Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Aug 2013 12:38:35 -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/Aug/10/t1376152857ioribg6nuvfmcu0.htm/, Retrieved Sun, 05 May 2024 01:01:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211014, Retrieved Sun, 05 May 2024 01:01:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [stap 14/1] [2013-08-10 16:38:35] [38a0db91cd47487c7649642dcb33e029] [Current]
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Dataseries X:
57
56
55
53
73
72
57
47
48
48
49
51
45
39
34
34
53
55
40
22
31
31
39
43
42
31
37
35
52
48
31
19
30
34
37
41
32
25
28
29
56
56
41
39
45
42
50
60
62
48
44
40
67
69
64
69
68
60
69
79
83
71
63
69
95
103
101
105
104
94
111
116
122
103
96
104
124
141
137
137
139
132
150
150
147
130
133
135
148
165
153
159
154
151
174
169
162
152
162
167
173
181
173
178
172
171
196
199
190
176
188
193
200
209
200
207
204
192
216
216




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211014&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211014&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.96666666666675.4155592490026818.0898522502008
Geometric Mean80.0114021759021
Harmonic Mean64.8268272223692
Quadratic Mean114.400757573249
Winsorized Mean ( 1 / 40 )97.99166666666675.4125527902968118.1045193392549
Winsorized Mean ( 2 / 40 )97.9255.3859600979278118.181530909907
Winsorized Mean ( 3 / 40 )97.955.3689877455405618.2436624261913
Winsorized Mean ( 4 / 40 )97.88333333333335.3484884030860418.3011209815572
Winsorized Mean ( 5 / 40 )97.75833333333335.3166404884193518.3872378706572
Winsorized Mean ( 6 / 40 )97.80833333333335.3113205012363418.4150689664776
Winsorized Mean ( 7 / 40 )97.755.3019240997645318.4367030083176
Winsorized Mean ( 8 / 40 )97.555.2701773127251618.5098136574
Winsorized Mean ( 9 / 40 )97.3255.235238852271818.5903647849355
Winsorized Mean ( 10 / 40 )97.3255.2136585661373818.6673137040703
Winsorized Mean ( 11 / 40 )97.3255.166759227055618.8367593152706
Winsorized Mean ( 12 / 40 )97.1255.1368193968063718.9076143226651
Winsorized Mean ( 13 / 40 )96.36666666666675.0267761097834719.1706701396768
Winsorized Mean ( 14 / 40 )96.13333333333334.9656513917274119.3596621570109
Winsorized Mean ( 15 / 40 )96.13333333333334.9056352054932119.5965108097898
Winsorized Mean ( 16 / 40 )95.86666666666674.8694142506799119.6875151160699
Winsorized Mean ( 17 / 40 )96.00833333333334.8218906736397619.9109311744023
Winsorized Mean ( 18 / 40 )96.00833333333334.8218906736397619.9109311744023
Winsorized Mean ( 19 / 40 )95.854.8007155454056219.965773662997
Winsorized Mean ( 20 / 40 )95.854.7620501728498720.1278853688847
Winsorized Mean ( 21 / 40 )95.54.7159215394646420.2505489543919
Winsorized Mean ( 22 / 40 )95.31666666666674.6500953776750920.4977874484635
Winsorized Mean ( 23 / 40 )94.93333333333334.6007357427281620.6343808125436
Winsorized Mean ( 24 / 40 )94.53333333333334.5049293470636720.9844208533371
Winsorized Mean ( 25 / 40 )94.53333333333334.5049293470636720.9844208533371
Winsorized Mean ( 26 / 40 )94.14.4025775490762521.3738426980676
Winsorized Mean ( 27 / 40 )93.24.2431952444299521.9645796696119
Winsorized Mean ( 28 / 40 )93.24.1925236912819922.2300473086894
Winsorized Mean ( 29 / 40 )92.95833333333334.1636414087405422.326210210656
Winsorized Mean ( 30 / 40 )93.20833333333334.0859274758617422.8120381196133
Winsorized Mean ( 31 / 40 )93.20833333333334.0308317328375423.1238462707345
Winsorized Mean ( 32 / 40 )93.20833333333334.0308317328375423.1238462707345
Winsorized Mean ( 33 / 40 )92.65833333333333.9660233424839923.3630327741086
Winsorized Mean ( 34 / 40 )92.3753.9328762701491823.4878988441953
Winsorized Mean ( 35 / 40 )90.91666666666673.7035372472709724.5486032936919
Winsorized Mean ( 36 / 40 )90.61666666666673.6071665232973925.1212873266056
Winsorized Mean ( 37 / 40 )90.30833333333333.5088283182757125.7374613807587
Winsorized Mean ( 38 / 40 )90.6253.4791508369454926.0480227064728
Winsorized Mean ( 39 / 40 )90.33.3763388256432826.7449461274952
Winsorized Mean ( 40 / 40 )89.63333333333333.3024677415442327.1413198699167
Trimmed Mean ( 1 / 40 )97.6355932203395.3734053219182918.1701523281857
Trimmed Mean ( 2 / 40 )97.26724137931035.3293388649460418.2512772867738
Trimmed Mean ( 3 / 40 )96.92105263157895.2949071495961718.3045802113774
Trimmed Mean ( 4 / 40 )96.55357142857145.2624009219131918.3478174432724
Trimmed Mean ( 5 / 40 )96.19090909090915.2315443981437318.3867137063846
Trimmed Mean ( 6 / 40 )95.84259259259265.2042425186885618.416242565257
Trimmed Mean ( 7 / 40 )95.47169811320765.1736808467023318.4533412365513
Trimmed Mean ( 8 / 40 )95.09615384615385.1401841901199118.5005342860944
Trimmed Mean ( 9 / 40 )94.73529411764715.1073113752452618.5489560273967
Trimmed Mean ( 10 / 40 )94.395.0751303909208618.5985369299789
Trimmed Mean ( 11 / 40 )94.0306122448985.040973586782318.6532642209138
Trimmed Mean ( 12 / 40 )93.656255.0080380154561918.7011859157121
Trimmed Mean ( 13 / 40 )93.28723404255324.9737499528119318.7559155421179
Trimmed Mean ( 14 / 40 )92.97826086956524.9489022623903418.787653491596
Trimmed Mean ( 15 / 40 )92.67777777777784.9270034240923918.8101711731304
Trimmed Mean ( 16 / 40 )92.36363636363644.9076418194857218.8203703043095
Trimmed Mean ( 17 / 40 )92.05813953488374.8880309624412818.8333789704364
Trimmed Mean ( 18 / 40 )91.72619047619054.8689171618420618.8391355669497
Trimmed Mean ( 19 / 40 )91.37804878048784.8445463877510918.8620443415564
Trimmed Mean ( 20 / 40 )91.0254.8167684095659418.8975247012556
Trimmed Mean ( 21 / 40 )90.65384615384624.7868599602884718.9380610475146
Trimmed Mean ( 22 / 40 )90.28947368421054.7555624232280718.9860768608989
Trimmed Mean ( 23 / 40 )89.91891891891894.7246177483587919.031998715696
Trimmed Mean ( 24 / 40 )89.55555555555564.6920790681283719.0865401574058
Trimmed Mean ( 25 / 40 )89.24.6630835105203719.1289733067735
Trimmed Mean ( 26 / 40 )88.82352941176474.6257638799909319.2019159896979
Trimmed Mean ( 27 / 40 )88.45454545454554.5918333210788119.2634486640652
Trimmed Mean ( 28 / 40 )88.1254.5691067082211119.2871398344535
Trimmed Mean ( 29 / 40 )87.77419354838714.5442427796523319.3154718628617
Trimmed Mean ( 30 / 40 )87.41666666666674.5141517379648419.3650261978295
Trimmed Mean ( 31 / 40 )87.01724137931034.4833152662909219.4091283371424
Trimmed Mean ( 32 / 40 )86.58928571428574.4485352022063419.4646736011755
Trimmed Mean ( 33 / 40 )86.12962962962964.4008644008535919.5710709952627
Trimmed Mean ( 34 / 40 )85.67307692307694.3480479795146619.7038021030853
Trimmed Mean ( 35 / 40 )85.24.2831420852510819.8919387459465
Trimmed Mean ( 36 / 40 )84.79166666666674.2377230200662120.0087797775283
Trimmed Mean ( 37 / 40 )84.36956521739134.1908986613854220.1316166374447
Trimmed Mean ( 38 / 40 )83.93181818181824.1423402562302320.2619323836524
Trimmed Mean ( 39 / 40 )83.42857142857144.0766669644544420.464897465505
Trimmed Mean ( 40 / 40 )82.94.004932855802620.6994731209761
Median71.5
Midrange117.5
Midmean - Weighted Average at Xnp86.0483870967742
Midmean - Weighted Average at X(n+1)p87.4166666666667
Midmean - Empirical Distribution Function86.0483870967742
Midmean - Empirical Distribution Function - Averaging87.4166666666667
Midmean - Empirical Distribution Function - Interpolation87.4166666666667
Midmean - Closest Observation86.0483870967742
Midmean - True Basic - Statistics Graphics Toolkit87.4166666666667
Midmean - MS Excel (old versions)87.0952380952381
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.9666666666667 & 5.41555924900268 & 18.0898522502008 \tabularnewline
Geometric Mean & 80.0114021759021 &  &  \tabularnewline
Harmonic Mean & 64.8268272223692 &  &  \tabularnewline
Quadratic Mean & 114.400757573249 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 97.9916666666667 & 5.41255279029681 & 18.1045193392549 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 97.925 & 5.38596009792781 & 18.181530909907 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 97.95 & 5.36898774554056 & 18.2436624261913 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 97.8833333333333 & 5.34848840308604 & 18.3011209815572 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 97.7583333333333 & 5.31664048841935 & 18.3872378706572 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 97.8083333333333 & 5.31132050123634 & 18.4150689664776 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 97.75 & 5.30192409976453 & 18.4367030083176 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 97.55 & 5.27017731272516 & 18.5098136574 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 97.325 & 5.2352388522718 & 18.5903647849355 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 97.325 & 5.21365856613738 & 18.6673137040703 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 97.325 & 5.1667592270556 & 18.8367593152706 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 97.125 & 5.13681939680637 & 18.9076143226651 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 96.3666666666667 & 5.02677610978347 & 19.1706701396768 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 96.1333333333333 & 4.96565139172741 & 19.3596621570109 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 96.1333333333333 & 4.90563520549321 & 19.5965108097898 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 95.8666666666667 & 4.86941425067991 & 19.6875151160699 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 96.0083333333333 & 4.82189067363976 & 19.9109311744023 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 96.0083333333333 & 4.82189067363976 & 19.9109311744023 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 95.85 & 4.80071554540562 & 19.965773662997 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 95.85 & 4.76205017284987 & 20.1278853688847 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 95.5 & 4.71592153946464 & 20.2505489543919 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 95.3166666666667 & 4.65009537767509 & 20.4977874484635 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 94.9333333333333 & 4.60073574272816 & 20.6343808125436 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 94.5333333333333 & 4.50492934706367 & 20.9844208533371 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 94.5333333333333 & 4.50492934706367 & 20.9844208533371 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 94.1 & 4.40257754907625 & 21.3738426980676 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 93.2 & 4.24319524442995 & 21.9645796696119 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 93.2 & 4.19252369128199 & 22.2300473086894 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 92.9583333333333 & 4.16364140874054 & 22.326210210656 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 93.2083333333333 & 4.08592747586174 & 22.8120381196133 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 93.2083333333333 & 4.03083173283754 & 23.1238462707345 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 93.2083333333333 & 4.03083173283754 & 23.1238462707345 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 92.6583333333333 & 3.96602334248399 & 23.3630327741086 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 92.375 & 3.93287627014918 & 23.4878988441953 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 90.9166666666667 & 3.70353724727097 & 24.5486032936919 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 90.6166666666667 & 3.60716652329739 & 25.1212873266056 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 90.3083333333333 & 3.50882831827571 & 25.7374613807587 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 90.625 & 3.47915083694549 & 26.0480227064728 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 90.3 & 3.37633882564328 & 26.7449461274952 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 89.6333333333333 & 3.30246774154423 & 27.1413198699167 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 97.635593220339 & 5.37340532191829 & 18.1701523281857 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 97.2672413793103 & 5.32933886494604 & 18.2512772867738 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 96.9210526315789 & 5.29490714959617 & 18.3045802113774 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 96.5535714285714 & 5.26240092191319 & 18.3478174432724 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 96.1909090909091 & 5.23154439814373 & 18.3867137063846 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 95.8425925925926 & 5.20424251868856 & 18.416242565257 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 95.4716981132076 & 5.17368084670233 & 18.4533412365513 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 95.0961538461538 & 5.14018419011991 & 18.5005342860944 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 94.7352941176471 & 5.10731137524526 & 18.5489560273967 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 94.39 & 5.07513039092086 & 18.5985369299789 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 94.030612244898 & 5.0409735867823 & 18.6532642209138 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 93.65625 & 5.00803801545619 & 18.7011859157121 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 93.2872340425532 & 4.97374995281193 & 18.7559155421179 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 92.9782608695652 & 4.94890226239034 & 18.787653491596 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 92.6777777777778 & 4.92700342409239 & 18.8101711731304 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 92.3636363636364 & 4.90764181948572 & 18.8203703043095 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 92.0581395348837 & 4.88803096244128 & 18.8333789704364 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 91.7261904761905 & 4.86891716184206 & 18.8391355669497 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 91.3780487804878 & 4.84454638775109 & 18.8620443415564 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 91.025 & 4.81676840956594 & 18.8975247012556 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 90.6538461538462 & 4.78685996028847 & 18.9380610475146 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 90.2894736842105 & 4.75556242322807 & 18.9860768608989 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 89.9189189189189 & 4.72461774835879 & 19.031998715696 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 89.5555555555556 & 4.69207906812837 & 19.0865401574058 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 89.2 & 4.66308351052037 & 19.1289733067735 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 88.8235294117647 & 4.62576387999093 & 19.2019159896979 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 88.4545454545455 & 4.59183332107881 & 19.2634486640652 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 88.125 & 4.56910670822111 & 19.2871398344535 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 87.7741935483871 & 4.54424277965233 & 19.3154718628617 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 87.4166666666667 & 4.51415173796484 & 19.3650261978295 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 87.0172413793103 & 4.48331526629092 & 19.4091283371424 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 86.5892857142857 & 4.44853520220634 & 19.4646736011755 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 86.1296296296296 & 4.40086440085359 & 19.5710709952627 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 85.6730769230769 & 4.34804797951466 & 19.7038021030853 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 85.2 & 4.28314208525108 & 19.8919387459465 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 84.7916666666667 & 4.23772302006621 & 20.0087797775283 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 84.3695652173913 & 4.19089866138542 & 20.1316166374447 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 83.9318181818182 & 4.14234025623023 & 20.2619323836524 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 83.4285714285714 & 4.07666696445444 & 20.464897465505 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 82.9 & 4.0049328558026 & 20.6994731209761 \tabularnewline
Median & 71.5 &  &  \tabularnewline
Midrange & 117.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 86.0483870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.4166666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 86.0483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.4166666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.4166666666667 &  &  \tabularnewline
Midmean - Closest Observation & 86.0483870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.4166666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 87.0952380952381 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211014&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]97.9666666666667[/C][C]5.41555924900268[/C][C]18.0898522502008[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.0114021759021[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.8268272223692[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.400757573249[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]97.9916666666667[/C][C]5.41255279029681[/C][C]18.1045193392549[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]97.925[/C][C]5.38596009792781[/C][C]18.181530909907[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]97.95[/C][C]5.36898774554056[/C][C]18.2436624261913[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]97.8833333333333[/C][C]5.34848840308604[/C][C]18.3011209815572[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]97.7583333333333[/C][C]5.31664048841935[/C][C]18.3872378706572[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]97.8083333333333[/C][C]5.31132050123634[/C][C]18.4150689664776[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]97.75[/C][C]5.30192409976453[/C][C]18.4367030083176[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]97.55[/C][C]5.27017731272516[/C][C]18.5098136574[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]97.325[/C][C]5.2352388522718[/C][C]18.5903647849355[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]97.325[/C][C]5.21365856613738[/C][C]18.6673137040703[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]97.325[/C][C]5.1667592270556[/C][C]18.8367593152706[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]97.125[/C][C]5.13681939680637[/C][C]18.9076143226651[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]96.3666666666667[/C][C]5.02677610978347[/C][C]19.1706701396768[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]96.1333333333333[/C][C]4.96565139172741[/C][C]19.3596621570109[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]96.1333333333333[/C][C]4.90563520549321[/C][C]19.5965108097898[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]95.8666666666667[/C][C]4.86941425067991[/C][C]19.6875151160699[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]96.0083333333333[/C][C]4.82189067363976[/C][C]19.9109311744023[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]96.0083333333333[/C][C]4.82189067363976[/C][C]19.9109311744023[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]95.85[/C][C]4.80071554540562[/C][C]19.965773662997[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]95.85[/C][C]4.76205017284987[/C][C]20.1278853688847[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]95.5[/C][C]4.71592153946464[/C][C]20.2505489543919[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]95.3166666666667[/C][C]4.65009537767509[/C][C]20.4977874484635[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]94.9333333333333[/C][C]4.60073574272816[/C][C]20.6343808125436[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]94.5333333333333[/C][C]4.50492934706367[/C][C]20.9844208533371[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]94.5333333333333[/C][C]4.50492934706367[/C][C]20.9844208533371[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]94.1[/C][C]4.40257754907625[/C][C]21.3738426980676[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]93.2[/C][C]4.24319524442995[/C][C]21.9645796696119[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]93.2[/C][C]4.19252369128199[/C][C]22.2300473086894[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]92.9583333333333[/C][C]4.16364140874054[/C][C]22.326210210656[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]93.2083333333333[/C][C]4.08592747586174[/C][C]22.8120381196133[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]93.2083333333333[/C][C]4.03083173283754[/C][C]23.1238462707345[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]93.2083333333333[/C][C]4.03083173283754[/C][C]23.1238462707345[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]92.6583333333333[/C][C]3.96602334248399[/C][C]23.3630327741086[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]92.375[/C][C]3.93287627014918[/C][C]23.4878988441953[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]90.9166666666667[/C][C]3.70353724727097[/C][C]24.5486032936919[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]90.6166666666667[/C][C]3.60716652329739[/C][C]25.1212873266056[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]90.3083333333333[/C][C]3.50882831827571[/C][C]25.7374613807587[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]90.625[/C][C]3.47915083694549[/C][C]26.0480227064728[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]90.3[/C][C]3.37633882564328[/C][C]26.7449461274952[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]89.6333333333333[/C][C]3.30246774154423[/C][C]27.1413198699167[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]97.635593220339[/C][C]5.37340532191829[/C][C]18.1701523281857[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]97.2672413793103[/C][C]5.32933886494604[/C][C]18.2512772867738[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]96.9210526315789[/C][C]5.29490714959617[/C][C]18.3045802113774[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]96.5535714285714[/C][C]5.26240092191319[/C][C]18.3478174432724[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]96.1909090909091[/C][C]5.23154439814373[/C][C]18.3867137063846[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]95.8425925925926[/C][C]5.20424251868856[/C][C]18.416242565257[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]95.4716981132076[/C][C]5.17368084670233[/C][C]18.4533412365513[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]95.0961538461538[/C][C]5.14018419011991[/C][C]18.5005342860944[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]94.7352941176471[/C][C]5.10731137524526[/C][C]18.5489560273967[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]94.39[/C][C]5.07513039092086[/C][C]18.5985369299789[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]94.030612244898[/C][C]5.0409735867823[/C][C]18.6532642209138[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]93.65625[/C][C]5.00803801545619[/C][C]18.7011859157121[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]93.2872340425532[/C][C]4.97374995281193[/C][C]18.7559155421179[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]92.9782608695652[/C][C]4.94890226239034[/C][C]18.787653491596[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]92.6777777777778[/C][C]4.92700342409239[/C][C]18.8101711731304[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]92.3636363636364[/C][C]4.90764181948572[/C][C]18.8203703043095[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]92.0581395348837[/C][C]4.88803096244128[/C][C]18.8333789704364[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]91.7261904761905[/C][C]4.86891716184206[/C][C]18.8391355669497[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]91.3780487804878[/C][C]4.84454638775109[/C][C]18.8620443415564[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]91.025[/C][C]4.81676840956594[/C][C]18.8975247012556[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]90.6538461538462[/C][C]4.78685996028847[/C][C]18.9380610475146[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]90.2894736842105[/C][C]4.75556242322807[/C][C]18.9860768608989[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]89.9189189189189[/C][C]4.72461774835879[/C][C]19.031998715696[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]89.5555555555556[/C][C]4.69207906812837[/C][C]19.0865401574058[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]89.2[/C][C]4.66308351052037[/C][C]19.1289733067735[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]88.8235294117647[/C][C]4.62576387999093[/C][C]19.2019159896979[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]88.4545454545455[/C][C]4.59183332107881[/C][C]19.2634486640652[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]88.125[/C][C]4.56910670822111[/C][C]19.2871398344535[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]87.7741935483871[/C][C]4.54424277965233[/C][C]19.3154718628617[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]87.4166666666667[/C][C]4.51415173796484[/C][C]19.3650261978295[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]87.0172413793103[/C][C]4.48331526629092[/C][C]19.4091283371424[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]86.5892857142857[/C][C]4.44853520220634[/C][C]19.4646736011755[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]86.1296296296296[/C][C]4.40086440085359[/C][C]19.5710709952627[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]85.6730769230769[/C][C]4.34804797951466[/C][C]19.7038021030853[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]85.2[/C][C]4.28314208525108[/C][C]19.8919387459465[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]84.7916666666667[/C][C]4.23772302006621[/C][C]20.0087797775283[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]84.3695652173913[/C][C]4.19089866138542[/C][C]20.1316166374447[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]83.9318181818182[/C][C]4.14234025623023[/C][C]20.2619323836524[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]83.4285714285714[/C][C]4.07666696445444[/C][C]20.464897465505[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]82.9[/C][C]4.0049328558026[/C][C]20.6994731209761[/C][/ROW]
[ROW][C]Median[/C][C]71.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]86.0483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.4166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]86.0483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.4166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.4166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.0483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.4166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]87.0952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211014&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 Mean97.96666666666675.4155592490026818.0898522502008
Geometric Mean80.0114021759021
Harmonic Mean64.8268272223692
Quadratic Mean114.400757573249
Winsorized Mean ( 1 / 40 )97.99166666666675.4125527902968118.1045193392549
Winsorized Mean ( 2 / 40 )97.9255.3859600979278118.181530909907
Winsorized Mean ( 3 / 40 )97.955.3689877455405618.2436624261913
Winsorized Mean ( 4 / 40 )97.88333333333335.3484884030860418.3011209815572
Winsorized Mean ( 5 / 40 )97.75833333333335.3166404884193518.3872378706572
Winsorized Mean ( 6 / 40 )97.80833333333335.3113205012363418.4150689664776
Winsorized Mean ( 7 / 40 )97.755.3019240997645318.4367030083176
Winsorized Mean ( 8 / 40 )97.555.2701773127251618.5098136574
Winsorized Mean ( 9 / 40 )97.3255.235238852271818.5903647849355
Winsorized Mean ( 10 / 40 )97.3255.2136585661373818.6673137040703
Winsorized Mean ( 11 / 40 )97.3255.166759227055618.8367593152706
Winsorized Mean ( 12 / 40 )97.1255.1368193968063718.9076143226651
Winsorized Mean ( 13 / 40 )96.36666666666675.0267761097834719.1706701396768
Winsorized Mean ( 14 / 40 )96.13333333333334.9656513917274119.3596621570109
Winsorized Mean ( 15 / 40 )96.13333333333334.9056352054932119.5965108097898
Winsorized Mean ( 16 / 40 )95.86666666666674.8694142506799119.6875151160699
Winsorized Mean ( 17 / 40 )96.00833333333334.8218906736397619.9109311744023
Winsorized Mean ( 18 / 40 )96.00833333333334.8218906736397619.9109311744023
Winsorized Mean ( 19 / 40 )95.854.8007155454056219.965773662997
Winsorized Mean ( 20 / 40 )95.854.7620501728498720.1278853688847
Winsorized Mean ( 21 / 40 )95.54.7159215394646420.2505489543919
Winsorized Mean ( 22 / 40 )95.31666666666674.6500953776750920.4977874484635
Winsorized Mean ( 23 / 40 )94.93333333333334.6007357427281620.6343808125436
Winsorized Mean ( 24 / 40 )94.53333333333334.5049293470636720.9844208533371
Winsorized Mean ( 25 / 40 )94.53333333333334.5049293470636720.9844208533371
Winsorized Mean ( 26 / 40 )94.14.4025775490762521.3738426980676
Winsorized Mean ( 27 / 40 )93.24.2431952444299521.9645796696119
Winsorized Mean ( 28 / 40 )93.24.1925236912819922.2300473086894
Winsorized Mean ( 29 / 40 )92.95833333333334.1636414087405422.326210210656
Winsorized Mean ( 30 / 40 )93.20833333333334.0859274758617422.8120381196133
Winsorized Mean ( 31 / 40 )93.20833333333334.0308317328375423.1238462707345
Winsorized Mean ( 32 / 40 )93.20833333333334.0308317328375423.1238462707345
Winsorized Mean ( 33 / 40 )92.65833333333333.9660233424839923.3630327741086
Winsorized Mean ( 34 / 40 )92.3753.9328762701491823.4878988441953
Winsorized Mean ( 35 / 40 )90.91666666666673.7035372472709724.5486032936919
Winsorized Mean ( 36 / 40 )90.61666666666673.6071665232973925.1212873266056
Winsorized Mean ( 37 / 40 )90.30833333333333.5088283182757125.7374613807587
Winsorized Mean ( 38 / 40 )90.6253.4791508369454926.0480227064728
Winsorized Mean ( 39 / 40 )90.33.3763388256432826.7449461274952
Winsorized Mean ( 40 / 40 )89.63333333333333.3024677415442327.1413198699167
Trimmed Mean ( 1 / 40 )97.6355932203395.3734053219182918.1701523281857
Trimmed Mean ( 2 / 40 )97.26724137931035.3293388649460418.2512772867738
Trimmed Mean ( 3 / 40 )96.92105263157895.2949071495961718.3045802113774
Trimmed Mean ( 4 / 40 )96.55357142857145.2624009219131918.3478174432724
Trimmed Mean ( 5 / 40 )96.19090909090915.2315443981437318.3867137063846
Trimmed Mean ( 6 / 40 )95.84259259259265.2042425186885618.416242565257
Trimmed Mean ( 7 / 40 )95.47169811320765.1736808467023318.4533412365513
Trimmed Mean ( 8 / 40 )95.09615384615385.1401841901199118.5005342860944
Trimmed Mean ( 9 / 40 )94.73529411764715.1073113752452618.5489560273967
Trimmed Mean ( 10 / 40 )94.395.0751303909208618.5985369299789
Trimmed Mean ( 11 / 40 )94.0306122448985.040973586782318.6532642209138
Trimmed Mean ( 12 / 40 )93.656255.0080380154561918.7011859157121
Trimmed Mean ( 13 / 40 )93.28723404255324.9737499528119318.7559155421179
Trimmed Mean ( 14 / 40 )92.97826086956524.9489022623903418.787653491596
Trimmed Mean ( 15 / 40 )92.67777777777784.9270034240923918.8101711731304
Trimmed Mean ( 16 / 40 )92.36363636363644.9076418194857218.8203703043095
Trimmed Mean ( 17 / 40 )92.05813953488374.8880309624412818.8333789704364
Trimmed Mean ( 18 / 40 )91.72619047619054.8689171618420618.8391355669497
Trimmed Mean ( 19 / 40 )91.37804878048784.8445463877510918.8620443415564
Trimmed Mean ( 20 / 40 )91.0254.8167684095659418.8975247012556
Trimmed Mean ( 21 / 40 )90.65384615384624.7868599602884718.9380610475146
Trimmed Mean ( 22 / 40 )90.28947368421054.7555624232280718.9860768608989
Trimmed Mean ( 23 / 40 )89.91891891891894.7246177483587919.031998715696
Trimmed Mean ( 24 / 40 )89.55555555555564.6920790681283719.0865401574058
Trimmed Mean ( 25 / 40 )89.24.6630835105203719.1289733067735
Trimmed Mean ( 26 / 40 )88.82352941176474.6257638799909319.2019159896979
Trimmed Mean ( 27 / 40 )88.45454545454554.5918333210788119.2634486640652
Trimmed Mean ( 28 / 40 )88.1254.5691067082211119.2871398344535
Trimmed Mean ( 29 / 40 )87.77419354838714.5442427796523319.3154718628617
Trimmed Mean ( 30 / 40 )87.41666666666674.5141517379648419.3650261978295
Trimmed Mean ( 31 / 40 )87.01724137931034.4833152662909219.4091283371424
Trimmed Mean ( 32 / 40 )86.58928571428574.4485352022063419.4646736011755
Trimmed Mean ( 33 / 40 )86.12962962962964.4008644008535919.5710709952627
Trimmed Mean ( 34 / 40 )85.67307692307694.3480479795146619.7038021030853
Trimmed Mean ( 35 / 40 )85.24.2831420852510819.8919387459465
Trimmed Mean ( 36 / 40 )84.79166666666674.2377230200662120.0087797775283
Trimmed Mean ( 37 / 40 )84.36956521739134.1908986613854220.1316166374447
Trimmed Mean ( 38 / 40 )83.93181818181824.1423402562302320.2619323836524
Trimmed Mean ( 39 / 40 )83.42857142857144.0766669644544420.464897465505
Trimmed Mean ( 40 / 40 )82.94.004932855802620.6994731209761
Median71.5
Midrange117.5
Midmean - Weighted Average at Xnp86.0483870967742
Midmean - Weighted Average at X(n+1)p87.4166666666667
Midmean - Empirical Distribution Function86.0483870967742
Midmean - Empirical Distribution Function - Averaging87.4166666666667
Midmean - Empirical Distribution Function - Interpolation87.4166666666667
Midmean - Closest Observation86.0483870967742
Midmean - True Basic - Statistics Graphics Toolkit87.4166666666667
Midmean - MS Excel (old versions)87.0952380952381
Number of observations120



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')