Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Dec 2014 14:30:26 +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/2014/Dec/17/t1418826807o4v0yc4r4bhi33t.htm/, Retrieved Thu, 16 May 2024 20:56:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270338, Retrieved Thu, 16 May 2024 20:56:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact47
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [hfghgfh] [2014-12-17 14:30:26] [ca907db95fc0b179b22bb0898c34dff4] [Current]
Feedback Forum

Post a new message
Dataseries X:
108
73
34
72
74
66
41
57
51
79
39
55
55
22
37
2
39
33
43
23
44
39
23
78
27
51
31
24
14
41
74
62
59
54
36
42
25
31
17
55
62
49
72
9
55
78
69
22
51
67
21
44
45
36
43
40
61
43
20
57
36
61
69
21
34
51
19
42
22
85
51
73
61
54
26
30




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=270338&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=270338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270338&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 Mean46.17105263157892.3359425129533319.7654918199185
Geometric Mean40.5692404105223
Harmonic Mean30.2175329633018
Quadratic Mean50.4084631574375
Winsorized Mean ( 1 / 25 )45.96052631578952.2248548771496820.6577636985791
Winsorized Mean ( 2 / 25 )45.93421052631582.162709113817221.2391995913132
Winsorized Mean ( 3 / 25 )46.01315789473682.132332009059721.5787962189938
Winsorized Mean ( 4 / 25 )46.11842105263162.1137782838854421.8180030536879
Winsorized Mean ( 5 / 25 )45.92105263157892.0521074454526922.3775089035111
Winsorized Mean ( 6 / 25 )462.0390056055953222.5600164481008
Winsorized Mean ( 7 / 25 )45.90789473684212.022346876347722.7003068928266
Winsorized Mean ( 8 / 25 )46.01315789473682.005299419481522.945779292468
Winsorized Mean ( 9 / 25 )45.89473684210531.9842873083008123.1290784606217
Winsorized Mean ( 10 / 25 )45.89473684210531.9842873083008123.1290784606217
Winsorized Mean ( 11 / 25 )45.60526315789471.8870824922111824.1670744899217
Winsorized Mean ( 12 / 25 )45.60526315789471.8870824922111824.1670744899217
Winsorized Mean ( 13 / 25 )45.43421052631581.8043160269262925.1808496118689
Winsorized Mean ( 14 / 25 )45.43421052631581.7462074720803926.0187928712654
Winsorized Mean ( 15 / 25 )44.84210526315791.5964931559656828.0878781694708
Winsorized Mean ( 16 / 25 )45.05263157894741.5637219137216728.8111531747494
Winsorized Mean ( 17 / 25 )45.51.4311693170394231.792185214062
Winsorized Mean ( 18 / 25 )45.73684210526321.3974121974178432.7296714525438
Winsorized Mean ( 19 / 25 )45.73684210526321.3974121974178432.7296714525438
Winsorized Mean ( 20 / 25 )45.73684210526321.2489108828702736.6213816634777
Winsorized Mean ( 21 / 25 )45.46052631578951.1348453468287440.0587854925135
Winsorized Mean ( 22 / 25 )45.46052631578951.1348453468287440.0587854925135
Winsorized Mean ( 23 / 25 )45.46052631578950.9741286325726146.6678884037431
Winsorized Mean ( 24 / 25 )45.46052631578950.9741286325726146.6678884037431
Winsorized Mean ( 25 / 25 )45.46052631578950.9741286325726146.6678884037431
Trimmed Mean ( 1 / 25 )45.93243243243242.1651826597422521.2141143038252
Trimmed Mean ( 2 / 25 )45.90277777777782.0948890523639921.9117941954867
Trimmed Mean ( 3 / 25 )45.88571428571432.0511616520987622.3705987476724
Trimmed Mean ( 4 / 25 )45.83823529411762.0126477057807622.7750913199862
Trimmed Mean ( 5 / 25 )45.75757575757581.973018537000523.1916603414883
Trimmed Mean ( 6 / 25 )45.718751.9440932045292523.5167480105823
Trimmed Mean ( 7 / 25 )45.66129032258061.9121288327057523.8798189439818
Trimmed Mean ( 8 / 25 )45.61666666666671.8770230768120924.302666935849
Trimmed Mean ( 9 / 25 )45.5517241379311.8376601442275624.7878936053642
Trimmed Mean ( 10 / 25 )45.51.7937481616805825.3658796546838
Trimmed Mean ( 11 / 25 )45.44444444444441.739030040955326.1320640668637
Trimmed Mean ( 12 / 25 )45.42307692307691.6924876498312126.8380551713963
Trimmed Mean ( 13 / 25 )45.41.6335762695911827.7917847149934
Trimmed Mean ( 14 / 25 )45.39583333333331.5774169745079228.7785880759237
Trimmed Mean ( 15 / 25 )45.39130434782611.5184782176437429.8926279089211
Trimmed Mean ( 16 / 25 )45.45454545454551.4758286973874330.7993370334991
Trimmed Mean ( 17 / 25 )45.51.4269880888806331.8853397267607
Trimmed Mean ( 18 / 25 )45.51.3927467787590132.6692552400246
Trimmed Mean ( 19 / 25 )45.47368421052631.3534303091983433.5988368972328
Trimmed Mean ( 20 / 25 )45.44444444444441.2986222518832934.9943521902078
Trimmed Mean ( 21 / 25 )45.41176470588241.2617488125845435.9911293380666
Trimmed Mean ( 22 / 25 )45.406251.238543772098236.6609973929933
Trimmed Mean ( 23 / 25 )45.41.2021054326740137.7670699807175
Trimmed Mean ( 24 / 25 )45.39285714285711.1933892929531238.0369234171102
Trimmed Mean ( 25 / 25 )45.38461538461541.1741798094210638.6521851427447
Median43.5
Midrange55
Midmean - Weighted Average at Xnp45.8780487804878
Midmean - Weighted Average at X(n+1)p45.8780487804878
Midmean - Empirical Distribution Function45.8780487804878
Midmean - Empirical Distribution Function - Averaging45.8780487804878
Midmean - Empirical Distribution Function - Interpolation45.8780487804878
Midmean - Closest Observation45.8780487804878
Midmean - True Basic - Statistics Graphics Toolkit45.8780487804878
Midmean - MS Excel (old versions)45.8780487804878
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 46.1710526315789 & 2.33594251295333 & 19.7654918199185 \tabularnewline
Geometric Mean & 40.5692404105223 &  &  \tabularnewline
Harmonic Mean & 30.2175329633018 &  &  \tabularnewline
Quadratic Mean & 50.4084631574375 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 45.9605263157895 & 2.22485487714968 & 20.6577636985791 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 45.9342105263158 & 2.1627091138172 & 21.2391995913132 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 46.0131578947368 & 2.1323320090597 & 21.5787962189938 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 46.1184210526316 & 2.11377828388544 & 21.8180030536879 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 45.9210526315789 & 2.05210744545269 & 22.3775089035111 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 46 & 2.03900560559532 & 22.5600164481008 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 45.9078947368421 & 2.0223468763477 & 22.7003068928266 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 46.0131578947368 & 2.0052994194815 & 22.945779292468 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 45.8947368421053 & 1.98428730830081 & 23.1290784606217 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 45.8947368421053 & 1.98428730830081 & 23.1290784606217 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 45.6052631578947 & 1.88708249221118 & 24.1670744899217 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 45.6052631578947 & 1.88708249221118 & 24.1670744899217 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 45.4342105263158 & 1.80431602692629 & 25.1808496118689 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 45.4342105263158 & 1.74620747208039 & 26.0187928712654 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 44.8421052631579 & 1.59649315596568 & 28.0878781694708 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 45.0526315789474 & 1.56372191372167 & 28.8111531747494 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 45.5 & 1.43116931703942 & 31.792185214062 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 45.7368421052632 & 1.39741219741784 & 32.7296714525438 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 45.7368421052632 & 1.39741219741784 & 32.7296714525438 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 45.7368421052632 & 1.24891088287027 & 36.6213816634777 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 45.4605263157895 & 1.13484534682874 & 40.0587854925135 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 45.4605263157895 & 1.13484534682874 & 40.0587854925135 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 45.4605263157895 & 0.97412863257261 & 46.6678884037431 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 45.4605263157895 & 0.97412863257261 & 46.6678884037431 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 45.4605263157895 & 0.97412863257261 & 46.6678884037431 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 45.9324324324324 & 2.16518265974225 & 21.2141143038252 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 45.9027777777778 & 2.09488905236399 & 21.9117941954867 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 45.8857142857143 & 2.05116165209876 & 22.3705987476724 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 45.8382352941176 & 2.01264770578076 & 22.7750913199862 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 45.7575757575758 & 1.9730185370005 & 23.1916603414883 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 45.71875 & 1.94409320452925 & 23.5167480105823 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 45.6612903225806 & 1.91212883270575 & 23.8798189439818 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 45.6166666666667 & 1.87702307681209 & 24.302666935849 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 45.551724137931 & 1.83766014422756 & 24.7878936053642 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 45.5 & 1.79374816168058 & 25.3658796546838 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 45.4444444444444 & 1.7390300409553 & 26.1320640668637 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 45.4230769230769 & 1.69248764983121 & 26.8380551713963 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 45.4 & 1.63357626959118 & 27.7917847149934 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 45.3958333333333 & 1.57741697450792 & 28.7785880759237 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 45.3913043478261 & 1.51847821764374 & 29.8926279089211 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 45.4545454545455 & 1.47582869738743 & 30.7993370334991 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 45.5 & 1.42698808888063 & 31.8853397267607 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 45.5 & 1.39274677875901 & 32.6692552400246 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 45.4736842105263 & 1.35343030919834 & 33.5988368972328 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 45.4444444444444 & 1.29862225188329 & 34.9943521902078 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 45.4117647058824 & 1.26174881258454 & 35.9911293380666 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 45.40625 & 1.2385437720982 & 36.6609973929933 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 45.4 & 1.20210543267401 & 37.7670699807175 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 45.3928571428571 & 1.19338929295312 & 38.0369234171102 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 45.3846153846154 & 1.17417980942106 & 38.6521851427447 \tabularnewline
Median & 43.5 &  &  \tabularnewline
Midrange & 55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 45.8780487804878 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 45.8780487804878 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 45.8780487804878 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 45.8780487804878 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 45.8780487804878 &  &  \tabularnewline
Midmean - Closest Observation & 45.8780487804878 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 45.8780487804878 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 45.8780487804878 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270338&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]46.1710526315789[/C][C]2.33594251295333[/C][C]19.7654918199185[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40.5692404105223[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]30.2175329633018[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]50.4084631574375[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]45.9605263157895[/C][C]2.22485487714968[/C][C]20.6577636985791[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]45.9342105263158[/C][C]2.1627091138172[/C][C]21.2391995913132[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]46.0131578947368[/C][C]2.1323320090597[/C][C]21.5787962189938[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]46.1184210526316[/C][C]2.11377828388544[/C][C]21.8180030536879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]45.9210526315789[/C][C]2.05210744545269[/C][C]22.3775089035111[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]46[/C][C]2.03900560559532[/C][C]22.5600164481008[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]45.9078947368421[/C][C]2.0223468763477[/C][C]22.7003068928266[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]46.0131578947368[/C][C]2.0052994194815[/C][C]22.945779292468[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]45.8947368421053[/C][C]1.98428730830081[/C][C]23.1290784606217[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]45.8947368421053[/C][C]1.98428730830081[/C][C]23.1290784606217[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]45.6052631578947[/C][C]1.88708249221118[/C][C]24.1670744899217[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]45.6052631578947[/C][C]1.88708249221118[/C][C]24.1670744899217[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]45.4342105263158[/C][C]1.80431602692629[/C][C]25.1808496118689[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]45.4342105263158[/C][C]1.74620747208039[/C][C]26.0187928712654[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]44.8421052631579[/C][C]1.59649315596568[/C][C]28.0878781694708[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]45.0526315789474[/C][C]1.56372191372167[/C][C]28.8111531747494[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]45.5[/C][C]1.43116931703942[/C][C]31.792185214062[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]45.7368421052632[/C][C]1.39741219741784[/C][C]32.7296714525438[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]45.7368421052632[/C][C]1.39741219741784[/C][C]32.7296714525438[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]45.7368421052632[/C][C]1.24891088287027[/C][C]36.6213816634777[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]45.4605263157895[/C][C]1.13484534682874[/C][C]40.0587854925135[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]45.4605263157895[/C][C]1.13484534682874[/C][C]40.0587854925135[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]45.4605263157895[/C][C]0.97412863257261[/C][C]46.6678884037431[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]45.4605263157895[/C][C]0.97412863257261[/C][C]46.6678884037431[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]45.4605263157895[/C][C]0.97412863257261[/C][C]46.6678884037431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]45.9324324324324[/C][C]2.16518265974225[/C][C]21.2141143038252[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]45.9027777777778[/C][C]2.09488905236399[/C][C]21.9117941954867[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]45.8857142857143[/C][C]2.05116165209876[/C][C]22.3705987476724[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]45.8382352941176[/C][C]2.01264770578076[/C][C]22.7750913199862[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]45.7575757575758[/C][C]1.9730185370005[/C][C]23.1916603414883[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]45.71875[/C][C]1.94409320452925[/C][C]23.5167480105823[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]45.6612903225806[/C][C]1.91212883270575[/C][C]23.8798189439818[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]45.6166666666667[/C][C]1.87702307681209[/C][C]24.302666935849[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]45.551724137931[/C][C]1.83766014422756[/C][C]24.7878936053642[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]45.5[/C][C]1.79374816168058[/C][C]25.3658796546838[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]45.4444444444444[/C][C]1.7390300409553[/C][C]26.1320640668637[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]45.4230769230769[/C][C]1.69248764983121[/C][C]26.8380551713963[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]45.4[/C][C]1.63357626959118[/C][C]27.7917847149934[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]45.3958333333333[/C][C]1.57741697450792[/C][C]28.7785880759237[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]45.3913043478261[/C][C]1.51847821764374[/C][C]29.8926279089211[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]45.4545454545455[/C][C]1.47582869738743[/C][C]30.7993370334991[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]45.5[/C][C]1.42698808888063[/C][C]31.8853397267607[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]45.5[/C][C]1.39274677875901[/C][C]32.6692552400246[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]45.4736842105263[/C][C]1.35343030919834[/C][C]33.5988368972328[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]45.4444444444444[/C][C]1.29862225188329[/C][C]34.9943521902078[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]45.4117647058824[/C][C]1.26174881258454[/C][C]35.9911293380666[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]45.40625[/C][C]1.2385437720982[/C][C]36.6609973929933[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]45.4[/C][C]1.20210543267401[/C][C]37.7670699807175[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]45.3928571428571[/C][C]1.19338929295312[/C][C]38.0369234171102[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]45.3846153846154[/C][C]1.17417980942106[/C][C]38.6521851427447[/C][/ROW]
[ROW][C]Median[/C][C]43.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]45.8780487804878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]45.8780487804878[/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=270338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270338&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 Mean46.17105263157892.3359425129533319.7654918199185
Geometric Mean40.5692404105223
Harmonic Mean30.2175329633018
Quadratic Mean50.4084631574375
Winsorized Mean ( 1 / 25 )45.96052631578952.2248548771496820.6577636985791
Winsorized Mean ( 2 / 25 )45.93421052631582.162709113817221.2391995913132
Winsorized Mean ( 3 / 25 )46.01315789473682.132332009059721.5787962189938
Winsorized Mean ( 4 / 25 )46.11842105263162.1137782838854421.8180030536879
Winsorized Mean ( 5 / 25 )45.92105263157892.0521074454526922.3775089035111
Winsorized Mean ( 6 / 25 )462.0390056055953222.5600164481008
Winsorized Mean ( 7 / 25 )45.90789473684212.022346876347722.7003068928266
Winsorized Mean ( 8 / 25 )46.01315789473682.005299419481522.945779292468
Winsorized Mean ( 9 / 25 )45.89473684210531.9842873083008123.1290784606217
Winsorized Mean ( 10 / 25 )45.89473684210531.9842873083008123.1290784606217
Winsorized Mean ( 11 / 25 )45.60526315789471.8870824922111824.1670744899217
Winsorized Mean ( 12 / 25 )45.60526315789471.8870824922111824.1670744899217
Winsorized Mean ( 13 / 25 )45.43421052631581.8043160269262925.1808496118689
Winsorized Mean ( 14 / 25 )45.43421052631581.7462074720803926.0187928712654
Winsorized Mean ( 15 / 25 )44.84210526315791.5964931559656828.0878781694708
Winsorized Mean ( 16 / 25 )45.05263157894741.5637219137216728.8111531747494
Winsorized Mean ( 17 / 25 )45.51.4311693170394231.792185214062
Winsorized Mean ( 18 / 25 )45.73684210526321.3974121974178432.7296714525438
Winsorized Mean ( 19 / 25 )45.73684210526321.3974121974178432.7296714525438
Winsorized Mean ( 20 / 25 )45.73684210526321.2489108828702736.6213816634777
Winsorized Mean ( 21 / 25 )45.46052631578951.1348453468287440.0587854925135
Winsorized Mean ( 22 / 25 )45.46052631578951.1348453468287440.0587854925135
Winsorized Mean ( 23 / 25 )45.46052631578950.9741286325726146.6678884037431
Winsorized Mean ( 24 / 25 )45.46052631578950.9741286325726146.6678884037431
Winsorized Mean ( 25 / 25 )45.46052631578950.9741286325726146.6678884037431
Trimmed Mean ( 1 / 25 )45.93243243243242.1651826597422521.2141143038252
Trimmed Mean ( 2 / 25 )45.90277777777782.0948890523639921.9117941954867
Trimmed Mean ( 3 / 25 )45.88571428571432.0511616520987622.3705987476724
Trimmed Mean ( 4 / 25 )45.83823529411762.0126477057807622.7750913199862
Trimmed Mean ( 5 / 25 )45.75757575757581.973018537000523.1916603414883
Trimmed Mean ( 6 / 25 )45.718751.9440932045292523.5167480105823
Trimmed Mean ( 7 / 25 )45.66129032258061.9121288327057523.8798189439818
Trimmed Mean ( 8 / 25 )45.61666666666671.8770230768120924.302666935849
Trimmed Mean ( 9 / 25 )45.5517241379311.8376601442275624.7878936053642
Trimmed Mean ( 10 / 25 )45.51.7937481616805825.3658796546838
Trimmed Mean ( 11 / 25 )45.44444444444441.739030040955326.1320640668637
Trimmed Mean ( 12 / 25 )45.42307692307691.6924876498312126.8380551713963
Trimmed Mean ( 13 / 25 )45.41.6335762695911827.7917847149934
Trimmed Mean ( 14 / 25 )45.39583333333331.5774169745079228.7785880759237
Trimmed Mean ( 15 / 25 )45.39130434782611.5184782176437429.8926279089211
Trimmed Mean ( 16 / 25 )45.45454545454551.4758286973874330.7993370334991
Trimmed Mean ( 17 / 25 )45.51.4269880888806331.8853397267607
Trimmed Mean ( 18 / 25 )45.51.3927467787590132.6692552400246
Trimmed Mean ( 19 / 25 )45.47368421052631.3534303091983433.5988368972328
Trimmed Mean ( 20 / 25 )45.44444444444441.2986222518832934.9943521902078
Trimmed Mean ( 21 / 25 )45.41176470588241.2617488125845435.9911293380666
Trimmed Mean ( 22 / 25 )45.406251.238543772098236.6609973929933
Trimmed Mean ( 23 / 25 )45.41.2021054326740137.7670699807175
Trimmed Mean ( 24 / 25 )45.39285714285711.1933892929531238.0369234171102
Trimmed Mean ( 25 / 25 )45.38461538461541.1741798094210638.6521851427447
Median43.5
Midrange55
Midmean - Weighted Average at Xnp45.8780487804878
Midmean - Weighted Average at X(n+1)p45.8780487804878
Midmean - Empirical Distribution Function45.8780487804878
Midmean - Empirical Distribution Function - Averaging45.8780487804878
Midmean - Empirical Distribution Function - Interpolation45.8780487804878
Midmean - Closest Observation45.8780487804878
Midmean - True Basic - Statistics Graphics Toolkit45.8780487804878
Midmean - MS Excel (old versions)45.8780487804878
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')