Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 29 Mar 2011 16:52:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Mar/29/t1301417548xi9t6acik9ydxdf.htm/, Retrieved Sun, 12 May 2024 03:44:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=119801, Retrieved Sun, 12 May 2024 03:44:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Berekening Centru...] [2011-03-29 16:52:51] [d324b46bbfd5b5abf133f66a31553d9d] [Current]
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Dataseries X:
15,57
12,73
13,56
15,54
17,22
12,14
11,07
12,02
11,55
6,92
10,33
8,38
12,11
11,46
12,75
13,32
13
11,9
11,79
12,55
11,84
11,25
11,15
10,99
11,7
14,01
17,51
17,27
16,9
15,79
15,45
16,24
16,71
16,77
16,64
17,8
16,87
16,13
15,76
15,66
15,54
15,3
15,05
14,69
14,39
14,18
13,7
13,66
13,27
13,56
13,14
14,19
22,57
23,09
23,31
22,91
22,36
43,06
64,67
64,68
56,9
48,79
45,21
41,4
22,17
25,52
20,28
22,87
27,63
22,95
21,35
18,38
17,15
18,27
19,4
20,52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119801&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119801&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.13763157894741.3374553459464514.3089873145668
Geometric Mean17.0553994410916
Harmonic Mean15.7511002790208
Quadratic Mean22.3698000132227
Winsorized Mean ( 1 / 25 )19.15671052631581.335191850176414.3475340444783
Winsorized Mean ( 2 / 25 )19.00355263157891.241784167815315.3034264118637
Winsorized Mean ( 3 / 25 )18.70947368421051.1163239468009716.7598963883431
Winsorized Mean ( 4 / 25 )18.52526315789471.0501033111027317.6413720079037
Winsorized Mean ( 5 / 25 )18.38907894736841.002412496555318.344822127179
Winsorized Mean ( 6 / 25 )18.26592105263160.95906065478989419.0456369588357
Winsorized Mean ( 7 / 25 )17.01697368421050.58811014661555528.9350112085967
Winsorized Mean ( 8 / 25 )16.80434210526320.53597376001253631.3529194132006
Winsorized Mean ( 9 / 25 )16.56039473684210.48052746752422434.4629513525307
Winsorized Mean ( 10 / 25 )16.54328947368420.4735575841958434.9340608740895
Winsorized Mean ( 11 / 25 )16.53026315789470.46887349035089635.255273539828
Winsorized Mean ( 12 / 25 )16.53342105263160.46646225670941635.4442847514909
Winsorized Mean ( 13 / 25 )16.54710526315790.4625163748941735.7762582285742
Winsorized Mean ( 14 / 25 )16.50842105263160.45035872846305836.6561587669678
Winsorized Mean ( 15 / 25 )16.47289473684210.44218825140071737.2531262073586
Winsorized Mean ( 16 / 25 )16.51921052631580.42405448024524738.9553967611947
Winsorized Mean ( 17 / 25 )16.37605263157890.38697545499693342.3180654486439
Winsorized Mean ( 18 / 25 )16.18421052631580.35341408857817245.7939030994119
Winsorized Mean ( 19 / 25 )16.18671052631580.33562005398533548.2292709690794
Winsorized Mean ( 20 / 25 )15.99197368421050.29413005953249854.3704159637026
Winsorized Mean ( 21 / 25 )15.74605263157890.24749857904588563.620779934497
Winsorized Mean ( 22 / 25 )15.72868421052630.24107190032540265.2447846028324
Winsorized Mean ( 23 / 25 )15.65907894736840.21182640837562973.9241111032786
Winsorized Mean ( 24 / 25 )15.56750.19971067889113577.950263283047
Winsorized Mean ( 25 / 25 )15.52144736842110.18520834204502183.8053361799872
Trimmed Mean ( 1 / 25 )18.68729729729731.2137143368889115.3967838471762
Trimmed Mean ( 2 / 25 )18.19180555555561.0577397012877617.1987546022974
Trimmed Mean ( 3 / 25 )17.75114285714290.92645144460318919.1603596287185
Trimmed Mean ( 4 / 25 )17.39411764705880.82857452496935220.9928221576716
Trimmed Mean ( 5 / 25 )17.06848484848490.73334509131570623.274833431914
Trimmed Mean ( 6 / 25 )16.754843750.62802000493344326.6788376459053
Trimmed Mean ( 7 / 25 )16.44612903225810.50030706355643132.8720704348062
Trimmed Mean ( 8 / 25 )16.34283333333330.47421687401123434.4627832305819
Trimmed Mean ( 9 / 25 )16.26724137931030.45637182712330135.6447098889724
Trimmed Mean ( 10 / 25 )16.22303571428570.44793479346617936.2174047448954
Trimmed Mean ( 11 / 25 )16.1779629629630.43880263831238736.868426828933
Trimmed Mean ( 12 / 25 )16.13115384615380.4282093493799437.6711855299569
Trimmed Mean ( 13 / 25 )16.08020.41516856571660638.7317377274086
Trimmed Mean ( 14 / 25 )16.02333333333330.39921924393512440.136675715806
Trimmed Mean ( 15 / 25 )15.96608695652170.38147216463636641.8538714921474
Trimmed Mean ( 16 / 25 )15.90772727272730.36026004579443744.1562350819334
Trimmed Mean ( 17 / 25 )15.83857142857140.33639676594468847.0830074245591
Trimmed Mean ( 18 / 25 )15.77850.31488999910835850.107974355103
Trimmed Mean ( 19 / 25 )15.73342105263160.29571628119506653.2044464682457
Trimmed Mean ( 20 / 25 )15.68305555555560.27417663737679257.2005540136624
Trimmed Mean ( 21 / 25 )15.64852941176470.25749794743412660.7714724241363
Trimmed Mean ( 22 / 25 )15.63750.24852832966316262.9203922997188
Trimmed Mean ( 23 / 25 )15.6270.23724479331277865.8686742153186
Trimmed Mean ( 24 / 25 )15.62321428571430.22994481369871967.9433209838961
Trimmed Mean ( 25 / 25 )15.630.22241748686094570.2732515351721
Median15.615
Midrange35.8
Midmean - Weighted Average at Xnp15.6569230769231
Midmean - Weighted Average at X(n+1)p15.7334210526316
Midmean - Empirical Distribution Function15.6569230769231
Midmean - Empirical Distribution Function - Averaging15.7334210526316
Midmean - Empirical Distribution Function - Interpolation15.7334210526316
Midmean - Closest Observation15.6569230769231
Midmean - True Basic - Statistics Graphics Toolkit15.7334210526316
Midmean - MS Excel (old versions)15.7785
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.1376315789474 & 1.33745534594645 & 14.3089873145668 \tabularnewline
Geometric Mean & 17.0553994410916 &  &  \tabularnewline
Harmonic Mean & 15.7511002790208 &  &  \tabularnewline
Quadratic Mean & 22.3698000132227 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 19.1567105263158 & 1.3351918501764 & 14.3475340444783 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 19.0035526315789 & 1.2417841678153 & 15.3034264118637 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 18.7094736842105 & 1.11632394680097 & 16.7598963883431 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 18.5252631578947 & 1.05010331110273 & 17.6413720079037 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 18.3890789473684 & 1.0024124965553 & 18.344822127179 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 18.2659210526316 & 0.959060654789894 & 19.0456369588357 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 17.0169736842105 & 0.588110146615555 & 28.9350112085967 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 16.8043421052632 & 0.535973760012536 & 31.3529194132006 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 16.5603947368421 & 0.480527467524224 & 34.4629513525307 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 16.5432894736842 & 0.47355758419584 & 34.9340608740895 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 16.5302631578947 & 0.468873490350896 & 35.255273539828 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 16.5334210526316 & 0.466462256709416 & 35.4442847514909 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 16.5471052631579 & 0.46251637489417 & 35.7762582285742 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 16.5084210526316 & 0.450358728463058 & 36.6561587669678 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 16.4728947368421 & 0.442188251400717 & 37.2531262073586 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 16.5192105263158 & 0.424054480245247 & 38.9553967611947 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 16.3760526315789 & 0.386975454996933 & 42.3180654486439 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 16.1842105263158 & 0.353414088578172 & 45.7939030994119 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 16.1867105263158 & 0.335620053985335 & 48.2292709690794 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 15.9919736842105 & 0.294130059532498 & 54.3704159637026 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 15.7460526315789 & 0.247498579045885 & 63.620779934497 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 15.7286842105263 & 0.241071900325402 & 65.2447846028324 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 15.6590789473684 & 0.211826408375629 & 73.9241111032786 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 15.5675 & 0.199710678891135 & 77.950263283047 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 15.5214473684211 & 0.185208342045021 & 83.8053361799872 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 18.6872972972973 & 1.21371433688891 & 15.3967838471762 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 18.1918055555556 & 1.05773970128776 & 17.1987546022974 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 17.7511428571429 & 0.926451444603189 & 19.1603596287185 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 17.3941176470588 & 0.828574524969352 & 20.9928221576716 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 17.0684848484849 & 0.733345091315706 & 23.274833431914 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 16.75484375 & 0.628020004933443 & 26.6788376459053 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 16.4461290322581 & 0.500307063556431 & 32.8720704348062 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 16.3428333333333 & 0.474216874011234 & 34.4627832305819 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 16.2672413793103 & 0.456371827123301 & 35.6447098889724 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 16.2230357142857 & 0.447934793466179 & 36.2174047448954 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 16.177962962963 & 0.438802638312387 & 36.868426828933 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 16.1311538461538 & 0.42820934937994 & 37.6711855299569 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 16.0802 & 0.415168565716606 & 38.7317377274086 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 16.0233333333333 & 0.399219243935124 & 40.136675715806 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 15.9660869565217 & 0.381472164636366 & 41.8538714921474 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 15.9077272727273 & 0.360260045794437 & 44.1562350819334 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 15.8385714285714 & 0.336396765944688 & 47.0830074245591 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 15.7785 & 0.314889999108358 & 50.107974355103 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 15.7334210526316 & 0.295716281195066 & 53.2044464682457 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 15.6830555555556 & 0.274176637376792 & 57.2005540136624 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 15.6485294117647 & 0.257497947434126 & 60.7714724241363 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 15.6375 & 0.248528329663162 & 62.9203922997188 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 15.627 & 0.237244793312778 & 65.8686742153186 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 15.6232142857143 & 0.229944813698719 & 67.9433209838961 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 15.63 & 0.222417486860945 & 70.2732515351721 \tabularnewline
Median & 15.615 &  &  \tabularnewline
Midrange & 35.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.6569230769231 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.7334210526316 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.6569230769231 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.7334210526316 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.7334210526316 &  &  \tabularnewline
Midmean - Closest Observation & 15.6569230769231 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.7334210526316 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.7785 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119801&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]19.1376315789474[/C][C]1.33745534594645[/C][C]14.3089873145668[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.0553994410916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.7511002790208[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22.3698000132227[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]19.1567105263158[/C][C]1.3351918501764[/C][C]14.3475340444783[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]19.0035526315789[/C][C]1.2417841678153[/C][C]15.3034264118637[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]18.7094736842105[/C][C]1.11632394680097[/C][C]16.7598963883431[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]18.5252631578947[/C][C]1.05010331110273[/C][C]17.6413720079037[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]18.3890789473684[/C][C]1.0024124965553[/C][C]18.344822127179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]18.2659210526316[/C][C]0.959060654789894[/C][C]19.0456369588357[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]17.0169736842105[/C][C]0.588110146615555[/C][C]28.9350112085967[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]16.8043421052632[/C][C]0.535973760012536[/C][C]31.3529194132006[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]16.5603947368421[/C][C]0.480527467524224[/C][C]34.4629513525307[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]16.5432894736842[/C][C]0.47355758419584[/C][C]34.9340608740895[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]16.5302631578947[/C][C]0.468873490350896[/C][C]35.255273539828[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]16.5334210526316[/C][C]0.466462256709416[/C][C]35.4442847514909[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]16.5471052631579[/C][C]0.46251637489417[/C][C]35.7762582285742[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]16.5084210526316[/C][C]0.450358728463058[/C][C]36.6561587669678[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]16.4728947368421[/C][C]0.442188251400717[/C][C]37.2531262073586[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]16.5192105263158[/C][C]0.424054480245247[/C][C]38.9553967611947[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]16.3760526315789[/C][C]0.386975454996933[/C][C]42.3180654486439[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]16.1842105263158[/C][C]0.353414088578172[/C][C]45.7939030994119[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]16.1867105263158[/C][C]0.335620053985335[/C][C]48.2292709690794[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]15.9919736842105[/C][C]0.294130059532498[/C][C]54.3704159637026[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]15.7460526315789[/C][C]0.247498579045885[/C][C]63.620779934497[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]15.7286842105263[/C][C]0.241071900325402[/C][C]65.2447846028324[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]15.6590789473684[/C][C]0.211826408375629[/C][C]73.9241111032786[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]15.5675[/C][C]0.199710678891135[/C][C]77.950263283047[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]15.5214473684211[/C][C]0.185208342045021[/C][C]83.8053361799872[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]18.6872972972973[/C][C]1.21371433688891[/C][C]15.3967838471762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]18.1918055555556[/C][C]1.05773970128776[/C][C]17.1987546022974[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]17.7511428571429[/C][C]0.926451444603189[/C][C]19.1603596287185[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]17.3941176470588[/C][C]0.828574524969352[/C][C]20.9928221576716[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]17.0684848484849[/C][C]0.733345091315706[/C][C]23.274833431914[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]16.75484375[/C][C]0.628020004933443[/C][C]26.6788376459053[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]16.4461290322581[/C][C]0.500307063556431[/C][C]32.8720704348062[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]16.3428333333333[/C][C]0.474216874011234[/C][C]34.4627832305819[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]16.2672413793103[/C][C]0.456371827123301[/C][C]35.6447098889724[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]16.2230357142857[/C][C]0.447934793466179[/C][C]36.2174047448954[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]16.177962962963[/C][C]0.438802638312387[/C][C]36.868426828933[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]16.1311538461538[/C][C]0.42820934937994[/C][C]37.6711855299569[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]16.0802[/C][C]0.415168565716606[/C][C]38.7317377274086[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]16.0233333333333[/C][C]0.399219243935124[/C][C]40.136675715806[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]15.9660869565217[/C][C]0.381472164636366[/C][C]41.8538714921474[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]15.9077272727273[/C][C]0.360260045794437[/C][C]44.1562350819334[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]15.8385714285714[/C][C]0.336396765944688[/C][C]47.0830074245591[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]15.7785[/C][C]0.314889999108358[/C][C]50.107974355103[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]15.7334210526316[/C][C]0.295716281195066[/C][C]53.2044464682457[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]15.6830555555556[/C][C]0.274176637376792[/C][C]57.2005540136624[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]15.6485294117647[/C][C]0.257497947434126[/C][C]60.7714724241363[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]15.6375[/C][C]0.248528329663162[/C][C]62.9203922997188[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]15.627[/C][C]0.237244793312778[/C][C]65.8686742153186[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]15.6232142857143[/C][C]0.229944813698719[/C][C]67.9433209838961[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]15.63[/C][C]0.222417486860945[/C][C]70.2732515351721[/C][/ROW]
[ROW][C]Median[/C][C]15.615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]35.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.6569230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.7334210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.6569230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.7334210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.7334210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.6569230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.7334210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.7785[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]76[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119801&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 Mean19.13763157894741.3374553459464514.3089873145668
Geometric Mean17.0553994410916
Harmonic Mean15.7511002790208
Quadratic Mean22.3698000132227
Winsorized Mean ( 1 / 25 )19.15671052631581.335191850176414.3475340444783
Winsorized Mean ( 2 / 25 )19.00355263157891.241784167815315.3034264118637
Winsorized Mean ( 3 / 25 )18.70947368421051.1163239468009716.7598963883431
Winsorized Mean ( 4 / 25 )18.52526315789471.0501033111027317.6413720079037
Winsorized Mean ( 5 / 25 )18.38907894736841.002412496555318.344822127179
Winsorized Mean ( 6 / 25 )18.26592105263160.95906065478989419.0456369588357
Winsorized Mean ( 7 / 25 )17.01697368421050.58811014661555528.9350112085967
Winsorized Mean ( 8 / 25 )16.80434210526320.53597376001253631.3529194132006
Winsorized Mean ( 9 / 25 )16.56039473684210.48052746752422434.4629513525307
Winsorized Mean ( 10 / 25 )16.54328947368420.4735575841958434.9340608740895
Winsorized Mean ( 11 / 25 )16.53026315789470.46887349035089635.255273539828
Winsorized Mean ( 12 / 25 )16.53342105263160.46646225670941635.4442847514909
Winsorized Mean ( 13 / 25 )16.54710526315790.4625163748941735.7762582285742
Winsorized Mean ( 14 / 25 )16.50842105263160.45035872846305836.6561587669678
Winsorized Mean ( 15 / 25 )16.47289473684210.44218825140071737.2531262073586
Winsorized Mean ( 16 / 25 )16.51921052631580.42405448024524738.9553967611947
Winsorized Mean ( 17 / 25 )16.37605263157890.38697545499693342.3180654486439
Winsorized Mean ( 18 / 25 )16.18421052631580.35341408857817245.7939030994119
Winsorized Mean ( 19 / 25 )16.18671052631580.33562005398533548.2292709690794
Winsorized Mean ( 20 / 25 )15.99197368421050.29413005953249854.3704159637026
Winsorized Mean ( 21 / 25 )15.74605263157890.24749857904588563.620779934497
Winsorized Mean ( 22 / 25 )15.72868421052630.24107190032540265.2447846028324
Winsorized Mean ( 23 / 25 )15.65907894736840.21182640837562973.9241111032786
Winsorized Mean ( 24 / 25 )15.56750.19971067889113577.950263283047
Winsorized Mean ( 25 / 25 )15.52144736842110.18520834204502183.8053361799872
Trimmed Mean ( 1 / 25 )18.68729729729731.2137143368889115.3967838471762
Trimmed Mean ( 2 / 25 )18.19180555555561.0577397012877617.1987546022974
Trimmed Mean ( 3 / 25 )17.75114285714290.92645144460318919.1603596287185
Trimmed Mean ( 4 / 25 )17.39411764705880.82857452496935220.9928221576716
Trimmed Mean ( 5 / 25 )17.06848484848490.73334509131570623.274833431914
Trimmed Mean ( 6 / 25 )16.754843750.62802000493344326.6788376459053
Trimmed Mean ( 7 / 25 )16.44612903225810.50030706355643132.8720704348062
Trimmed Mean ( 8 / 25 )16.34283333333330.47421687401123434.4627832305819
Trimmed Mean ( 9 / 25 )16.26724137931030.45637182712330135.6447098889724
Trimmed Mean ( 10 / 25 )16.22303571428570.44793479346617936.2174047448954
Trimmed Mean ( 11 / 25 )16.1779629629630.43880263831238736.868426828933
Trimmed Mean ( 12 / 25 )16.13115384615380.4282093493799437.6711855299569
Trimmed Mean ( 13 / 25 )16.08020.41516856571660638.7317377274086
Trimmed Mean ( 14 / 25 )16.02333333333330.39921924393512440.136675715806
Trimmed Mean ( 15 / 25 )15.96608695652170.38147216463636641.8538714921474
Trimmed Mean ( 16 / 25 )15.90772727272730.36026004579443744.1562350819334
Trimmed Mean ( 17 / 25 )15.83857142857140.33639676594468847.0830074245591
Trimmed Mean ( 18 / 25 )15.77850.31488999910835850.107974355103
Trimmed Mean ( 19 / 25 )15.73342105263160.29571628119506653.2044464682457
Trimmed Mean ( 20 / 25 )15.68305555555560.27417663737679257.2005540136624
Trimmed Mean ( 21 / 25 )15.64852941176470.25749794743412660.7714724241363
Trimmed Mean ( 22 / 25 )15.63750.24852832966316262.9203922997188
Trimmed Mean ( 23 / 25 )15.6270.23724479331277865.8686742153186
Trimmed Mean ( 24 / 25 )15.62321428571430.22994481369871967.9433209838961
Trimmed Mean ( 25 / 25 )15.630.22241748686094570.2732515351721
Median15.615
Midrange35.8
Midmean - Weighted Average at Xnp15.6569230769231
Midmean - Weighted Average at X(n+1)p15.7334210526316
Midmean - Empirical Distribution Function15.6569230769231
Midmean - Empirical Distribution Function - Averaging15.7334210526316
Midmean - Empirical Distribution Function - Interpolation15.7334210526316
Midmean - Closest Observation15.6569230769231
Midmean - True Basic - Statistics Graphics Toolkit15.7334210526316
Midmean - MS Excel (old versions)15.7785
Number of observations76



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')