Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 14 Mar 2010 12:50:31 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/14/t1268592767ums7q6wt37pjchw.htm/, Retrieved Wed, 19 Jan 2022 10:20:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74407, Retrieved Wed, 19 Jan 2022 10:20:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centurmmaten - Wi...] [2010-03-14 18:50:31] [5c964c3d7ddd2ed48ce2db94081575d2] [Current]
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Dataseries X:
2550
2867
3458
2961
3163
2880
3331
3062
3534
3622
4464
5411
2564
2820
3508
3088
3299
2939
3320
3418
3604
3495
4163
4882
2211
3260
2992
2425
2707
3244
3965
3315
3333
3583
4021
4904
2252
2952
3573
3048
3059
2731
3563
3092
3478
3478
4308
5029
2075
3264
3308
3688
3136
2824
3644
4694
2914
3686
4358
5587
2265
3685
3754
3708
3210
3517
3905
3670
4221
4404
5086
5725
2367
3819
4067
4022
3937
4365
4290




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74407&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74407&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3545.8354430379787.643724277249640.4573798327098
Geometric Mean3464.43762502466
Harmonic Mean3385.20721563031
Quadratic Mean3629.33877403431
Winsorized Mean ( 1 / 26 )3545.8101265822886.746662596227340.8754644900482
Winsorized Mean ( 2 / 26 )3542.3924050632985.244967313971841.5554432910515
Winsorized Mean ( 3 / 26 )3530.5443037974781.906931766655643.1043408371788
Winsorized Mean ( 4 / 26 )3532.8227848101380.21749030738344.0405548873794
Winsorized Mean ( 5 / 26 )3528.5822784810177.696725236616645.414813400888
Winsorized Mean ( 6 / 26 )3536.4050632911475.657864559136246.7420681762302
Winsorized Mean ( 7 / 26 )3520.9873417721571.800510932913949.0384719554705
Winsorized Mean ( 8 / 26 )3512.1772151898764.758592881516954.2349217132589
Winsorized Mean ( 9 / 26 )3508.0759493670963.057803016824455.6327017677907
Winsorized Mean ( 10 / 26 )3514.4050632911460.44183987488358.1452363224894
Winsorized Mean ( 11 / 26 )3513.9873417721560.18434165208158.3870695485235
Winsorized Mean ( 12 / 26 )3512.9240506329157.885122140239960.6878576177494
Winsorized Mean ( 13 / 26 )3512.1012658227857.060518943619261.55046134952
Winsorized Mean ( 14 / 26 )3505.8987341772254.104511348943264.7986396470004
Winsorized Mean ( 15 / 26 )3499.6329113924151.599763545269167.8226540383685
Winsorized Mean ( 16 / 26 )3482.8227848101348.111518321777972.3906230004305
Winsorized Mean ( 17 / 26 )3475.0759493670946.350294631726774.9741933029354
Winsorized Mean ( 18 / 26 )3481.9113924050645.323959893557376.8227533644961
Winsorized Mean ( 19 / 26 )3481.9113924050641.451696762809183.999248868603
Winsorized Mean ( 20 / 26 )3477.6075949367140.026911661577886.881736576117
Winsorized Mean ( 21 / 26 )3469.8987341772238.680150455400589.7074776939692
Winsorized Mean ( 22 / 26 )3453.1898734177234.3289406879959100.591215581121
Winsorized Mean ( 23 / 26 )3435.4303797468431.6520902077992108.537235841074
Winsorized Mean ( 24 / 26 )3434.8227848101328.0316089464692122.533914887635
Winsorized Mean ( 25 / 26 )3437.0379746835426.08617682919131.757060346135
Winsorized Mean ( 26 / 26 )3451.8481012658223.9601400618685144.066273917960
Trimmed Mean ( 1 / 26 )3536.6363636363683.102739099015442.5573982516091
Trimmed Mean ( 2 / 26 )3526.9733333333378.781243419450544.7692011479797
Trimmed Mean ( 3 / 26 )3518.630136986374.619523264530247.1542832632764
Trimmed Mean ( 4 / 26 )3514.2112676056371.257983182239949.3167377277316
Trimmed Mean ( 5 / 26 )3508.8840579710167.886641811929651.6874007067824
Trimmed Mean ( 6 / 26 )3504.2388059701564.682598704000654.1759124738662
Trimmed Mean ( 7 / 26 )3497.7230769230861.41241616698956.9546566513891
Trimmed Mean ( 8 / 26 )3493.5555555555658.539498649099859.6786039541744
Trimmed Mean ( 9 / 26 )3490.5409836065656.839288217926261.4107089135872
Trimmed Mean ( 10 / 26 )3487.9322033898355.162126829528463.2305606012772
Trimmed Mean ( 11 / 26 )3484.2631578947453.676018773991964.912846322779
Trimmed Mean ( 12 / 26 )3480.3818181818251.888013906336567.0748705946673
Trimmed Mean ( 13 / 26 )3476.3396226415150.160380975336369.3044900187424
Trimmed Mean ( 14 / 26 )3472.0784313725548.165082488126672.0870442239659
Trimmed Mean ( 15 / 26 )3468.1836734693946.302958955688874.9019879439754
Trimmed Mean ( 16 / 26 )3464.6595744680844.48915797404377.8764924364161
Trimmed Mean ( 17 / 26 )3462.6666666666742.955238624090180.611044835978
Trimmed Mean ( 18 / 26 )3461.3255813953541.355771080885683.6963134994032
Trimmed Mean ( 19 / 26 )3459.1219512195139.47135724587787.6362555681015
Trimmed Mean ( 20 / 26 )3456.6923076923137.910473306160491.180404944472
Trimmed Mean ( 21 / 26 )3456.6923076923136.152176584040695.6150537618878
Trimmed Mean ( 22 / 26 )3452.834.1005630944907101.253459962889
Trimmed Mean ( 23 / 26 )3452.7575757575832.5175951876218106.181209152635
Trimmed Mean ( 24 / 26 )3454.6774193548431.0324279609951111.324754340751
Trimmed Mean ( 25 / 26 )3456.9310344827629.9779447266765115.315811874406
Trimmed Mean ( 26 / 26 )3459.2592592592628.9854857377736119.344533003674
Median3478
Midrange3900
Midmean - Weighted Average at Xnp3446.475
Midmean - Weighted Average at X(n+1)p3459.12195121951
Midmean - Empirical Distribution Function3459.12195121951
Midmean - Empirical Distribution Function - Averaging3459.12195121951
Midmean - Empirical Distribution Function - Interpolation3456.69230769231
Midmean - Closest Observation3446.475
Midmean - True Basic - Statistics Graphics Toolkit3459.12195121951
Midmean - MS Excel (old versions)3459.12195121951
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3545.83544303797 & 87.6437242772496 & 40.4573798327098 \tabularnewline
Geometric Mean & 3464.43762502466 &  &  \tabularnewline
Harmonic Mean & 3385.20721563031 &  &  \tabularnewline
Quadratic Mean & 3629.33877403431 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 3545.81012658228 & 86.7466625962273 & 40.8754644900482 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 3542.39240506329 & 85.2449673139718 & 41.5554432910515 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 3530.54430379747 & 81.9069317666556 & 43.1043408371788 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 3532.82278481013 & 80.217490307383 & 44.0405548873794 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 3528.58227848101 & 77.6967252366166 & 45.414813400888 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 3536.40506329114 & 75.6578645591362 & 46.7420681762302 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 3520.98734177215 & 71.8005109329139 & 49.0384719554705 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 3512.17721518987 & 64.7585928815169 & 54.2349217132589 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 3508.07594936709 & 63.0578030168244 & 55.6327017677907 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 3514.40506329114 & 60.441839874883 & 58.1452363224894 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 3513.98734177215 & 60.184341652081 & 58.3870695485235 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 3512.92405063291 & 57.8851221402399 & 60.6878576177494 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 3512.10126582278 & 57.0605189436192 & 61.55046134952 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 3505.89873417722 & 54.1045113489432 & 64.7986396470004 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 3499.63291139241 & 51.5997635452691 & 67.8226540383685 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 3482.82278481013 & 48.1115183217779 & 72.3906230004305 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 3475.07594936709 & 46.3502946317267 & 74.9741933029354 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 3481.91139240506 & 45.3239598935573 & 76.8227533644961 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 3481.91139240506 & 41.4516967628091 & 83.999248868603 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 3477.60759493671 & 40.0269116615778 & 86.881736576117 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 3469.89873417722 & 38.6801504554005 & 89.7074776939692 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 3453.18987341772 & 34.3289406879959 & 100.591215581121 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 3435.43037974684 & 31.6520902077992 & 108.537235841074 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 3434.82278481013 & 28.0316089464692 & 122.533914887635 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 3437.03797468354 & 26.08617682919 & 131.757060346135 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 3451.84810126582 & 23.9601400618685 & 144.066273917960 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 3536.63636363636 & 83.1027390990154 & 42.5573982516091 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 3526.97333333333 & 78.7812434194505 & 44.7692011479797 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 3518.6301369863 & 74.6195232645302 & 47.1542832632764 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 3514.21126760563 & 71.2579831822399 & 49.3167377277316 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 3508.88405797101 & 67.8866418119296 & 51.6874007067824 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 3504.23880597015 & 64.6825987040006 & 54.1759124738662 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 3497.72307692308 & 61.412416166989 & 56.9546566513891 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 3493.55555555556 & 58.5394986490998 & 59.6786039541744 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 3490.54098360656 & 56.8392882179262 & 61.4107089135872 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 3487.93220338983 & 55.1621268295284 & 63.2305606012772 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 3484.26315789474 & 53.6760187739919 & 64.912846322779 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 3480.38181818182 & 51.8880139063365 & 67.0748705946673 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 3476.33962264151 & 50.1603809753363 & 69.3044900187424 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 3472.07843137255 & 48.1650824881266 & 72.0870442239659 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 3468.18367346939 & 46.3029589556888 & 74.9019879439754 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 3464.65957446808 & 44.489157974043 & 77.8764924364161 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 3462.66666666667 & 42.9552386240901 & 80.611044835978 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 3461.32558139535 & 41.3557710808856 & 83.6963134994032 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 3459.12195121951 & 39.471357245877 & 87.6362555681015 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 3456.69230769231 & 37.9104733061604 & 91.180404944472 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 3456.69230769231 & 36.1521765840406 & 95.6150537618878 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 3452.8 & 34.1005630944907 & 101.253459962889 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 3452.75757575758 & 32.5175951876218 & 106.181209152635 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 3454.67741935484 & 31.0324279609951 & 111.324754340751 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 3456.93103448276 & 29.9779447266765 & 115.315811874406 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 3459.25925925926 & 28.9854857377736 & 119.344533003674 \tabularnewline
Median & 3478 &  &  \tabularnewline
Midrange & 3900 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3446.475 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3459.12195121951 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3459.12195121951 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3459.12195121951 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3456.69230769231 &  &  \tabularnewline
Midmean - Closest Observation & 3446.475 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3459.12195121951 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3459.12195121951 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74407&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]3545.83544303797[/C][C]87.6437242772496[/C][C]40.4573798327098[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3464.43762502466[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3385.20721563031[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3629.33877403431[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]3545.81012658228[/C][C]86.7466625962273[/C][C]40.8754644900482[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]3542.39240506329[/C][C]85.2449673139718[/C][C]41.5554432910515[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]3530.54430379747[/C][C]81.9069317666556[/C][C]43.1043408371788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]3532.82278481013[/C][C]80.217490307383[/C][C]44.0405548873794[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]3528.58227848101[/C][C]77.6967252366166[/C][C]45.414813400888[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]3536.40506329114[/C][C]75.6578645591362[/C][C]46.7420681762302[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]3520.98734177215[/C][C]71.8005109329139[/C][C]49.0384719554705[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]3512.17721518987[/C][C]64.7585928815169[/C][C]54.2349217132589[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]3508.07594936709[/C][C]63.0578030168244[/C][C]55.6327017677907[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]3514.40506329114[/C][C]60.441839874883[/C][C]58.1452363224894[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]3513.98734177215[/C][C]60.184341652081[/C][C]58.3870695485235[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]3512.92405063291[/C][C]57.8851221402399[/C][C]60.6878576177494[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]3512.10126582278[/C][C]57.0605189436192[/C][C]61.55046134952[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]3505.89873417722[/C][C]54.1045113489432[/C][C]64.7986396470004[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]3499.63291139241[/C][C]51.5997635452691[/C][C]67.8226540383685[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]3482.82278481013[/C][C]48.1115183217779[/C][C]72.3906230004305[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]3475.07594936709[/C][C]46.3502946317267[/C][C]74.9741933029354[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]3481.91139240506[/C][C]45.3239598935573[/C][C]76.8227533644961[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]3481.91139240506[/C][C]41.4516967628091[/C][C]83.999248868603[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]3477.60759493671[/C][C]40.0269116615778[/C][C]86.881736576117[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]3469.89873417722[/C][C]38.6801504554005[/C][C]89.7074776939692[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]3453.18987341772[/C][C]34.3289406879959[/C][C]100.591215581121[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]3435.43037974684[/C][C]31.6520902077992[/C][C]108.537235841074[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]3434.82278481013[/C][C]28.0316089464692[/C][C]122.533914887635[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]3437.03797468354[/C][C]26.08617682919[/C][C]131.757060346135[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]3451.84810126582[/C][C]23.9601400618685[/C][C]144.066273917960[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]3536.63636363636[/C][C]83.1027390990154[/C][C]42.5573982516091[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]3526.97333333333[/C][C]78.7812434194505[/C][C]44.7692011479797[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]3518.6301369863[/C][C]74.6195232645302[/C][C]47.1542832632764[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]3514.21126760563[/C][C]71.2579831822399[/C][C]49.3167377277316[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]3508.88405797101[/C][C]67.8866418119296[/C][C]51.6874007067824[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]3504.23880597015[/C][C]64.6825987040006[/C][C]54.1759124738662[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]3497.72307692308[/C][C]61.412416166989[/C][C]56.9546566513891[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]3493.55555555556[/C][C]58.5394986490998[/C][C]59.6786039541744[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]3490.54098360656[/C][C]56.8392882179262[/C][C]61.4107089135872[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]3487.93220338983[/C][C]55.1621268295284[/C][C]63.2305606012772[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]3484.26315789474[/C][C]53.6760187739919[/C][C]64.912846322779[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]3480.38181818182[/C][C]51.8880139063365[/C][C]67.0748705946673[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]3476.33962264151[/C][C]50.1603809753363[/C][C]69.3044900187424[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]3472.07843137255[/C][C]48.1650824881266[/C][C]72.0870442239659[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]3468.18367346939[/C][C]46.3029589556888[/C][C]74.9019879439754[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]3464.65957446808[/C][C]44.489157974043[/C][C]77.8764924364161[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]3462.66666666667[/C][C]42.9552386240901[/C][C]80.611044835978[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]3461.32558139535[/C][C]41.3557710808856[/C][C]83.6963134994032[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]3459.12195121951[/C][C]39.471357245877[/C][C]87.6362555681015[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]3456.69230769231[/C][C]37.9104733061604[/C][C]91.180404944472[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]3456.69230769231[/C][C]36.1521765840406[/C][C]95.6150537618878[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]3452.8[/C][C]34.1005630944907[/C][C]101.253459962889[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]3452.75757575758[/C][C]32.5175951876218[/C][C]106.181209152635[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]3454.67741935484[/C][C]31.0324279609951[/C][C]111.324754340751[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]3456.93103448276[/C][C]29.9779447266765[/C][C]115.315811874406[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]3459.25925925926[/C][C]28.9854857377736[/C][C]119.344533003674[/C][/ROW]
[ROW][C]Median[/C][C]3478[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3900[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3446.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3459.12195121951[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3459.12195121951[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3459.12195121951[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3456.69230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3446.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3459.12195121951[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3459.12195121951[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74407&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 Mean3545.8354430379787.643724277249640.4573798327098
Geometric Mean3464.43762502466
Harmonic Mean3385.20721563031
Quadratic Mean3629.33877403431
Winsorized Mean ( 1 / 26 )3545.8101265822886.746662596227340.8754644900482
Winsorized Mean ( 2 / 26 )3542.3924050632985.244967313971841.5554432910515
Winsorized Mean ( 3 / 26 )3530.5443037974781.906931766655643.1043408371788
Winsorized Mean ( 4 / 26 )3532.8227848101380.21749030738344.0405548873794
Winsorized Mean ( 5 / 26 )3528.5822784810177.696725236616645.414813400888
Winsorized Mean ( 6 / 26 )3536.4050632911475.657864559136246.7420681762302
Winsorized Mean ( 7 / 26 )3520.9873417721571.800510932913949.0384719554705
Winsorized Mean ( 8 / 26 )3512.1772151898764.758592881516954.2349217132589
Winsorized Mean ( 9 / 26 )3508.0759493670963.057803016824455.6327017677907
Winsorized Mean ( 10 / 26 )3514.4050632911460.44183987488358.1452363224894
Winsorized Mean ( 11 / 26 )3513.9873417721560.18434165208158.3870695485235
Winsorized Mean ( 12 / 26 )3512.9240506329157.885122140239960.6878576177494
Winsorized Mean ( 13 / 26 )3512.1012658227857.060518943619261.55046134952
Winsorized Mean ( 14 / 26 )3505.8987341772254.104511348943264.7986396470004
Winsorized Mean ( 15 / 26 )3499.6329113924151.599763545269167.8226540383685
Winsorized Mean ( 16 / 26 )3482.8227848101348.111518321777972.3906230004305
Winsorized Mean ( 17 / 26 )3475.0759493670946.350294631726774.9741933029354
Winsorized Mean ( 18 / 26 )3481.9113924050645.323959893557376.8227533644961
Winsorized Mean ( 19 / 26 )3481.9113924050641.451696762809183.999248868603
Winsorized Mean ( 20 / 26 )3477.6075949367140.026911661577886.881736576117
Winsorized Mean ( 21 / 26 )3469.8987341772238.680150455400589.7074776939692
Winsorized Mean ( 22 / 26 )3453.1898734177234.3289406879959100.591215581121
Winsorized Mean ( 23 / 26 )3435.4303797468431.6520902077992108.537235841074
Winsorized Mean ( 24 / 26 )3434.8227848101328.0316089464692122.533914887635
Winsorized Mean ( 25 / 26 )3437.0379746835426.08617682919131.757060346135
Winsorized Mean ( 26 / 26 )3451.8481012658223.9601400618685144.066273917960
Trimmed Mean ( 1 / 26 )3536.6363636363683.102739099015442.5573982516091
Trimmed Mean ( 2 / 26 )3526.9733333333378.781243419450544.7692011479797
Trimmed Mean ( 3 / 26 )3518.630136986374.619523264530247.1542832632764
Trimmed Mean ( 4 / 26 )3514.2112676056371.257983182239949.3167377277316
Trimmed Mean ( 5 / 26 )3508.8840579710167.886641811929651.6874007067824
Trimmed Mean ( 6 / 26 )3504.2388059701564.682598704000654.1759124738662
Trimmed Mean ( 7 / 26 )3497.7230769230861.41241616698956.9546566513891
Trimmed Mean ( 8 / 26 )3493.5555555555658.539498649099859.6786039541744
Trimmed Mean ( 9 / 26 )3490.5409836065656.839288217926261.4107089135872
Trimmed Mean ( 10 / 26 )3487.9322033898355.162126829528463.2305606012772
Trimmed Mean ( 11 / 26 )3484.2631578947453.676018773991964.912846322779
Trimmed Mean ( 12 / 26 )3480.3818181818251.888013906336567.0748705946673
Trimmed Mean ( 13 / 26 )3476.3396226415150.160380975336369.3044900187424
Trimmed Mean ( 14 / 26 )3472.0784313725548.165082488126672.0870442239659
Trimmed Mean ( 15 / 26 )3468.1836734693946.302958955688874.9019879439754
Trimmed Mean ( 16 / 26 )3464.6595744680844.48915797404377.8764924364161
Trimmed Mean ( 17 / 26 )3462.6666666666742.955238624090180.611044835978
Trimmed Mean ( 18 / 26 )3461.3255813953541.355771080885683.6963134994032
Trimmed Mean ( 19 / 26 )3459.1219512195139.47135724587787.6362555681015
Trimmed Mean ( 20 / 26 )3456.6923076923137.910473306160491.180404944472
Trimmed Mean ( 21 / 26 )3456.6923076923136.152176584040695.6150537618878
Trimmed Mean ( 22 / 26 )3452.834.1005630944907101.253459962889
Trimmed Mean ( 23 / 26 )3452.7575757575832.5175951876218106.181209152635
Trimmed Mean ( 24 / 26 )3454.6774193548431.0324279609951111.324754340751
Trimmed Mean ( 25 / 26 )3456.9310344827629.9779447266765115.315811874406
Trimmed Mean ( 26 / 26 )3459.2592592592628.9854857377736119.344533003674
Median3478
Midrange3900
Midmean - Weighted Average at Xnp3446.475
Midmean - Weighted Average at X(n+1)p3459.12195121951
Midmean - Empirical Distribution Function3459.12195121951
Midmean - Empirical Distribution Function - Averaging3459.12195121951
Midmean - Empirical Distribution Function - Interpolation3456.69230769231
Midmean - Closest Observation3446.475
Midmean - True Basic - Statistics Graphics Toolkit3459.12195121951
Midmean - MS Excel (old versions)3459.12195121951
Number of observations79



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')