Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 15:42:08 +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/2016/Mar/05/t1457193858nk6hunvsw0ugqf8.htm/, Retrieved Sat, 27 Apr 2024 11:15:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293501, Retrieved Sat, 27 Apr 2024 11:15:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 15:42:08] [aeeb828bd20a6dc3c22e186b82add773] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,1216
1,0569
1,0486
1,038
0,9865
0,9332
0,9052
0,8683
0,9232
0,8725
0,8903
0,8959
0,8766
0,9188
0,9838
0,9994
1,0731
1,1372
1,1248
1,189
1,2497
1,2046
1,222
1,2977
1,3113
1,2594
1,2199
1,1884
1,2023
1,2582
1,2743
1,2887
1,3106
1,3481
1,3738
1,4486
1,4976
1,5622
1,505
1,318
1,3029
1,3632
1,4303
1,4779
1,3829
1,2708
1,291
1,3583
1,368
1,4391
1,4127
1,3482
1,3108
1,2814
1,2502
1,2967
1,3206
1,3062
1,3242
1,361
1,3696
1,3711
1,3256
1,2498
1,1261
1,1053
1,1117
1,0953




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293501&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293501&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.218150.021641188566740356.288498029731
Geometric Mean1.20441372611054
Harmonic Mean1.18983760212822
Quadratic Mean1.2309623358791
Winsorized Mean ( 1 / 22 )1.217370588235290.021442246896495156.7743946850218
Winsorized Mean ( 2 / 22 )1.217273529411760.021370332448160356.9609074807141
Winsorized Mean ( 3 / 22 )1.217008823529410.021063000291476257.7794619326816
Winsorized Mean ( 4 / 22 )1.215614705882350.020682532325419858.774945289862
Winsorized Mean ( 5 / 22 )1.21560.020410212157546759.5584205894955
Winsorized Mean ( 6 / 22 )1.216023529411760.020015506731908260.7540716155446
Winsorized Mean ( 7 / 22 )1.214664705882350.019633933885239361.8655799180181
Winsorized Mean ( 8 / 22 )1.212335294117650.01887284978533464.2370022496417
Winsorized Mean ( 9 / 22 )1.217827941176470.017292216202702470.4263656491962
Winsorized Mean ( 10 / 22 )1.217827941176470.017158970455738770.9732524056637
Winsorized Mean ( 11 / 22 )1.219672058823530.016711277078287872.9849701557637
Winsorized Mean ( 12 / 22 )1.226201470588240.015378837450203679.7330405863676
Winsorized Mean ( 13 / 22 )1.227310294117650.014886497576504982.4445298707933
Winsorized Mean ( 14 / 22 )1.228566176470590.014520935449598584.6065448562104
Winsorized Mean ( 15 / 22 )1.231544117647060.013818345884288989.1238450650805
Winsorized Mean ( 16 / 22 )1.234391176470590.01261812747867297.8268113519254
Winsorized Mean ( 17 / 22 )1.236866176470590.0122079488437068101.316461291382
Winsorized Mean ( 18 / 22 )1.232604411764710.0111577546654307110.470650119562
Winsorized Mean ( 19 / 22 )1.234979411764710.010665783409011115.788907800371
Winsorized Mean ( 20 / 22 )1.234861764705880.0103853373941023118.904347335614
Winsorized Mean ( 21 / 22 )1.234460294117650.010223393086306120.748589406308
Winsorized Mean ( 22 / 22 )1.235883823529410.00939561514168539131.538361766883
Trimmed Mean ( 1 / 22 )1.218237878787880.021006136606451757.9943804808788
Trimmed Mean ( 2 / 22 )1.2191593750.020480187352701159.5287217838469
Trimmed Mean ( 3 / 22 )1.22019354838710.019890179032657761.3465342058338
Trimmed Mean ( 4 / 22 )1.221396666666670.019316737563423163.2299663779365
Trimmed Mean ( 5 / 22 )1.223091379310340.018757266514422165.2062697072591
Trimmed Mean ( 6 / 22 )1.224910714285710.018155771269222767.466740802257
Trimmed Mean ( 7 / 22 )1.226775925925930.017526960949750269.9936474693527
Trimmed Mean ( 8 / 22 )1.229038461538460.016841443655102172.9770254087524
Trimmed Mean ( 9 / 22 )1.2318780.016170028281120876.1827981116319
Trimmed Mean ( 10 / 22 )1.234089583333330.015736664465729278.421293535291
Trimmed Mean ( 11 / 22 )1.236493478260870.015201440435871681.3405468696937
Trimmed Mean ( 12 / 22 )1.238856818181820.014615708554532384.7620088728201
Trimmed Mean ( 13 / 22 )1.240564285714290.014195890942273887.3889698616958
Trimmed Mean ( 14 / 22 )1.24229750.013751764216656590.337318210801
Trimmed Mean ( 15 / 22 )1.244052631578950.013239064967242193.9683153347422
Trimmed Mean ( 16 / 22 )1.245627777777780.012726270548795197.8784611722493
Trimmed Mean ( 17 / 22 )1.247032352941180.0123409833579912101.048054013758
Trimmed Mean ( 18 / 22 )1.2483031250.0119020722683806104.88115824303
Trimmed Mean ( 19 / 22 )1.250280.011535730997868108.383248554519
Trimmed Mean ( 20 / 22 )1.252235714285710.0111295749932946112.514243808966
Trimmed Mean ( 21 / 22 )1.254507692307690.0105681698045476118.706239160528
Trimmed Mean ( 22 / 22 )1.25721250.00969654112935063129.655769333512
Median1.2651
Midrange1.21525
Midmean - Weighted Average at Xnp1.24269714285714
Midmean - Weighted Average at X(n+1)p1.24703235294118
Midmean - Empirical Distribution Function1.24269714285714
Midmean - Empirical Distribution Function - Averaging1.24703235294118
Midmean - Empirical Distribution Function - Interpolation1.24703235294118
Midmean - Closest Observation1.24269714285714
Midmean - True Basic - Statistics Graphics Toolkit1.24703235294118
Midmean - MS Excel (old versions)1.24562777777778
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.21815 & 0.0216411885667403 & 56.288498029731 \tabularnewline
Geometric Mean & 1.20441372611054 &  &  \tabularnewline
Harmonic Mean & 1.18983760212822 &  &  \tabularnewline
Quadratic Mean & 1.2309623358791 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 1.21737058823529 & 0.0214422468964951 & 56.7743946850218 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 1.21727352941176 & 0.0213703324481603 & 56.9609074807141 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 1.21700882352941 & 0.0210630002914762 & 57.7794619326816 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 1.21561470588235 & 0.0206825323254198 & 58.774945289862 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 1.2156 & 0.0204102121575467 & 59.5584205894955 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 1.21602352941176 & 0.0200155067319082 & 60.7540716155446 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 1.21466470588235 & 0.0196339338852393 & 61.8655799180181 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 1.21233529411765 & 0.018872849785334 & 64.2370022496417 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 1.21782794117647 & 0.0172922162027024 & 70.4263656491962 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 1.21782794117647 & 0.0171589704557387 & 70.9732524056637 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 1.21967205882353 & 0.0167112770782878 & 72.9849701557637 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 1.22620147058824 & 0.0153788374502036 & 79.7330405863676 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 1.22731029411765 & 0.0148864975765049 & 82.4445298707933 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 1.22856617647059 & 0.0145209354495985 & 84.6065448562104 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 1.23154411764706 & 0.0138183458842889 & 89.1238450650805 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 1.23439117647059 & 0.012618127478672 & 97.8268113519254 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 1.23686617647059 & 0.0122079488437068 & 101.316461291382 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 1.23260441176471 & 0.0111577546654307 & 110.470650119562 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 1.23497941176471 & 0.010665783409011 & 115.788907800371 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 1.23486176470588 & 0.0103853373941023 & 118.904347335614 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 1.23446029411765 & 0.010223393086306 & 120.748589406308 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 1.23588382352941 & 0.00939561514168539 & 131.538361766883 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 1.21823787878788 & 0.0210061366064517 & 57.9943804808788 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 1.219159375 & 0.0204801873527011 & 59.5287217838469 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 1.2201935483871 & 0.0198901790326577 & 61.3465342058338 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 1.22139666666667 & 0.0193167375634231 & 63.2299663779365 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 1.22309137931034 & 0.0187572665144221 & 65.2062697072591 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 1.22491071428571 & 0.0181557712692227 & 67.466740802257 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 1.22677592592593 & 0.0175269609497502 & 69.9936474693527 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 1.22903846153846 & 0.0168414436551021 & 72.9770254087524 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 1.231878 & 0.0161700282811208 & 76.1827981116319 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 1.23408958333333 & 0.0157366644657292 & 78.421293535291 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 1.23649347826087 & 0.0152014404358716 & 81.3405468696937 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 1.23885681818182 & 0.0146157085545323 & 84.7620088728201 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 1.24056428571429 & 0.0141958909422738 & 87.3889698616958 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 1.2422975 & 0.0137517642166565 & 90.337318210801 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 1.24405263157895 & 0.0132390649672421 & 93.9683153347422 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 1.24562777777778 & 0.0127262705487951 & 97.8784611722493 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 1.24703235294118 & 0.0123409833579912 & 101.048054013758 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 1.248303125 & 0.0119020722683806 & 104.88115824303 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 1.25028 & 0.011535730997868 & 108.383248554519 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 1.25223571428571 & 0.0111295749932946 & 112.514243808966 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 1.25450769230769 & 0.0105681698045476 & 118.706239160528 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 1.2572125 & 0.00969654112935063 & 129.655769333512 \tabularnewline
Median & 1.2651 &  &  \tabularnewline
Midrange & 1.21525 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.24269714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.24703235294118 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.24269714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.24703235294118 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.24703235294118 &  &  \tabularnewline
Midmean - Closest Observation & 1.24269714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.24703235294118 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.24562777777778 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293501&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]1.21815[/C][C]0.0216411885667403[/C][C]56.288498029731[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.20441372611054[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.18983760212822[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.2309623358791[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]1.21737058823529[/C][C]0.0214422468964951[/C][C]56.7743946850218[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]1.21727352941176[/C][C]0.0213703324481603[/C][C]56.9609074807141[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]1.21700882352941[/C][C]0.0210630002914762[/C][C]57.7794619326816[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]1.21561470588235[/C][C]0.0206825323254198[/C][C]58.774945289862[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]1.2156[/C][C]0.0204102121575467[/C][C]59.5584205894955[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]1.21602352941176[/C][C]0.0200155067319082[/C][C]60.7540716155446[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]1.21466470588235[/C][C]0.0196339338852393[/C][C]61.8655799180181[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]1.21233529411765[/C][C]0.018872849785334[/C][C]64.2370022496417[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]1.21782794117647[/C][C]0.0172922162027024[/C][C]70.4263656491962[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]1.21782794117647[/C][C]0.0171589704557387[/C][C]70.9732524056637[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]1.21967205882353[/C][C]0.0167112770782878[/C][C]72.9849701557637[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]1.22620147058824[/C][C]0.0153788374502036[/C][C]79.7330405863676[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]1.22731029411765[/C][C]0.0148864975765049[/C][C]82.4445298707933[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]1.22856617647059[/C][C]0.0145209354495985[/C][C]84.6065448562104[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]1.23154411764706[/C][C]0.0138183458842889[/C][C]89.1238450650805[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]1.23439117647059[/C][C]0.012618127478672[/C][C]97.8268113519254[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]1.23686617647059[/C][C]0.0122079488437068[/C][C]101.316461291382[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]1.23260441176471[/C][C]0.0111577546654307[/C][C]110.470650119562[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]1.23497941176471[/C][C]0.010665783409011[/C][C]115.788907800371[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]1.23486176470588[/C][C]0.0103853373941023[/C][C]118.904347335614[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]1.23446029411765[/C][C]0.010223393086306[/C][C]120.748589406308[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]1.23588382352941[/C][C]0.00939561514168539[/C][C]131.538361766883[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]1.21823787878788[/C][C]0.0210061366064517[/C][C]57.9943804808788[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]1.219159375[/C][C]0.0204801873527011[/C][C]59.5287217838469[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]1.2201935483871[/C][C]0.0198901790326577[/C][C]61.3465342058338[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]1.22139666666667[/C][C]0.0193167375634231[/C][C]63.2299663779365[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]1.22309137931034[/C][C]0.0187572665144221[/C][C]65.2062697072591[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]1.22491071428571[/C][C]0.0181557712692227[/C][C]67.466740802257[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]1.22677592592593[/C][C]0.0175269609497502[/C][C]69.9936474693527[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]1.22903846153846[/C][C]0.0168414436551021[/C][C]72.9770254087524[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]1.231878[/C][C]0.0161700282811208[/C][C]76.1827981116319[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]1.23408958333333[/C][C]0.0157366644657292[/C][C]78.421293535291[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]1.23649347826087[/C][C]0.0152014404358716[/C][C]81.3405468696937[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]1.23885681818182[/C][C]0.0146157085545323[/C][C]84.7620088728201[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]1.24056428571429[/C][C]0.0141958909422738[/C][C]87.3889698616958[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]1.2422975[/C][C]0.0137517642166565[/C][C]90.337318210801[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]1.24405263157895[/C][C]0.0132390649672421[/C][C]93.9683153347422[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]1.24562777777778[/C][C]0.0127262705487951[/C][C]97.8784611722493[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]1.24703235294118[/C][C]0.0123409833579912[/C][C]101.048054013758[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]1.248303125[/C][C]0.0119020722683806[/C][C]104.88115824303[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]1.25028[/C][C]0.011535730997868[/C][C]108.383248554519[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]1.25223571428571[/C][C]0.0111295749932946[/C][C]112.514243808966[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]1.25450769230769[/C][C]0.0105681698045476[/C][C]118.706239160528[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]1.2572125[/C][C]0.00969654112935063[/C][C]129.655769333512[/C][/ROW]
[ROW][C]Median[/C][C]1.2651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.21525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.24269714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.24703235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.24269714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.24703235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.24703235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.24269714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.24703235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.24562777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293501&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 Mean1.218150.021641188566740356.288498029731
Geometric Mean1.20441372611054
Harmonic Mean1.18983760212822
Quadratic Mean1.2309623358791
Winsorized Mean ( 1 / 22 )1.217370588235290.021442246896495156.7743946850218
Winsorized Mean ( 2 / 22 )1.217273529411760.021370332448160356.9609074807141
Winsorized Mean ( 3 / 22 )1.217008823529410.021063000291476257.7794619326816
Winsorized Mean ( 4 / 22 )1.215614705882350.020682532325419858.774945289862
Winsorized Mean ( 5 / 22 )1.21560.020410212157546759.5584205894955
Winsorized Mean ( 6 / 22 )1.216023529411760.020015506731908260.7540716155446
Winsorized Mean ( 7 / 22 )1.214664705882350.019633933885239361.8655799180181
Winsorized Mean ( 8 / 22 )1.212335294117650.01887284978533464.2370022496417
Winsorized Mean ( 9 / 22 )1.217827941176470.017292216202702470.4263656491962
Winsorized Mean ( 10 / 22 )1.217827941176470.017158970455738770.9732524056637
Winsorized Mean ( 11 / 22 )1.219672058823530.016711277078287872.9849701557637
Winsorized Mean ( 12 / 22 )1.226201470588240.015378837450203679.7330405863676
Winsorized Mean ( 13 / 22 )1.227310294117650.014886497576504982.4445298707933
Winsorized Mean ( 14 / 22 )1.228566176470590.014520935449598584.6065448562104
Winsorized Mean ( 15 / 22 )1.231544117647060.013818345884288989.1238450650805
Winsorized Mean ( 16 / 22 )1.234391176470590.01261812747867297.8268113519254
Winsorized Mean ( 17 / 22 )1.236866176470590.0122079488437068101.316461291382
Winsorized Mean ( 18 / 22 )1.232604411764710.0111577546654307110.470650119562
Winsorized Mean ( 19 / 22 )1.234979411764710.010665783409011115.788907800371
Winsorized Mean ( 20 / 22 )1.234861764705880.0103853373941023118.904347335614
Winsorized Mean ( 21 / 22 )1.234460294117650.010223393086306120.748589406308
Winsorized Mean ( 22 / 22 )1.235883823529410.00939561514168539131.538361766883
Trimmed Mean ( 1 / 22 )1.218237878787880.021006136606451757.9943804808788
Trimmed Mean ( 2 / 22 )1.2191593750.020480187352701159.5287217838469
Trimmed Mean ( 3 / 22 )1.22019354838710.019890179032657761.3465342058338
Trimmed Mean ( 4 / 22 )1.221396666666670.019316737563423163.2299663779365
Trimmed Mean ( 5 / 22 )1.223091379310340.018757266514422165.2062697072591
Trimmed Mean ( 6 / 22 )1.224910714285710.018155771269222767.466740802257
Trimmed Mean ( 7 / 22 )1.226775925925930.017526960949750269.9936474693527
Trimmed Mean ( 8 / 22 )1.229038461538460.016841443655102172.9770254087524
Trimmed Mean ( 9 / 22 )1.2318780.016170028281120876.1827981116319
Trimmed Mean ( 10 / 22 )1.234089583333330.015736664465729278.421293535291
Trimmed Mean ( 11 / 22 )1.236493478260870.015201440435871681.3405468696937
Trimmed Mean ( 12 / 22 )1.238856818181820.014615708554532384.7620088728201
Trimmed Mean ( 13 / 22 )1.240564285714290.014195890942273887.3889698616958
Trimmed Mean ( 14 / 22 )1.24229750.013751764216656590.337318210801
Trimmed Mean ( 15 / 22 )1.244052631578950.013239064967242193.9683153347422
Trimmed Mean ( 16 / 22 )1.245627777777780.012726270548795197.8784611722493
Trimmed Mean ( 17 / 22 )1.247032352941180.0123409833579912101.048054013758
Trimmed Mean ( 18 / 22 )1.2483031250.0119020722683806104.88115824303
Trimmed Mean ( 19 / 22 )1.250280.011535730997868108.383248554519
Trimmed Mean ( 20 / 22 )1.252235714285710.0111295749932946112.514243808966
Trimmed Mean ( 21 / 22 )1.254507692307690.0105681698045476118.706239160528
Trimmed Mean ( 22 / 22 )1.25721250.00969654112935063129.655769333512
Median1.2651
Midrange1.21525
Midmean - Weighted Average at Xnp1.24269714285714
Midmean - Weighted Average at X(n+1)p1.24703235294118
Midmean - Empirical Distribution Function1.24269714285714
Midmean - Empirical Distribution Function - Averaging1.24703235294118
Midmean - Empirical Distribution Function - Interpolation1.24703235294118
Midmean - Closest Observation1.24269714285714
Midmean - True Basic - Statistics Graphics Toolkit1.24703235294118
Midmean - MS Excel (old versions)1.24562777777778
Number of observations68



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')