][C]101.128975325279[/C][C]325.074509546394[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]32877.0547945205[/C][C]100.039748360634[/C][C]328.639918965028[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]32875.6849315068[/C][C]96.8938891374149[/C][C]339.295751508979[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]32881.4383561644[/C][C]95.29851159057[/C][C]345.036221524976[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]32899.5205479452[/C][C]91.9440678316587[/C][C]357.821024496994[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]32897.9452054795[/C][C]90.909326617581[/C][C]361.876458989383[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]32945.6164383562[/C][C]83.9502816145196[/C][C]392.442000250039[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]32782.4647887324[/C][C]136.046058053387[/C][C]240.965929169869[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]32789.4202898551[/C][C]134.973851159881[/C][C]242.931649412707[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]32796.7910447761[/C][C]133.838779421812[/C][C]245.046997488017[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]32804.9230769231[/C][C]132.526643380195[/C][C]247.534550338016[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]32813.3333333333[/C][C]131.071932580918[/C][C]250.345994655079[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]32819.7540983607[/C][C]130.104173594631[/C][C]252.257504056849[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]32826.4406779661[/C][C]129.120799078377[/C][C]254.230464125616[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]32834.298245614[/C][C]127.98059446443[/C][C]256.556850536741[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]32842.6363636364[/C][C]126.574185706633[/C][C]259.473416165262[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]32853.9622641509[/C][C]125.331733866486[/C][C]262.136022941721[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]32863.5294117647[/C][C]124.580023429123[/C][C]263.794535489565[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]32873.4693877551[/C][C]123.663278216641[/C][C]265.830486315956[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]32883.2978723404[/C][C]122.685159635981[/C][C]268.029955455968[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]32893.7777777778[/C][C]121.464979734523[/C][C]270.808737215215[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]32904.7674418605[/C][C]119.94611117983[/C][C]274.329589498134[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]32916.4634146341[/C][C]118.066775739879[/C][C]278.795310605878[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]32929.1025641026[/C][C]115.602317492097[/C][C]284.848117913845[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]32934.7297297297[/C][C]115.146620520058[/C][C]286.024284351383[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]32941.7142857143[/C][C]114.638808536067[/C][C]287.352203903535[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]32949.2424242424[/C][C]113.800172337562[/C][C]289.535962445699[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]32957.9032258065[/C][C]112.976059456886[/C][C]291.724666130561[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]32967.0689655172[/C][C]111.745972597273[/C][C]295.017960820198[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]32975.3703703704[/C][C]110.449717171273[/C][C]298.555498510114[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]32985.2[/C][C]108.213323270905[/C][C]304.816440369582[/C][/ROW]
[ROW][C]Median[/C][C]32910[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]32352.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32910.4166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32904.7368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32934.7297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120023&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120023&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 Mean32770.6849315068138.409793300726236.765651837261
Geometric Mean32749.4449682093
Harmonic Mean32728.0204939476
Quadratic Mean32791.7232603528
Winsorized Mean ( 1 / 24 )32775.8904109589136.888752843744239.434502324468
Winsorized Mean ( 2 / 24 )32775.8904109589136.543906556363240.039202316433
Winsorized Mean ( 3 / 24 )32775.0684931507136.272174446767240.511818544099
Winsorized Mean ( 4 / 24 )32775.8904109589135.723102262245241.490872700722
Winsorized Mean ( 5 / 24 )32786.5068493151132.87308853663246.750543773779
Winsorized Mean ( 6 / 24 )32787.3287671233131.773412100194248.815965562107
Winsorized Mean ( 7 / 24 )32783.4931506849131.063175541363250.135043770083
Winsorized Mean ( 8 / 24 )32784.0410958904130.610273507859251.006603197396
Winsorized Mean ( 9 / 24 )32768.6301369863127.722343968176256.561452905618
Winsorized Mean ( 10 / 24 )32787.1232876712123.424312280646265.645582153368
Winsorized Mean ( 11 / 24 )32790.1369863014122.459571987391267.762956003778
Winsorized Mean ( 12 / 24 )32797.5342465753120.731027517371271.657873878828
Winsorized Mean ( 13 / 24 )32799.3150684932119.647873895947274.132034281005
Winsorized Mean ( 14 / 24 )32803.1506849315118.455926706967276.922831949801
Winsorized Mean ( 15 / 24 )32806.2328767123117.05552371361280.262151122202
Winsorized Mean ( 16 / 24 )32808.4246575342116.065102574786282.672602959138
Winsorized Mean ( 17 / 24 )32880.6164383562103.287612565539318.340366493536
Winsorized Mean ( 18 / 24 )32874.4520547945101.128975325279325.074509546394
Winsorized Mean ( 19 / 24 )32877.0547945205100.039748360634328.639918965028
Winsorized Mean ( 20 / 24 )32875.684931506896.8938891374149339.295751508979
Winsorized Mean ( 21 / 24 )32881.438356164495.29851159057345.036221524976
Winsorized Mean ( 22 / 24 )32899.520547945291.9440678316587357.821024496994
Winsorized Mean ( 23 / 24 )32897.945205479590.909326617581361.876458989383
Winsorized Mean ( 24 / 24 )32945.616438356283.9502816145196392.442000250039
Trimmed Mean ( 1 / 24 )32782.4647887324136.046058053387240.965929169869
Trimmed Mean ( 2 / 24 )32789.4202898551134.973851159881242.931649412707
Trimmed Mean ( 3 / 24 )32796.7910447761133.838779421812245.046997488017
Trimmed Mean ( 4 / 24 )32804.9230769231132.526643380195247.534550338016
Trimmed Mean ( 5 / 24 )32813.3333333333131.071932580918250.345994655079
Trimmed Mean ( 6 / 24 )32819.7540983607130.104173594631252.257504056849
Trimmed Mean ( 7 / 24 )32826.4406779661129.120799078377254.230464125616
Trimmed Mean ( 8 / 24 )32834.298245614127.98059446443256.556850536741
Trimmed Mean ( 9 / 24 )32842.6363636364126.574185706633259.473416165262
Trimmed Mean ( 10 / 24 )32853.9622641509125.331733866486262.136022941721
Trimmed Mean ( 11 / 24 )32863.5294117647124.580023429123263.794535489565
Trimmed Mean ( 12 / 24 )32873.4693877551123.663278216641265.830486315956
Trimmed Mean ( 13 / 24 )32883.2978723404122.685159635981268.029955455968
Trimmed Mean ( 14 / 24 )32893.7777777778121.464979734523270.808737215215
Trimmed Mean ( 15 / 24 )32904.7674418605119.94611117983274.329589498134
Trimmed Mean ( 16 / 24 )32916.4634146341118.066775739879278.795310605878
Trimmed Mean ( 17 / 24 )32929.1025641026115.602317492097284.848117913845
Trimmed Mean ( 18 / 24 )32934.7297297297115.146620520058286.024284351383
Trimmed Mean ( 19 / 24 )32941.7142857143114.638808536067287.352203903535
Trimmed Mean ( 20 / 24 )32949.2424242424113.800172337562289.535962445699
Trimmed Mean ( 21 / 24 )32957.9032258065112.976059456886291.724666130561
Trimmed Mean ( 22 / 24 )32967.0689655172111.745972597273295.017960820198
Trimmed Mean ( 23 / 24 )32975.3703703704110.449717171273298.555498510114
Trimmed Mean ( 24 / 24 )32985.2108.213323270905304.816440369582
Median32910
Midrange32352.5
Midmean - Weighted Average at Xnp32910.4166666667
Midmean - Weighted Average at X(n+1)p32934.7297297297
Midmean - Empirical Distribution Function32934.7297297297
Midmean - Empirical Distribution Function - Averaging32934.7297297297
Midmean - Empirical Distribution Function - Interpolation32934.7297297297
Midmean - Closest Observation32904.7368421053
Midmean - True Basic - Statistics Graphics Toolkit32934.7297297297
Midmean - MS Excel (old versions)32934.7297297297
Number of observations73



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')