Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 12 Oct 2013 12:04:38 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/12/t1381593886d94kac485d0aiz8.htm/, Retrieved Sun, 28 Apr 2024 23:35:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214968, Retrieved Sun, 28 Apr 2024 23:35:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-12 16:04:38] [982f1398cb3cf8a81b54f385eadfb987] [Current]
Feedback Forum

Post a new message
Dataseries X:
110,12
112,28
113,77
114,38
119,06
119,94
120,98
122,33
121,7
123,73
121,73
119,75
117,4
120,99
125,18
126,41
129,38
131,93
129,34
128,58
125,37
123,25
122,78
120,37
116,83
116,39
120,69
123,51
127,43
125,99
120,62
113,71
110,79
108,15
111,22
112,65
112,47
117,48
122,46
123,46
122,33
129,2
129,22
131,17
120,22
120,38
115,32
112,25
109,83
107,05
112,87
113,68
115,08
120,61
119,14
118,63
115,78
117,26
117,61
113,92
113,65
115,89
116,55
117,78
117,36
121,09
124,26
121,88
119,52
122,49
120,86
120,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214968&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214968&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214968&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.413750.67057015767585178.077936563535
Geometric Mean119.280126368476
Harmonic Mean119.146554882848
Quadratic Mean119.547354035731
Winsorized Mean ( 1 / 24 )119.4184722222220.664056676754465179.831746901292
Winsorized Mean ( 2 / 24 )119.4154166666670.641916204679554186.029602923452
Winsorized Mean ( 3 / 24 )119.4258333333330.639042030193381186.88259565211
Winsorized Mean ( 4 / 24 )119.4563888888890.630162662060787189.564371361256
Winsorized Mean ( 5 / 24 )119.4848611111110.624181874334612191.426355080374
Winsorized Mean ( 6 / 24 )119.5190277777780.597628992883271199.988670564921
Winsorized Mean ( 7 / 24 )119.4101388888890.574170064895044207.969983441607
Winsorized Mean ( 8 / 24 )119.3179166666670.54899242384193217.339823802417
Winsorized Mean ( 9 / 24 )119.2879166666670.535648289352763222.698212685054
Winsorized Mean ( 10 / 24 )119.2323611111110.515511258946655231.289538379315
Winsorized Mean ( 11 / 24 )119.32250.49055925855113243.237688250793
Winsorized Mean ( 12 / 24 )119.1741666666670.465003775625374256.286449516226
Winsorized Mean ( 13 / 24 )119.0838888888890.449758349112132264.773047846632
Winsorized Mean ( 14 / 24 )119.0527777777780.441640898452049269.569186628905
Winsorized Mean ( 15 / 24 )119.0736111111110.434920365129665273.782560344378
Winsorized Mean ( 16 / 24 )119.1291666666670.411468834922739289.521724504446
Winsorized Mean ( 17 / 24 )119.1834722222220.369644129483678322.427607300835
Winsorized Mean ( 18 / 24 )119.1709722222220.350504005529332339.998888293017
Winsorized Mean ( 19 / 24 )119.2844444444440.330988400342877360.388594648257
Winsorized Mean ( 20 / 24 )119.2788888888890.321589457490198370.90422621371
Winsorized Mean ( 21 / 24 )119.4247222222220.300376001475177397.584100046993
Winsorized Mean ( 22 / 24 )119.3361111111110.275072159799665433.835656789198
Winsorized Mean ( 23 / 24 )119.3776388888890.256204884043625465.945992148073
Winsorized Mean ( 24 / 24 )119.5109722222220.235189228888279508.148152817801
Trimmed Mean ( 1 / 24 )119.4115714285710.641744021119335186.073523864379
Trimmed Mean ( 2 / 24 )119.4042647058820.615157828102432194.103462966905
Trimmed Mean ( 3 / 24 )119.3981818181820.597760658307004199.742455711865
Trimmed Mean ( 4 / 24 )119.38781250.578200653297547206.481628512727
Trimmed Mean ( 5 / 24 )119.3679032258060.557944219755317213.942360184598
Trimmed Mean ( 6 / 24 )119.3398333333330.535264203819733222.955005176331
Trimmed Mean ( 7 / 24 )119.302758620690.515492398950643231.43456404701
Trimmed Mean ( 8 / 24 )119.2830357142860.497760694578949239.639322697398
Trimmed Mean ( 9 / 24 )119.2772222222220.482360215839123247.278316713424
Trimmed Mean ( 10 / 24 )119.2755769230770.466414989244203255.728438565741
Trimmed Mean ( 11 / 24 )119.28180.451188244346786264.372579504353
Trimmed Mean ( 12 / 24 )119.276250.437717081401976272.496219745336
Trimmed Mean ( 13 / 24 )119.2895652173910.426239137764808279.865349397393
Trimmed Mean ( 14 / 24 )119.3154545454550.414585232318776287.794753030934
Trimmed Mean ( 15 / 24 )119.3476190476190.400934565829759297.673558777906
Trimmed Mean ( 16 / 24 )119.38050.384303390765481310.641287244981
Trimmed Mean ( 17 / 24 )119.4102631578950.367977921372538324.503879777626
Trimmed Mean ( 18 / 24 )119.4369444444440.356628128635472334.906124487245
Trimmed Mean ( 19 / 24 )119.4682352941180.345518409906557345.765180287866
Trimmed Mean ( 20 / 24 )119.490.335077627019519356.603934028216
Trimmed Mean ( 21 / 24 )119.5153333333330.322229921958474370.900792226041
Trimmed Mean ( 22 / 24 )119.5264285714290.309976195657872385.598733856817
Trimmed Mean ( 23 / 24 )119.5503846153850.299299428547724399.434055706264
Trimmed Mean ( 24 / 24 )119.5729166666670.28887492853439413.926252698084
Median120.08
Midrange119.49
Midmean - Weighted Average at Xnp119.319189189189
Midmean - Weighted Average at X(n+1)p119.436944444444
Midmean - Empirical Distribution Function119.319189189189
Midmean - Empirical Distribution Function - Averaging119.436944444444
Midmean - Empirical Distribution Function - Interpolation119.436944444444
Midmean - Closest Observation119.319189189189
Midmean - True Basic - Statistics Graphics Toolkit119.436944444444
Midmean - MS Excel (old versions)119.410263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.41375 & 0.67057015767585 & 178.077936563535 \tabularnewline
Geometric Mean & 119.280126368476 &  &  \tabularnewline
Harmonic Mean & 119.146554882848 &  &  \tabularnewline
Quadratic Mean & 119.547354035731 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 119.418472222222 & 0.664056676754465 & 179.831746901292 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 119.415416666667 & 0.641916204679554 & 186.029602923452 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 119.425833333333 & 0.639042030193381 & 186.88259565211 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 119.456388888889 & 0.630162662060787 & 189.564371361256 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 119.484861111111 & 0.624181874334612 & 191.426355080374 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 119.519027777778 & 0.597628992883271 & 199.988670564921 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 119.410138888889 & 0.574170064895044 & 207.969983441607 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 119.317916666667 & 0.54899242384193 & 217.339823802417 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 119.287916666667 & 0.535648289352763 & 222.698212685054 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 119.232361111111 & 0.515511258946655 & 231.289538379315 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 119.3225 & 0.49055925855113 & 243.237688250793 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 119.174166666667 & 0.465003775625374 & 256.286449516226 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 119.083888888889 & 0.449758349112132 & 264.773047846632 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 119.052777777778 & 0.441640898452049 & 269.569186628905 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 119.073611111111 & 0.434920365129665 & 273.782560344378 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 119.129166666667 & 0.411468834922739 & 289.521724504446 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 119.183472222222 & 0.369644129483678 & 322.427607300835 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 119.170972222222 & 0.350504005529332 & 339.998888293017 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 119.284444444444 & 0.330988400342877 & 360.388594648257 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 119.278888888889 & 0.321589457490198 & 370.90422621371 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 119.424722222222 & 0.300376001475177 & 397.584100046993 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 119.336111111111 & 0.275072159799665 & 433.835656789198 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 119.377638888889 & 0.256204884043625 & 465.945992148073 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 119.510972222222 & 0.235189228888279 & 508.148152817801 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 119.411571428571 & 0.641744021119335 & 186.073523864379 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 119.404264705882 & 0.615157828102432 & 194.103462966905 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 119.398181818182 & 0.597760658307004 & 199.742455711865 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 119.3878125 & 0.578200653297547 & 206.481628512727 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 119.367903225806 & 0.557944219755317 & 213.942360184598 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 119.339833333333 & 0.535264203819733 & 222.955005176331 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 119.30275862069 & 0.515492398950643 & 231.43456404701 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 119.283035714286 & 0.497760694578949 & 239.639322697398 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 119.277222222222 & 0.482360215839123 & 247.278316713424 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 119.275576923077 & 0.466414989244203 & 255.728438565741 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 119.2818 & 0.451188244346786 & 264.372579504353 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 119.27625 & 0.437717081401976 & 272.496219745336 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 119.289565217391 & 0.426239137764808 & 279.865349397393 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 119.315454545455 & 0.414585232318776 & 287.794753030934 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 119.347619047619 & 0.400934565829759 & 297.673558777906 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 119.3805 & 0.384303390765481 & 310.641287244981 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 119.410263157895 & 0.367977921372538 & 324.503879777626 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 119.436944444444 & 0.356628128635472 & 334.906124487245 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 119.468235294118 & 0.345518409906557 & 345.765180287866 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 119.49 & 0.335077627019519 & 356.603934028216 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 119.515333333333 & 0.322229921958474 & 370.900792226041 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 119.526428571429 & 0.309976195657872 & 385.598733856817 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 119.550384615385 & 0.299299428547724 & 399.434055706264 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 119.572916666667 & 0.28887492853439 & 413.926252698084 \tabularnewline
Median & 120.08 &  &  \tabularnewline
Midrange & 119.49 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 119.319189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 119.436944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 119.319189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 119.436944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 119.436944444444 &  &  \tabularnewline
Midmean - Closest Observation & 119.319189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 119.436944444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 119.410263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214968&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]119.41375[/C][C]0.67057015767585[/C][C]178.077936563535[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.280126368476[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]119.146554882848[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]119.547354035731[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]119.418472222222[/C][C]0.664056676754465[/C][C]179.831746901292[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]119.415416666667[/C][C]0.641916204679554[/C][C]186.029602923452[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]119.425833333333[/C][C]0.639042030193381[/C][C]186.88259565211[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]119.456388888889[/C][C]0.630162662060787[/C][C]189.564371361256[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]119.484861111111[/C][C]0.624181874334612[/C][C]191.426355080374[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]119.519027777778[/C][C]0.597628992883271[/C][C]199.988670564921[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]119.410138888889[/C][C]0.574170064895044[/C][C]207.969983441607[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]119.317916666667[/C][C]0.54899242384193[/C][C]217.339823802417[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]119.287916666667[/C][C]0.535648289352763[/C][C]222.698212685054[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]119.232361111111[/C][C]0.515511258946655[/C][C]231.289538379315[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]119.3225[/C][C]0.49055925855113[/C][C]243.237688250793[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]119.174166666667[/C][C]0.465003775625374[/C][C]256.286449516226[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]119.083888888889[/C][C]0.449758349112132[/C][C]264.773047846632[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]119.052777777778[/C][C]0.441640898452049[/C][C]269.569186628905[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]119.073611111111[/C][C]0.434920365129665[/C][C]273.782560344378[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]119.129166666667[/C][C]0.411468834922739[/C][C]289.521724504446[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]119.183472222222[/C][C]0.369644129483678[/C][C]322.427607300835[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]119.170972222222[/C][C]0.350504005529332[/C][C]339.998888293017[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]119.284444444444[/C][C]0.330988400342877[/C][C]360.388594648257[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]119.278888888889[/C][C]0.321589457490198[/C][C]370.90422621371[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]119.424722222222[/C][C]0.300376001475177[/C][C]397.584100046993[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]119.336111111111[/C][C]0.275072159799665[/C][C]433.835656789198[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]119.377638888889[/C][C]0.256204884043625[/C][C]465.945992148073[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]119.510972222222[/C][C]0.235189228888279[/C][C]508.148152817801[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]119.411571428571[/C][C]0.641744021119335[/C][C]186.073523864379[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]119.404264705882[/C][C]0.615157828102432[/C][C]194.103462966905[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]119.398181818182[/C][C]0.597760658307004[/C][C]199.742455711865[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]119.3878125[/C][C]0.578200653297547[/C][C]206.481628512727[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]119.367903225806[/C][C]0.557944219755317[/C][C]213.942360184598[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]119.339833333333[/C][C]0.535264203819733[/C][C]222.955005176331[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]119.30275862069[/C][C]0.515492398950643[/C][C]231.43456404701[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]119.283035714286[/C][C]0.497760694578949[/C][C]239.639322697398[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]119.277222222222[/C][C]0.482360215839123[/C][C]247.278316713424[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]119.275576923077[/C][C]0.466414989244203[/C][C]255.728438565741[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]119.2818[/C][C]0.451188244346786[/C][C]264.372579504353[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]119.27625[/C][C]0.437717081401976[/C][C]272.496219745336[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]119.289565217391[/C][C]0.426239137764808[/C][C]279.865349397393[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]119.315454545455[/C][C]0.414585232318776[/C][C]287.794753030934[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]119.347619047619[/C][C]0.400934565829759[/C][C]297.673558777906[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]119.3805[/C][C]0.384303390765481[/C][C]310.641287244981[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]119.410263157895[/C][C]0.367977921372538[/C][C]324.503879777626[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]119.436944444444[/C][C]0.356628128635472[/C][C]334.906124487245[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]119.468235294118[/C][C]0.345518409906557[/C][C]345.765180287866[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]119.49[/C][C]0.335077627019519[/C][C]356.603934028216[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]119.515333333333[/C][C]0.322229921958474[/C][C]370.900792226041[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]119.526428571429[/C][C]0.309976195657872[/C][C]385.598733856817[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]119.550384615385[/C][C]0.299299428547724[/C][C]399.434055706264[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]119.572916666667[/C][C]0.28887492853439[/C][C]413.926252698084[/C][/ROW]
[ROW][C]Median[/C][C]120.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]119.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]119.319189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]119.436944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]119.319189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]119.436944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]119.436944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]119.319189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]119.436944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]119.410263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214968&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214968&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 Mean119.413750.67057015767585178.077936563535
Geometric Mean119.280126368476
Harmonic Mean119.146554882848
Quadratic Mean119.547354035731
Winsorized Mean ( 1 / 24 )119.4184722222220.664056676754465179.831746901292
Winsorized Mean ( 2 / 24 )119.4154166666670.641916204679554186.029602923452
Winsorized Mean ( 3 / 24 )119.4258333333330.639042030193381186.88259565211
Winsorized Mean ( 4 / 24 )119.4563888888890.630162662060787189.564371361256
Winsorized Mean ( 5 / 24 )119.4848611111110.624181874334612191.426355080374
Winsorized Mean ( 6 / 24 )119.5190277777780.597628992883271199.988670564921
Winsorized Mean ( 7 / 24 )119.4101388888890.574170064895044207.969983441607
Winsorized Mean ( 8 / 24 )119.3179166666670.54899242384193217.339823802417
Winsorized Mean ( 9 / 24 )119.2879166666670.535648289352763222.698212685054
Winsorized Mean ( 10 / 24 )119.2323611111110.515511258946655231.289538379315
Winsorized Mean ( 11 / 24 )119.32250.49055925855113243.237688250793
Winsorized Mean ( 12 / 24 )119.1741666666670.465003775625374256.286449516226
Winsorized Mean ( 13 / 24 )119.0838888888890.449758349112132264.773047846632
Winsorized Mean ( 14 / 24 )119.0527777777780.441640898452049269.569186628905
Winsorized Mean ( 15 / 24 )119.0736111111110.434920365129665273.782560344378
Winsorized Mean ( 16 / 24 )119.1291666666670.411468834922739289.521724504446
Winsorized Mean ( 17 / 24 )119.1834722222220.369644129483678322.427607300835
Winsorized Mean ( 18 / 24 )119.1709722222220.350504005529332339.998888293017
Winsorized Mean ( 19 / 24 )119.2844444444440.330988400342877360.388594648257
Winsorized Mean ( 20 / 24 )119.2788888888890.321589457490198370.90422621371
Winsorized Mean ( 21 / 24 )119.4247222222220.300376001475177397.584100046993
Winsorized Mean ( 22 / 24 )119.3361111111110.275072159799665433.835656789198
Winsorized Mean ( 23 / 24 )119.3776388888890.256204884043625465.945992148073
Winsorized Mean ( 24 / 24 )119.5109722222220.235189228888279508.148152817801
Trimmed Mean ( 1 / 24 )119.4115714285710.641744021119335186.073523864379
Trimmed Mean ( 2 / 24 )119.4042647058820.615157828102432194.103462966905
Trimmed Mean ( 3 / 24 )119.3981818181820.597760658307004199.742455711865
Trimmed Mean ( 4 / 24 )119.38781250.578200653297547206.481628512727
Trimmed Mean ( 5 / 24 )119.3679032258060.557944219755317213.942360184598
Trimmed Mean ( 6 / 24 )119.3398333333330.535264203819733222.955005176331
Trimmed Mean ( 7 / 24 )119.302758620690.515492398950643231.43456404701
Trimmed Mean ( 8 / 24 )119.2830357142860.497760694578949239.639322697398
Trimmed Mean ( 9 / 24 )119.2772222222220.482360215839123247.278316713424
Trimmed Mean ( 10 / 24 )119.2755769230770.466414989244203255.728438565741
Trimmed Mean ( 11 / 24 )119.28180.451188244346786264.372579504353
Trimmed Mean ( 12 / 24 )119.276250.437717081401976272.496219745336
Trimmed Mean ( 13 / 24 )119.2895652173910.426239137764808279.865349397393
Trimmed Mean ( 14 / 24 )119.3154545454550.414585232318776287.794753030934
Trimmed Mean ( 15 / 24 )119.3476190476190.400934565829759297.673558777906
Trimmed Mean ( 16 / 24 )119.38050.384303390765481310.641287244981
Trimmed Mean ( 17 / 24 )119.4102631578950.367977921372538324.503879777626
Trimmed Mean ( 18 / 24 )119.4369444444440.356628128635472334.906124487245
Trimmed Mean ( 19 / 24 )119.4682352941180.345518409906557345.765180287866
Trimmed Mean ( 20 / 24 )119.490.335077627019519356.603934028216
Trimmed Mean ( 21 / 24 )119.5153333333330.322229921958474370.900792226041
Trimmed Mean ( 22 / 24 )119.5264285714290.309976195657872385.598733856817
Trimmed Mean ( 23 / 24 )119.5503846153850.299299428547724399.434055706264
Trimmed Mean ( 24 / 24 )119.5729166666670.28887492853439413.926252698084
Median120.08
Midrange119.49
Midmean - Weighted Average at Xnp119.319189189189
Midmean - Weighted Average at X(n+1)p119.436944444444
Midmean - Empirical Distribution Function119.319189189189
Midmean - Empirical Distribution Function - Averaging119.436944444444
Midmean - Empirical Distribution Function - Interpolation119.436944444444
Midmean - Closest Observation119.319189189189
Midmean - True Basic - Statistics Graphics Toolkit119.436944444444
Midmean - MS Excel (old versions)119.410263157895
Number of observations72



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')