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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 computationSat, 10 Oct 2015 15:56:13 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t1444489037y65zcxyb603td31.htm/, Retrieved Mon, 13 May 2024 21:53:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282209, Retrieved Mon, 13 May 2024 21:53:13 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-10 14:56:13] [047b71d569822bc9ea0d1a14ab5e311b] [Current]
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Dataseries X:
72,04
72,26
72,53
72,41
72,91
72,84
72,92
73,03
72,98
72,99
73,15
73,34
73,8
74,46
74,54
74,92
74,19
74,34
74,54
74,4
73,78
74,42
73,54
74,45
76,31
76,44
76,64
76,44
76,49
76,52
78,15
78,54
78,79
78,75
78,28
78,44
78,75
80,54
80,84
81,11
80,47
80,53
80,35
80,29
80,27
80,1
79,8
79,84
79,92
80,26
80,69
84,5
85,45
86,19
86,4
85,98
85,87
86,06
86,43
86,43
86,37
86,84
86,73
90,99
92,61
93,83
94,2
94,01
93,47
93,27
94,3
94,53
94,59
94,69
94,67
96,55
97,14
97,32
97,97
98,49
99,11
99,09
98,76
99,2
99,61
99,54
99,68
100,75
100,38
100,79
100,39
100,39
100,12
100
99,17
99,17
99,59
99,96
99,68
101,03
100,99
101,38
101,84
101,52
101,37
101,22
101,45
101,99




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282209&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282209&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.59611111111111.0291283301879284.1451047172108
Geometric Mean85.9441878597696
Harmonic Mean85.2999931345459
Quadratic Mean87.2479839733126
Winsorized Mean ( 1 / 36 )86.59675925925931.028667772964584.1834084193163
Winsorized Mean ( 2 / 36 )86.59361111111111.0274950675557584.276425109372
Winsorized Mean ( 3 / 36 )86.5951.0268032412092684.3345604343999
Winsorized Mean ( 4 / 36 )86.60388888888891.0249979512962684.4917677926727
Winsorized Mean ( 5 / 36 )86.60666666666671.0245297868687884.5330880338372
Winsorized Mean ( 6 / 36 )86.59888888888891.0233428747033884.6235323756856
Winsorized Mean ( 7 / 36 )86.5904629629631.0212219025179684.7910358654299
Winsorized Mean ( 8 / 36 )86.58824074074071.0207385376012884.8290111042751
Winsorized Mean ( 9 / 36 )86.57490740740741.0181375779558185.0326216042727
Winsorized Mean ( 10 / 36 )86.58231481481481.0162776744761585.1955297152861
Winsorized Mean ( 11 / 36 )86.5651.0091613362741785.7791483764118
Winsorized Mean ( 12 / 36 )86.58722222222221.0064543079682986.0319455505283
Winsorized Mean ( 13 / 36 )86.61490740740741.0028221383574686.3711560549267
Winsorized Mean ( 14 / 36 )86.58379629629630.99821436904932586.7386795671521
Winsorized Mean ( 15 / 36 )86.62129629629630.98968425455843487.5241733889603
Winsorized Mean ( 16 / 36 )86.63759259259260.98633683260762187.8377342591426
Winsorized Mean ( 17 / 36 )86.6029629629630.97970590648032888.3968978752931
Winsorized Mean ( 18 / 36 )86.60629629629630.9793180653824288.4353095870614
Winsorized Mean ( 19 / 36 )86.59925925925930.97717010674169988.6225015089932
Winsorized Mean ( 20 / 36 )86.59740740740740.97649424307373788.6819436178368
Winsorized Mean ( 21 / 36 )86.60324074074080.97348176677181388.9623654975356
Winsorized Mean ( 22 / 36 )86.53398148148150.96493238759558989.6788029854674
Winsorized Mean ( 23 / 36 )86.60851851851850.95481763643333990.7068692635792
Winsorized Mean ( 24 / 36 )86.91740740740740.92049582905701494.4245532285012
Winsorized Mean ( 25 / 36 )86.93361111111110.91553655871759194.9537299011638
Winsorized Mean ( 26 / 36 )86.92879629629630.91493827158061295.010558631591
Winsorized Mean ( 27 / 36 )86.85879629629630.90339504946407896.1470802256706
Winsorized Mean ( 28 / 36 )86.79657407407410.89397213294939197.0909169033211
Winsorized Mean ( 29 / 36 )86.68916666666670.87354735399075299.2380851142552
Winsorized Mean ( 30 / 36 )86.92805555555550.807904747245552107.596911457602
Winsorized Mean ( 31 / 36 )86.91370370370370.797923627166445108.924840353892
Winsorized Mean ( 32 / 36 )86.78629629629630.772333884729544112.36888347413
Winsorized Mean ( 33 / 36 )86.24851851851850.703716987176735122.561370679059
Winsorized Mean ( 34 / 36 )86.30833333333330.696272967552532123.957610528405
Winsorized Mean ( 35 / 36 )86.28240740740740.693366505496517124.439826157482
Winsorized Mean ( 36 / 36 )86.27574074074070.689775338332073125.078030405323
Trimmed Mean ( 1 / 36 )86.58820754716981.0292295969760484.1291465010072
Trimmed Mean ( 2 / 36 )86.57932692307691.0294504401963484.1024720981847
Trimmed Mean ( 3 / 36 )86.57176470588241.0299456157953784.0546951006024
Trimmed Mean ( 4 / 36 )86.56341.0303327717810784.0149924090675
Trimmed Mean ( 5 / 36 )86.55224489795921.0308630025342683.9609576492516
Trimmed Mean ( 6 / 36 )86.541.0311024482426283.9295844438115
Trimmed Mean ( 7 / 36 )86.52872340425531.0311501712561583.9147641306653
Trimmed Mean ( 8 / 36 )86.51836956521741.0311238386790283.9068658096941
Trimmed Mean ( 9 / 36 )86.50788888888891.030665439558783.9340154123424
Trimmed Mean ( 10 / 36 )86.498751.0300572390343483.9747023001277
Trimmed Mean ( 11 / 36 )86.48825581395351.0291149052216784.0413984630069
Trimmed Mean ( 12 / 36 )86.47928571428571.0285451515018684.0792313181495
Trimmed Mean ( 13 / 36 )86.46743902439021.0276785246292884.1386065312421
Trimmed Mean ( 14 / 36 )86.4521251.0265633908199984.2150867380381
Trimmed Mean ( 15 / 36 )86.43910256410261.0252652846747984.3090113906668
Trimmed Mean ( 16 / 36 )86.42184210526321.0242120927306384.3788534802939
Trimmed Mean ( 17 / 36 )86.40216216216221.0227039511628984.4840406296627
Trimmed Mean ( 18 / 36 )86.38444444444441.0210712885237884.6017760124618
Trimmed Mean ( 19 / 36 )86.36542857142861.0184384524339484.8018143512022
Trimmed Mean ( 20 / 36 )86.34588235294121.0148518974735785.0822495064504
Trimmed Mean ( 21 / 36 )86.3253030303031.0099304880346385.4764798697147
Trimmed Mean ( 22 / 36 )86.302968751.0037223794774585.982907738822
Trimmed Mean ( 23 / 36 )86.28467741935480.9967360195336386.5672311709245
Trimmed Mean ( 24 / 36 )86.25933333333330.98893962120442387.2240645270928
Trimmed Mean ( 25 / 36 )86.2082758620690.98326896355182187.6751723665338
Trimmed Mean ( 26 / 36 )86.15232142857140.97605267818343488.2660571035086
Trimmed Mean ( 27 / 36 )86.09259259259260.96629889574494689.0951991890889
Trimmed Mean ( 28 / 36 )86.03365384615390.95515822087833990.0726727421552
Trimmed Mean ( 29 / 36 )85.97480.94191477754798291.2766229486407
Trimmed Mean ( 30 / 36 )85.9193750.92791558936123692.5939557273153
Trimmed Mean ( 31 / 36 )85.84043478260870.91994895660342193.3099974367528
Trimmed Mean ( 32 / 36 )85.75545454545450.90997975574823294.2388597150076
Trimmed Mean ( 33 / 36 )85.67261904761910.90049967156089495.1389786729374
Trimmed Mean ( 34 / 36 )85.62550.90017554911848795.1208906794351
Trimmed Mean ( 35 / 36 )85.56842105263160.89843142322357195.2420171877027
Trimmed Mean ( 36 / 36 )85.50722222222220.89392975924402595.6531778229797
Median85.925
Midrange87.015
Midmean - Weighted Average at Xnp85.7478571428571
Midmean - Weighted Average at X(n+1)p86.0925925925926
Midmean - Empirical Distribution Function85.7478571428571
Midmean - Empirical Distribution Function - Averaging86.0925925925926
Midmean - Empirical Distribution Function - Interpolation86.0925925925926
Midmean - Closest Observation85.7478571428571
Midmean - True Basic - Statistics Graphics Toolkit86.0925925925926
Midmean - MS Excel (old versions)85.9819298245614
Number of observations108

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.5961111111111 & 1.02912833018792 & 84.1451047172108 \tabularnewline
Geometric Mean & 85.9441878597696 &  &  \tabularnewline
Harmonic Mean & 85.2999931345459 &  &  \tabularnewline
Quadratic Mean & 87.2479839733126 &  &  \tabularnewline
Winsorized Mean ( 1 / 36 ) & 86.5967592592593 & 1.0286677729645 & 84.1834084193163 \tabularnewline
Winsorized Mean ( 2 / 36 ) & 86.5936111111111 & 1.02749506755575 & 84.276425109372 \tabularnewline
Winsorized Mean ( 3 / 36 ) & 86.595 & 1.02680324120926 & 84.3345604343999 \tabularnewline
Winsorized Mean ( 4 / 36 ) & 86.6038888888889 & 1.02499795129626 & 84.4917677926727 \tabularnewline
Winsorized Mean ( 5 / 36 ) & 86.6066666666667 & 1.02452978686878 & 84.5330880338372 \tabularnewline
Winsorized Mean ( 6 / 36 ) & 86.5988888888889 & 1.02334287470338 & 84.6235323756856 \tabularnewline
Winsorized Mean ( 7 / 36 ) & 86.590462962963 & 1.02122190251796 & 84.7910358654299 \tabularnewline
Winsorized Mean ( 8 / 36 ) & 86.5882407407407 & 1.02073853760128 & 84.8290111042751 \tabularnewline
Winsorized Mean ( 9 / 36 ) & 86.5749074074074 & 1.01813757795581 & 85.0326216042727 \tabularnewline
Winsorized Mean ( 10 / 36 ) & 86.5823148148148 & 1.01627767447615 & 85.1955297152861 \tabularnewline
Winsorized Mean ( 11 / 36 ) & 86.565 & 1.00916133627417 & 85.7791483764118 \tabularnewline
Winsorized Mean ( 12 / 36 ) & 86.5872222222222 & 1.00645430796829 & 86.0319455505283 \tabularnewline
Winsorized Mean ( 13 / 36 ) & 86.6149074074074 & 1.00282213835746 & 86.3711560549267 \tabularnewline
Winsorized Mean ( 14 / 36 ) & 86.5837962962963 & 0.998214369049325 & 86.7386795671521 \tabularnewline
Winsorized Mean ( 15 / 36 ) & 86.6212962962963 & 0.989684254558434 & 87.5241733889603 \tabularnewline
Winsorized Mean ( 16 / 36 ) & 86.6375925925926 & 0.986336832607621 & 87.8377342591426 \tabularnewline
Winsorized Mean ( 17 / 36 ) & 86.602962962963 & 0.979705906480328 & 88.3968978752931 \tabularnewline
Winsorized Mean ( 18 / 36 ) & 86.6062962962963 & 0.97931806538242 & 88.4353095870614 \tabularnewline
Winsorized Mean ( 19 / 36 ) & 86.5992592592593 & 0.977170106741699 & 88.6225015089932 \tabularnewline
Winsorized Mean ( 20 / 36 ) & 86.5974074074074 & 0.976494243073737 & 88.6819436178368 \tabularnewline
Winsorized Mean ( 21 / 36 ) & 86.6032407407408 & 0.973481766771813 & 88.9623654975356 \tabularnewline
Winsorized Mean ( 22 / 36 ) & 86.5339814814815 & 0.964932387595589 & 89.6788029854674 \tabularnewline
Winsorized Mean ( 23 / 36 ) & 86.6085185185185 & 0.954817636433339 & 90.7068692635792 \tabularnewline
Winsorized Mean ( 24 / 36 ) & 86.9174074074074 & 0.920495829057014 & 94.4245532285012 \tabularnewline
Winsorized Mean ( 25 / 36 ) & 86.9336111111111 & 0.915536558717591 & 94.9537299011638 \tabularnewline
Winsorized Mean ( 26 / 36 ) & 86.9287962962963 & 0.914938271580612 & 95.010558631591 \tabularnewline
Winsorized Mean ( 27 / 36 ) & 86.8587962962963 & 0.903395049464078 & 96.1470802256706 \tabularnewline
Winsorized Mean ( 28 / 36 ) & 86.7965740740741 & 0.893972132949391 & 97.0909169033211 \tabularnewline
Winsorized Mean ( 29 / 36 ) & 86.6891666666667 & 0.873547353990752 & 99.2380851142552 \tabularnewline
Winsorized Mean ( 30 / 36 ) & 86.9280555555555 & 0.807904747245552 & 107.596911457602 \tabularnewline
Winsorized Mean ( 31 / 36 ) & 86.9137037037037 & 0.797923627166445 & 108.924840353892 \tabularnewline
Winsorized Mean ( 32 / 36 ) & 86.7862962962963 & 0.772333884729544 & 112.36888347413 \tabularnewline
Winsorized Mean ( 33 / 36 ) & 86.2485185185185 & 0.703716987176735 & 122.561370679059 \tabularnewline
Winsorized Mean ( 34 / 36 ) & 86.3083333333333 & 0.696272967552532 & 123.957610528405 \tabularnewline
Winsorized Mean ( 35 / 36 ) & 86.2824074074074 & 0.693366505496517 & 124.439826157482 \tabularnewline
Winsorized Mean ( 36 / 36 ) & 86.2757407407407 & 0.689775338332073 & 125.078030405323 \tabularnewline
Trimmed Mean ( 1 / 36 ) & 86.5882075471698 & 1.02922959697604 & 84.1291465010072 \tabularnewline
Trimmed Mean ( 2 / 36 ) & 86.5793269230769 & 1.02945044019634 & 84.1024720981847 \tabularnewline
Trimmed Mean ( 3 / 36 ) & 86.5717647058824 & 1.02994561579537 & 84.0546951006024 \tabularnewline
Trimmed Mean ( 4 / 36 ) & 86.5634 & 1.03033277178107 & 84.0149924090675 \tabularnewline
Trimmed Mean ( 5 / 36 ) & 86.5522448979592 & 1.03086300253426 & 83.9609576492516 \tabularnewline
Trimmed Mean ( 6 / 36 ) & 86.54 & 1.03110244824262 & 83.9295844438115 \tabularnewline
Trimmed Mean ( 7 / 36 ) & 86.5287234042553 & 1.03115017125615 & 83.9147641306653 \tabularnewline
Trimmed Mean ( 8 / 36 ) & 86.5183695652174 & 1.03112383867902 & 83.9068658096941 \tabularnewline
Trimmed Mean ( 9 / 36 ) & 86.5078888888889 & 1.0306654395587 & 83.9340154123424 \tabularnewline
Trimmed Mean ( 10 / 36 ) & 86.49875 & 1.03005723903434 & 83.9747023001277 \tabularnewline
Trimmed Mean ( 11 / 36 ) & 86.4882558139535 & 1.02911490522167 & 84.0413984630069 \tabularnewline
Trimmed Mean ( 12 / 36 ) & 86.4792857142857 & 1.02854515150186 & 84.0792313181495 \tabularnewline
Trimmed Mean ( 13 / 36 ) & 86.4674390243902 & 1.02767852462928 & 84.1386065312421 \tabularnewline
Trimmed Mean ( 14 / 36 ) & 86.452125 & 1.02656339081999 & 84.2150867380381 \tabularnewline
Trimmed Mean ( 15 / 36 ) & 86.4391025641026 & 1.02526528467479 & 84.3090113906668 \tabularnewline
Trimmed Mean ( 16 / 36 ) & 86.4218421052632 & 1.02421209273063 & 84.3788534802939 \tabularnewline
Trimmed Mean ( 17 / 36 ) & 86.4021621621622 & 1.02270395116289 & 84.4840406296627 \tabularnewline
Trimmed Mean ( 18 / 36 ) & 86.3844444444444 & 1.02107128852378 & 84.6017760124618 \tabularnewline
Trimmed Mean ( 19 / 36 ) & 86.3654285714286 & 1.01843845243394 & 84.8018143512022 \tabularnewline
Trimmed Mean ( 20 / 36 ) & 86.3458823529412 & 1.01485189747357 & 85.0822495064504 \tabularnewline
Trimmed Mean ( 21 / 36 ) & 86.325303030303 & 1.00993048803463 & 85.4764798697147 \tabularnewline
Trimmed Mean ( 22 / 36 ) & 86.30296875 & 1.00372237947745 & 85.982907738822 \tabularnewline
Trimmed Mean ( 23 / 36 ) & 86.2846774193548 & 0.99673601953363 & 86.5672311709245 \tabularnewline
Trimmed Mean ( 24 / 36 ) & 86.2593333333333 & 0.988939621204423 & 87.2240645270928 \tabularnewline
Trimmed Mean ( 25 / 36 ) & 86.208275862069 & 0.983268963551821 & 87.6751723665338 \tabularnewline
Trimmed Mean ( 26 / 36 ) & 86.1523214285714 & 0.976052678183434 & 88.2660571035086 \tabularnewline
Trimmed Mean ( 27 / 36 ) & 86.0925925925926 & 0.966298895744946 & 89.0951991890889 \tabularnewline
Trimmed Mean ( 28 / 36 ) & 86.0336538461539 & 0.955158220878339 & 90.0726727421552 \tabularnewline
Trimmed Mean ( 29 / 36 ) & 85.9748 & 0.941914777547982 & 91.2766229486407 \tabularnewline
Trimmed Mean ( 30 / 36 ) & 85.919375 & 0.927915589361236 & 92.5939557273153 \tabularnewline
Trimmed Mean ( 31 / 36 ) & 85.8404347826087 & 0.919948956603421 & 93.3099974367528 \tabularnewline
Trimmed Mean ( 32 / 36 ) & 85.7554545454545 & 0.909979755748232 & 94.2388597150076 \tabularnewline
Trimmed Mean ( 33 / 36 ) & 85.6726190476191 & 0.900499671560894 & 95.1389786729374 \tabularnewline
Trimmed Mean ( 34 / 36 ) & 85.6255 & 0.900175549118487 & 95.1208906794351 \tabularnewline
Trimmed Mean ( 35 / 36 ) & 85.5684210526316 & 0.898431423223571 & 95.2420171877027 \tabularnewline
Trimmed Mean ( 36 / 36 ) & 85.5072222222222 & 0.893929759244025 & 95.6531778229797 \tabularnewline
Median & 85.925 &  &  \tabularnewline
Midrange & 87.015 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 85.7478571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 86.0925925925926 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.7478571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 86.0925925925926 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 86.0925925925926 &  &  \tabularnewline
Midmean - Closest Observation & 85.7478571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 86.0925925925926 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 85.9819298245614 &  &  \tabularnewline
Number of observations & 108 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282209&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]86.5961111111111[/C][C]1.02912833018792[/C][C]84.1451047172108[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]85.9441878597696[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.2999931345459[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]87.2479839733126[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 36 )[/C][C]86.5967592592593[/C][C]1.0286677729645[/C][C]84.1834084193163[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 36 )[/C][C]86.5936111111111[/C][C]1.02749506755575[/C][C]84.276425109372[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 36 )[/C][C]86.595[/C][C]1.02680324120926[/C][C]84.3345604343999[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 36 )[/C][C]86.6038888888889[/C][C]1.02499795129626[/C][C]84.4917677926727[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 36 )[/C][C]86.6066666666667[/C][C]1.02452978686878[/C][C]84.5330880338372[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 36 )[/C][C]86.5988888888889[/C][C]1.02334287470338[/C][C]84.6235323756856[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 36 )[/C][C]86.590462962963[/C][C]1.02122190251796[/C][C]84.7910358654299[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 36 )[/C][C]86.5882407407407[/C][C]1.02073853760128[/C][C]84.8290111042751[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 36 )[/C][C]86.5749074074074[/C][C]1.01813757795581[/C][C]85.0326216042727[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 36 )[/C][C]86.5823148148148[/C][C]1.01627767447615[/C][C]85.1955297152861[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 36 )[/C][C]86.565[/C][C]1.00916133627417[/C][C]85.7791483764118[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 36 )[/C][C]86.5872222222222[/C][C]1.00645430796829[/C][C]86.0319455505283[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 36 )[/C][C]86.6149074074074[/C][C]1.00282213835746[/C][C]86.3711560549267[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 36 )[/C][C]86.5837962962963[/C][C]0.998214369049325[/C][C]86.7386795671521[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 36 )[/C][C]86.6212962962963[/C][C]0.989684254558434[/C][C]87.5241733889603[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 36 )[/C][C]86.6375925925926[/C][C]0.986336832607621[/C][C]87.8377342591426[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 36 )[/C][C]86.602962962963[/C][C]0.979705906480328[/C][C]88.3968978752931[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 36 )[/C][C]86.6062962962963[/C][C]0.97931806538242[/C][C]88.4353095870614[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 36 )[/C][C]86.5992592592593[/C][C]0.977170106741699[/C][C]88.6225015089932[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 36 )[/C][C]86.5974074074074[/C][C]0.976494243073737[/C][C]88.6819436178368[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 36 )[/C][C]86.6032407407408[/C][C]0.973481766771813[/C][C]88.9623654975356[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 36 )[/C][C]86.5339814814815[/C][C]0.964932387595589[/C][C]89.6788029854674[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 36 )[/C][C]86.6085185185185[/C][C]0.954817636433339[/C][C]90.7068692635792[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 36 )[/C][C]86.9174074074074[/C][C]0.920495829057014[/C][C]94.4245532285012[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 36 )[/C][C]86.9336111111111[/C][C]0.915536558717591[/C][C]94.9537299011638[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 36 )[/C][C]86.9287962962963[/C][C]0.914938271580612[/C][C]95.010558631591[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 36 )[/C][C]86.8587962962963[/C][C]0.903395049464078[/C][C]96.1470802256706[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 36 )[/C][C]86.7965740740741[/C][C]0.893972132949391[/C][C]97.0909169033211[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 36 )[/C][C]86.6891666666667[/C][C]0.873547353990752[/C][C]99.2380851142552[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 36 )[/C][C]86.9280555555555[/C][C]0.807904747245552[/C][C]107.596911457602[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 36 )[/C][C]86.9137037037037[/C][C]0.797923627166445[/C][C]108.924840353892[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 36 )[/C][C]86.7862962962963[/C][C]0.772333884729544[/C][C]112.36888347413[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 36 )[/C][C]86.2485185185185[/C][C]0.703716987176735[/C][C]122.561370679059[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 36 )[/C][C]86.3083333333333[/C][C]0.696272967552532[/C][C]123.957610528405[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 36 )[/C][C]86.2824074074074[/C][C]0.693366505496517[/C][C]124.439826157482[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 36 )[/C][C]86.2757407407407[/C][C]0.689775338332073[/C][C]125.078030405323[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 36 )[/C][C]86.5882075471698[/C][C]1.02922959697604[/C][C]84.1291465010072[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 36 )[/C][C]86.5793269230769[/C][C]1.02945044019634[/C][C]84.1024720981847[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 36 )[/C][C]86.5717647058824[/C][C]1.02994561579537[/C][C]84.0546951006024[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 36 )[/C][C]86.5634[/C][C]1.03033277178107[/C][C]84.0149924090675[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 36 )[/C][C]86.5522448979592[/C][C]1.03086300253426[/C][C]83.9609576492516[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 36 )[/C][C]86.54[/C][C]1.03110244824262[/C][C]83.9295844438115[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 36 )[/C][C]86.5287234042553[/C][C]1.03115017125615[/C][C]83.9147641306653[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 36 )[/C][C]86.5183695652174[/C][C]1.03112383867902[/C][C]83.9068658096941[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 36 )[/C][C]86.5078888888889[/C][C]1.0306654395587[/C][C]83.9340154123424[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 36 )[/C][C]86.49875[/C][C]1.03005723903434[/C][C]83.9747023001277[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 36 )[/C][C]86.4882558139535[/C][C]1.02911490522167[/C][C]84.0413984630069[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 36 )[/C][C]86.4792857142857[/C][C]1.02854515150186[/C][C]84.0792313181495[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 36 )[/C][C]86.4674390243902[/C][C]1.02767852462928[/C][C]84.1386065312421[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 36 )[/C][C]86.452125[/C][C]1.02656339081999[/C][C]84.2150867380381[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 36 )[/C][C]86.4391025641026[/C][C]1.02526528467479[/C][C]84.3090113906668[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 36 )[/C][C]86.4218421052632[/C][C]1.02421209273063[/C][C]84.3788534802939[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 36 )[/C][C]86.4021621621622[/C][C]1.02270395116289[/C][C]84.4840406296627[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 36 )[/C][C]86.3844444444444[/C][C]1.02107128852378[/C][C]84.6017760124618[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 36 )[/C][C]86.3654285714286[/C][C]1.01843845243394[/C][C]84.8018143512022[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 36 )[/C][C]86.3458823529412[/C][C]1.01485189747357[/C][C]85.0822495064504[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 36 )[/C][C]86.325303030303[/C][C]1.00993048803463[/C][C]85.4764798697147[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 36 )[/C][C]86.30296875[/C][C]1.00372237947745[/C][C]85.982907738822[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 36 )[/C][C]86.2846774193548[/C][C]0.99673601953363[/C][C]86.5672311709245[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 36 )[/C][C]86.2593333333333[/C][C]0.988939621204423[/C][C]87.2240645270928[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 36 )[/C][C]86.208275862069[/C][C]0.983268963551821[/C][C]87.6751723665338[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 36 )[/C][C]86.1523214285714[/C][C]0.976052678183434[/C][C]88.2660571035086[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 36 )[/C][C]86.0925925925926[/C][C]0.966298895744946[/C][C]89.0951991890889[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 36 )[/C][C]86.0336538461539[/C][C]0.955158220878339[/C][C]90.0726727421552[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 36 )[/C][C]85.9748[/C][C]0.941914777547982[/C][C]91.2766229486407[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 36 )[/C][C]85.919375[/C][C]0.927915589361236[/C][C]92.5939557273153[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 36 )[/C][C]85.8404347826087[/C][C]0.919948956603421[/C][C]93.3099974367528[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 36 )[/C][C]85.7554545454545[/C][C]0.909979755748232[/C][C]94.2388597150076[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 36 )[/C][C]85.6726190476191[/C][C]0.900499671560894[/C][C]95.1389786729374[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 36 )[/C][C]85.6255[/C][C]0.900175549118487[/C][C]95.1208906794351[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 36 )[/C][C]85.5684210526316[/C][C]0.898431423223571[/C][C]95.2420171877027[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 36 )[/C][C]85.5072222222222[/C][C]0.893929759244025[/C][C]95.6531778229797[/C][/ROW]
[ROW][C]Median[/C][C]85.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]87.015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]85.7478571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]86.0925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.7478571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]86.0925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]86.0925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]85.7478571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]86.0925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]85.9819298245614[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]108[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282209&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.59611111111111.0291283301879284.1451047172108
Geometric Mean85.9441878597696
Harmonic Mean85.2999931345459
Quadratic Mean87.2479839733126
Winsorized Mean ( 1 / 36 )86.59675925925931.028667772964584.1834084193163
Winsorized Mean ( 2 / 36 )86.59361111111111.0274950675557584.276425109372
Winsorized Mean ( 3 / 36 )86.5951.0268032412092684.3345604343999
Winsorized Mean ( 4 / 36 )86.60388888888891.0249979512962684.4917677926727
Winsorized Mean ( 5 / 36 )86.60666666666671.0245297868687884.5330880338372
Winsorized Mean ( 6 / 36 )86.59888888888891.0233428747033884.6235323756856
Winsorized Mean ( 7 / 36 )86.5904629629631.0212219025179684.7910358654299
Winsorized Mean ( 8 / 36 )86.58824074074071.0207385376012884.8290111042751
Winsorized Mean ( 9 / 36 )86.57490740740741.0181375779558185.0326216042727
Winsorized Mean ( 10 / 36 )86.58231481481481.0162776744761585.1955297152861
Winsorized Mean ( 11 / 36 )86.5651.0091613362741785.7791483764118
Winsorized Mean ( 12 / 36 )86.58722222222221.0064543079682986.0319455505283
Winsorized Mean ( 13 / 36 )86.61490740740741.0028221383574686.3711560549267
Winsorized Mean ( 14 / 36 )86.58379629629630.99821436904932586.7386795671521
Winsorized Mean ( 15 / 36 )86.62129629629630.98968425455843487.5241733889603
Winsorized Mean ( 16 / 36 )86.63759259259260.98633683260762187.8377342591426
Winsorized Mean ( 17 / 36 )86.6029629629630.97970590648032888.3968978752931
Winsorized Mean ( 18 / 36 )86.60629629629630.9793180653824288.4353095870614
Winsorized Mean ( 19 / 36 )86.59925925925930.97717010674169988.6225015089932
Winsorized Mean ( 20 / 36 )86.59740740740740.97649424307373788.6819436178368
Winsorized Mean ( 21 / 36 )86.60324074074080.97348176677181388.9623654975356
Winsorized Mean ( 22 / 36 )86.53398148148150.96493238759558989.6788029854674
Winsorized Mean ( 23 / 36 )86.60851851851850.95481763643333990.7068692635792
Winsorized Mean ( 24 / 36 )86.91740740740740.92049582905701494.4245532285012
Winsorized Mean ( 25 / 36 )86.93361111111110.91553655871759194.9537299011638
Winsorized Mean ( 26 / 36 )86.92879629629630.91493827158061295.010558631591
Winsorized Mean ( 27 / 36 )86.85879629629630.90339504946407896.1470802256706
Winsorized Mean ( 28 / 36 )86.79657407407410.89397213294939197.0909169033211
Winsorized Mean ( 29 / 36 )86.68916666666670.87354735399075299.2380851142552
Winsorized Mean ( 30 / 36 )86.92805555555550.807904747245552107.596911457602
Winsorized Mean ( 31 / 36 )86.91370370370370.797923627166445108.924840353892
Winsorized Mean ( 32 / 36 )86.78629629629630.772333884729544112.36888347413
Winsorized Mean ( 33 / 36 )86.24851851851850.703716987176735122.561370679059
Winsorized Mean ( 34 / 36 )86.30833333333330.696272967552532123.957610528405
Winsorized Mean ( 35 / 36 )86.28240740740740.693366505496517124.439826157482
Winsorized Mean ( 36 / 36 )86.27574074074070.689775338332073125.078030405323
Trimmed Mean ( 1 / 36 )86.58820754716981.0292295969760484.1291465010072
Trimmed Mean ( 2 / 36 )86.57932692307691.0294504401963484.1024720981847
Trimmed Mean ( 3 / 36 )86.57176470588241.0299456157953784.0546951006024
Trimmed Mean ( 4 / 36 )86.56341.0303327717810784.0149924090675
Trimmed Mean ( 5 / 36 )86.55224489795921.0308630025342683.9609576492516
Trimmed Mean ( 6 / 36 )86.541.0311024482426283.9295844438115
Trimmed Mean ( 7 / 36 )86.52872340425531.0311501712561583.9147641306653
Trimmed Mean ( 8 / 36 )86.51836956521741.0311238386790283.9068658096941
Trimmed Mean ( 9 / 36 )86.50788888888891.030665439558783.9340154123424
Trimmed Mean ( 10 / 36 )86.498751.0300572390343483.9747023001277
Trimmed Mean ( 11 / 36 )86.48825581395351.0291149052216784.0413984630069
Trimmed Mean ( 12 / 36 )86.47928571428571.0285451515018684.0792313181495
Trimmed Mean ( 13 / 36 )86.46743902439021.0276785246292884.1386065312421
Trimmed Mean ( 14 / 36 )86.4521251.0265633908199984.2150867380381
Trimmed Mean ( 15 / 36 )86.43910256410261.0252652846747984.3090113906668
Trimmed Mean ( 16 / 36 )86.42184210526321.0242120927306384.3788534802939
Trimmed Mean ( 17 / 36 )86.40216216216221.0227039511628984.4840406296627
Trimmed Mean ( 18 / 36 )86.38444444444441.0210712885237884.6017760124618
Trimmed Mean ( 19 / 36 )86.36542857142861.0184384524339484.8018143512022
Trimmed Mean ( 20 / 36 )86.34588235294121.0148518974735785.0822495064504
Trimmed Mean ( 21 / 36 )86.3253030303031.0099304880346385.4764798697147
Trimmed Mean ( 22 / 36 )86.302968751.0037223794774585.982907738822
Trimmed Mean ( 23 / 36 )86.28467741935480.9967360195336386.5672311709245
Trimmed Mean ( 24 / 36 )86.25933333333330.98893962120442387.2240645270928
Trimmed Mean ( 25 / 36 )86.2082758620690.98326896355182187.6751723665338
Trimmed Mean ( 26 / 36 )86.15232142857140.97605267818343488.2660571035086
Trimmed Mean ( 27 / 36 )86.09259259259260.96629889574494689.0951991890889
Trimmed Mean ( 28 / 36 )86.03365384615390.95515822087833990.0726727421552
Trimmed Mean ( 29 / 36 )85.97480.94191477754798291.2766229486407
Trimmed Mean ( 30 / 36 )85.9193750.92791558936123692.5939557273153
Trimmed Mean ( 31 / 36 )85.84043478260870.91994895660342193.3099974367528
Trimmed Mean ( 32 / 36 )85.75545454545450.90997975574823294.2388597150076
Trimmed Mean ( 33 / 36 )85.67261904761910.90049967156089495.1389786729374
Trimmed Mean ( 34 / 36 )85.62550.90017554911848795.1208906794351
Trimmed Mean ( 35 / 36 )85.56842105263160.89843142322357195.2420171877027
Trimmed Mean ( 36 / 36 )85.50722222222220.89392975924402595.6531778229797
Median85.925
Midrange87.015
Midmean - Weighted Average at Xnp85.7478571428571
Midmean - Weighted Average at X(n+1)p86.0925925925926
Midmean - Empirical Distribution Function85.7478571428571
Midmean - Empirical Distribution Function - Averaging86.0925925925926
Midmean - Empirical Distribution Function - Interpolation86.0925925925926
Midmean - Closest Observation85.7478571428571
Midmean - True Basic - Statistics Graphics Toolkit86.0925925925926
Midmean - MS Excel (old versions)85.9819298245614
Number of observations108



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')