Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 12:50:01 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t1476359423okmcgkc1dgxgqw6.htm/, Retrieved Tue, 30 Apr 2024 18:02:40 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 18:02:40 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
103,1
95,2
110,2
105,3
107,4
108,1
108
98,8
104,2
107,8
103,5
129,6
100,1
96
111,4
108,3
103,6
106,8
102,5
101
105,5
105,1
103,9
126,4
101
99,3
113,5
99,1
108,2
109,2
100,1
105,5
103
105,8
106,1
122,2
101,9
94,5
112,1
97,6
110
104,6
102,1
106
98,5
106,2
106
120,9
102,4
94,2
105,6
102,9
111,4
105,4
104,6
103,6
102,1
109,3
103,9
125,3
106,2
96,2
105,5
104,7
111
109,2
106,7
103,6
103,9
112,4
103,2
129,1
102,8
99,1
111,9
103,7
108,5
110,1
106,8




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

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

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

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

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.2088607594940.797599021767353133.160720939892
Geometric Mean105.987254112934
Harmonic Mean105.776437267457
Quadratic Mean106.442204559058
Winsorized Mean ( 1 / 26 )106.2063291139240.794514914445728133.67443100551
Winsorized Mean ( 2 / 26 )106.1556962025320.767008264292186138.402284753078
Winsorized Mean ( 3 / 26 )106.1443037974680.747651840348595141.970230084605
Winsorized Mean ( 4 / 26 )105.997468354430.696592938838234152.1655797017
Winsorized Mean ( 5 / 26 )106.0037974683540.657084931397039161.324346980501
Winsorized Mean ( 6 / 26 )105.5101265822780.503337110808327209.62119485455
Winsorized Mean ( 7 / 26 )105.4392405063290.479598101118319219.849161747029
Winsorized Mean ( 8 / 26 )105.4392405063290.468672663975128224.974163442835
Winsorized Mean ( 9 / 26 )105.4164556962030.464558332822789226.917586550783
Winsorized Mean ( 10 / 26 )105.3784810126580.449048439943144234.670631582643
Winsorized Mean ( 11 / 26 )105.4898734177220.430425900116128245.082541244058
Winsorized Mean ( 12 / 26 )105.4291139240510.419908460908794251.076421979862
Winsorized Mean ( 13 / 26 )105.4455696202530.374615663561691281.476670296486
Winsorized Mean ( 14 / 26 )105.4278481012660.371746130689706283.601736232369
Winsorized Mean ( 15 / 26 )105.5797468354430.343830399393386307.069261536256
Winsorized Mean ( 16 / 26 )105.4784810126580.315553078209356334.265416174067
Winsorized Mean ( 17 / 26 )105.4569620253160.312228764701446337.755434308414
Winsorized Mean ( 18 / 26 )105.5253164556960.302995262390244348.273816637385
Winsorized Mean ( 19 / 26 )105.3810126582280.274391575325183384.053382591431
Winsorized Mean ( 20 / 26 )105.4063291139240.256991442780282410.155015177071
Winsorized Mean ( 21 / 26 )105.4063291139240.249727808799895422.084867602331
Winsorized Mean ( 22 / 26 )105.4063291139240.24217947542932435.240554250382
Winsorized Mean ( 23 / 26 )105.4063291139240.234346632051231449.788111701477
Winsorized Mean ( 24 / 26 )105.3759493670890.221954780680446474.763143393614
Winsorized Mean ( 25 / 26 )105.3443037974680.192615598269369546.914708590457
Winsorized Mean ( 26 / 26 )105.1797468354430.162326278417372647.95267815483
Trimmed Mean ( 1 / 26 )106.0610389610390.742587327737961142.826351863716
Trimmed Mean ( 2 / 26 )105.9080.679267650150175155.914976926379
Trimmed Mean ( 3 / 26 )105.773972602740.620689174207929170.413754578078
Trimmed Mean ( 4 / 26 )105.636619718310.557871203256645189.356645587086
Trimmed Mean ( 5 / 26 )105.5333333333330.502048941933571210.205269882427
Trimmed Mean ( 6 / 26 )105.4223880597010.446792786636616235.953648341783
Trimmed Mean ( 7 / 26 )105.4046153846150.430101904121563245.068934535161
Trimmed Mean ( 8 / 26 )105.3984126984130.416317777516838253.168176788102
Trimmed Mean ( 9 / 26 )105.3918032786890.402317705261692261.961633555588
Trimmed Mean ( 10 / 26 )105.388135593220.386226062402017272.866452713705
Trimmed Mean ( 11 / 26 )105.3894736842110.370113816153977284.74882342778
Trimmed Mean ( 12 / 26 )105.3763636363640.354451856763921297.293868336394
Trimmed Mean ( 13 / 26 )105.3698113207550.337363474570549312.333193315864
Trimmed Mean ( 14 / 26 )105.3607843137250.326142978766982323.05090458195
Trimmed Mean ( 15 / 26 )105.353061224490.312550703924897337.075104619842
Trimmed Mean ( 16 / 26 )105.3276595744680.301257035380012349.627219299977
Trimmed Mean ( 17 / 26 )105.3111111111110.293020187917995359.398824563526
Trimmed Mean ( 18 / 26 )105.2953488372090.282920097747663372.173449943887
Trimmed Mean ( 19 / 26 )105.2707317073170.271518851307069387.710581422073
Trimmed Mean ( 20 / 26 )105.2589743589740.263366504394958399.667279636756
Trimmed Mean ( 21 / 26 )105.2589743589740.256288493499041410.70503369816
Trimmed Mean ( 22 / 26 )105.2257142857140.248096716609303424.131829408372
Trimmed Mean ( 23 / 26 )105.2060606060610.238402964264424441.295102729392
Trimmed Mean ( 24 / 26 )105.1838709677420.226620651916656464.140713029214
Trimmed Mean ( 25 / 26 )105.1620689655170.213371585099027492.858826149279
Trimmed Mean ( 26 / 26 )105.1407407407410.203897861368466515.653965348562
Median105.4
Midrange111.9
Midmean - Weighted Average at Xnp105.19
Midmean - Weighted Average at X(n+1)p105.270731707317
Midmean - Empirical Distribution Function105.270731707317
Midmean - Empirical Distribution Function - Averaging105.270731707317
Midmean - Empirical Distribution Function - Interpolation105.258974358974
Midmean - Closest Observation105.19
Midmean - True Basic - Statistics Graphics Toolkit105.270731707317
Midmean - MS Excel (old versions)105.270731707317
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.208860759494 & 0.797599021767353 & 133.160720939892 \tabularnewline
Geometric Mean & 105.987254112934 &  &  \tabularnewline
Harmonic Mean & 105.776437267457 &  &  \tabularnewline
Quadratic Mean & 106.442204559058 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 106.206329113924 & 0.794514914445728 & 133.67443100551 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 106.155696202532 & 0.767008264292186 & 138.402284753078 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 106.144303797468 & 0.747651840348595 & 141.970230084605 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 105.99746835443 & 0.696592938838234 & 152.1655797017 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 106.003797468354 & 0.657084931397039 & 161.324346980501 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 105.510126582278 & 0.503337110808327 & 209.62119485455 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 105.439240506329 & 0.479598101118319 & 219.849161747029 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 105.439240506329 & 0.468672663975128 & 224.974163442835 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 105.416455696203 & 0.464558332822789 & 226.917586550783 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 105.378481012658 & 0.449048439943144 & 234.670631582643 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 105.489873417722 & 0.430425900116128 & 245.082541244058 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 105.429113924051 & 0.419908460908794 & 251.076421979862 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 105.445569620253 & 0.374615663561691 & 281.476670296486 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 105.427848101266 & 0.371746130689706 & 283.601736232369 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 105.579746835443 & 0.343830399393386 & 307.069261536256 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 105.478481012658 & 0.315553078209356 & 334.265416174067 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 105.456962025316 & 0.312228764701446 & 337.755434308414 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 105.525316455696 & 0.302995262390244 & 348.273816637385 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 105.381012658228 & 0.274391575325183 & 384.053382591431 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 105.406329113924 & 0.256991442780282 & 410.155015177071 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 105.406329113924 & 0.249727808799895 & 422.084867602331 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 105.406329113924 & 0.24217947542932 & 435.240554250382 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 105.406329113924 & 0.234346632051231 & 449.788111701477 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 105.375949367089 & 0.221954780680446 & 474.763143393614 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 105.344303797468 & 0.192615598269369 & 546.914708590457 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 105.179746835443 & 0.162326278417372 & 647.95267815483 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 106.061038961039 & 0.742587327737961 & 142.826351863716 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 105.908 & 0.679267650150175 & 155.914976926379 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 105.77397260274 & 0.620689174207929 & 170.413754578078 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 105.63661971831 & 0.557871203256645 & 189.356645587086 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 105.533333333333 & 0.502048941933571 & 210.205269882427 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 105.422388059701 & 0.446792786636616 & 235.953648341783 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 105.404615384615 & 0.430101904121563 & 245.068934535161 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 105.398412698413 & 0.416317777516838 & 253.168176788102 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 105.391803278689 & 0.402317705261692 & 261.961633555588 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 105.38813559322 & 0.386226062402017 & 272.866452713705 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 105.389473684211 & 0.370113816153977 & 284.74882342778 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 105.376363636364 & 0.354451856763921 & 297.293868336394 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 105.369811320755 & 0.337363474570549 & 312.333193315864 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 105.360784313725 & 0.326142978766982 & 323.05090458195 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 105.35306122449 & 0.312550703924897 & 337.075104619842 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 105.327659574468 & 0.301257035380012 & 349.627219299977 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 105.311111111111 & 0.293020187917995 & 359.398824563526 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 105.295348837209 & 0.282920097747663 & 372.173449943887 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 105.270731707317 & 0.271518851307069 & 387.710581422073 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 105.258974358974 & 0.263366504394958 & 399.667279636756 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 105.258974358974 & 0.256288493499041 & 410.70503369816 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 105.225714285714 & 0.248096716609303 & 424.131829408372 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 105.206060606061 & 0.238402964264424 & 441.295102729392 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 105.183870967742 & 0.226620651916656 & 464.140713029214 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 105.162068965517 & 0.213371585099027 & 492.858826149279 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 105.140740740741 & 0.203897861368466 & 515.653965348562 \tabularnewline
Median & 105.4 &  &  \tabularnewline
Midrange & 111.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.19 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.270731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.270731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.270731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.258974358974 &  &  \tabularnewline
Midmean - Closest Observation & 105.19 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.270731707317 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.270731707317 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]106.208860759494[/C][C]0.797599021767353[/C][C]133.160720939892[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.987254112934[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.776437267457[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.442204559058[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]106.206329113924[/C][C]0.794514914445728[/C][C]133.67443100551[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]106.155696202532[/C][C]0.767008264292186[/C][C]138.402284753078[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]106.144303797468[/C][C]0.747651840348595[/C][C]141.970230084605[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]105.99746835443[/C][C]0.696592938838234[/C][C]152.1655797017[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]106.003797468354[/C][C]0.657084931397039[/C][C]161.324346980501[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]105.510126582278[/C][C]0.503337110808327[/C][C]209.62119485455[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]105.439240506329[/C][C]0.479598101118319[/C][C]219.849161747029[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]105.439240506329[/C][C]0.468672663975128[/C][C]224.974163442835[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]105.416455696203[/C][C]0.464558332822789[/C][C]226.917586550783[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]105.378481012658[/C][C]0.449048439943144[/C][C]234.670631582643[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]105.489873417722[/C][C]0.430425900116128[/C][C]245.082541244058[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]105.429113924051[/C][C]0.419908460908794[/C][C]251.076421979862[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]105.445569620253[/C][C]0.374615663561691[/C][C]281.476670296486[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]105.427848101266[/C][C]0.371746130689706[/C][C]283.601736232369[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]105.579746835443[/C][C]0.343830399393386[/C][C]307.069261536256[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]105.478481012658[/C][C]0.315553078209356[/C][C]334.265416174067[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]105.456962025316[/C][C]0.312228764701446[/C][C]337.755434308414[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]105.525316455696[/C][C]0.302995262390244[/C][C]348.273816637385[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]105.381012658228[/C][C]0.274391575325183[/C][C]384.053382591431[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]105.406329113924[/C][C]0.256991442780282[/C][C]410.155015177071[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]105.406329113924[/C][C]0.249727808799895[/C][C]422.084867602331[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]105.406329113924[/C][C]0.24217947542932[/C][C]435.240554250382[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]105.406329113924[/C][C]0.234346632051231[/C][C]449.788111701477[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]105.375949367089[/C][C]0.221954780680446[/C][C]474.763143393614[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]105.344303797468[/C][C]0.192615598269369[/C][C]546.914708590457[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]105.179746835443[/C][C]0.162326278417372[/C][C]647.95267815483[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]106.061038961039[/C][C]0.742587327737961[/C][C]142.826351863716[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]105.908[/C][C]0.679267650150175[/C][C]155.914976926379[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]105.77397260274[/C][C]0.620689174207929[/C][C]170.413754578078[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]105.63661971831[/C][C]0.557871203256645[/C][C]189.356645587086[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]105.533333333333[/C][C]0.502048941933571[/C][C]210.205269882427[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]105.422388059701[/C][C]0.446792786636616[/C][C]235.953648341783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]105.404615384615[/C][C]0.430101904121563[/C][C]245.068934535161[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]105.398412698413[/C][C]0.416317777516838[/C][C]253.168176788102[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]105.391803278689[/C][C]0.402317705261692[/C][C]261.961633555588[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]105.38813559322[/C][C]0.386226062402017[/C][C]272.866452713705[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]105.389473684211[/C][C]0.370113816153977[/C][C]284.74882342778[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]105.376363636364[/C][C]0.354451856763921[/C][C]297.293868336394[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]105.369811320755[/C][C]0.337363474570549[/C][C]312.333193315864[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]105.360784313725[/C][C]0.326142978766982[/C][C]323.05090458195[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]105.35306122449[/C][C]0.312550703924897[/C][C]337.075104619842[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]105.327659574468[/C][C]0.301257035380012[/C][C]349.627219299977[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]105.311111111111[/C][C]0.293020187917995[/C][C]359.398824563526[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]105.295348837209[/C][C]0.282920097747663[/C][C]372.173449943887[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]105.270731707317[/C][C]0.271518851307069[/C][C]387.710581422073[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]105.258974358974[/C][C]0.263366504394958[/C][C]399.667279636756[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]105.258974358974[/C][C]0.256288493499041[/C][C]410.70503369816[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]105.225714285714[/C][C]0.248096716609303[/C][C]424.131829408372[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]105.206060606061[/C][C]0.238402964264424[/C][C]441.295102729392[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]105.183870967742[/C][C]0.226620651916656[/C][C]464.140713029214[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]105.162068965517[/C][C]0.213371585099027[/C][C]492.858826149279[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]105.140740740741[/C][C]0.203897861368466[/C][C]515.653965348562[/C][/ROW]
[ROW][C]Median[/C][C]105.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.270731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.270731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.270731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.258974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.270731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.270731707317[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean106.2088607594940.797599021767353133.160720939892
Geometric Mean105.987254112934
Harmonic Mean105.776437267457
Quadratic Mean106.442204559058
Winsorized Mean ( 1 / 26 )106.2063291139240.794514914445728133.67443100551
Winsorized Mean ( 2 / 26 )106.1556962025320.767008264292186138.402284753078
Winsorized Mean ( 3 / 26 )106.1443037974680.747651840348595141.970230084605
Winsorized Mean ( 4 / 26 )105.997468354430.696592938838234152.1655797017
Winsorized Mean ( 5 / 26 )106.0037974683540.657084931397039161.324346980501
Winsorized Mean ( 6 / 26 )105.5101265822780.503337110808327209.62119485455
Winsorized Mean ( 7 / 26 )105.4392405063290.479598101118319219.849161747029
Winsorized Mean ( 8 / 26 )105.4392405063290.468672663975128224.974163442835
Winsorized Mean ( 9 / 26 )105.4164556962030.464558332822789226.917586550783
Winsorized Mean ( 10 / 26 )105.3784810126580.449048439943144234.670631582643
Winsorized Mean ( 11 / 26 )105.4898734177220.430425900116128245.082541244058
Winsorized Mean ( 12 / 26 )105.4291139240510.419908460908794251.076421979862
Winsorized Mean ( 13 / 26 )105.4455696202530.374615663561691281.476670296486
Winsorized Mean ( 14 / 26 )105.4278481012660.371746130689706283.601736232369
Winsorized Mean ( 15 / 26 )105.5797468354430.343830399393386307.069261536256
Winsorized Mean ( 16 / 26 )105.4784810126580.315553078209356334.265416174067
Winsorized Mean ( 17 / 26 )105.4569620253160.312228764701446337.755434308414
Winsorized Mean ( 18 / 26 )105.5253164556960.302995262390244348.273816637385
Winsorized Mean ( 19 / 26 )105.3810126582280.274391575325183384.053382591431
Winsorized Mean ( 20 / 26 )105.4063291139240.256991442780282410.155015177071
Winsorized Mean ( 21 / 26 )105.4063291139240.249727808799895422.084867602331
Winsorized Mean ( 22 / 26 )105.4063291139240.24217947542932435.240554250382
Winsorized Mean ( 23 / 26 )105.4063291139240.234346632051231449.788111701477
Winsorized Mean ( 24 / 26 )105.3759493670890.221954780680446474.763143393614
Winsorized Mean ( 25 / 26 )105.3443037974680.192615598269369546.914708590457
Winsorized Mean ( 26 / 26 )105.1797468354430.162326278417372647.95267815483
Trimmed Mean ( 1 / 26 )106.0610389610390.742587327737961142.826351863716
Trimmed Mean ( 2 / 26 )105.9080.679267650150175155.914976926379
Trimmed Mean ( 3 / 26 )105.773972602740.620689174207929170.413754578078
Trimmed Mean ( 4 / 26 )105.636619718310.557871203256645189.356645587086
Trimmed Mean ( 5 / 26 )105.5333333333330.502048941933571210.205269882427
Trimmed Mean ( 6 / 26 )105.4223880597010.446792786636616235.953648341783
Trimmed Mean ( 7 / 26 )105.4046153846150.430101904121563245.068934535161
Trimmed Mean ( 8 / 26 )105.3984126984130.416317777516838253.168176788102
Trimmed Mean ( 9 / 26 )105.3918032786890.402317705261692261.961633555588
Trimmed Mean ( 10 / 26 )105.388135593220.386226062402017272.866452713705
Trimmed Mean ( 11 / 26 )105.3894736842110.370113816153977284.74882342778
Trimmed Mean ( 12 / 26 )105.3763636363640.354451856763921297.293868336394
Trimmed Mean ( 13 / 26 )105.3698113207550.337363474570549312.333193315864
Trimmed Mean ( 14 / 26 )105.3607843137250.326142978766982323.05090458195
Trimmed Mean ( 15 / 26 )105.353061224490.312550703924897337.075104619842
Trimmed Mean ( 16 / 26 )105.3276595744680.301257035380012349.627219299977
Trimmed Mean ( 17 / 26 )105.3111111111110.293020187917995359.398824563526
Trimmed Mean ( 18 / 26 )105.2953488372090.282920097747663372.173449943887
Trimmed Mean ( 19 / 26 )105.2707317073170.271518851307069387.710581422073
Trimmed Mean ( 20 / 26 )105.2589743589740.263366504394958399.667279636756
Trimmed Mean ( 21 / 26 )105.2589743589740.256288493499041410.70503369816
Trimmed Mean ( 22 / 26 )105.2257142857140.248096716609303424.131829408372
Trimmed Mean ( 23 / 26 )105.2060606060610.238402964264424441.295102729392
Trimmed Mean ( 24 / 26 )105.1838709677420.226620651916656464.140713029214
Trimmed Mean ( 25 / 26 )105.1620689655170.213371585099027492.858826149279
Trimmed Mean ( 26 / 26 )105.1407407407410.203897861368466515.653965348562
Median105.4
Midrange111.9
Midmean - Weighted Average at Xnp105.19
Midmean - Weighted Average at X(n+1)p105.270731707317
Midmean - Empirical Distribution Function105.270731707317
Midmean - Empirical Distribution Function - Averaging105.270731707317
Midmean - Empirical Distribution Function - Interpolation105.258974358974
Midmean - Closest Observation105.19
Midmean - True Basic - Statistics Graphics Toolkit105.270731707317
Midmean - MS Excel (old versions)105.270731707317
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')