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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 08:39:52 -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/2012/Oct/21/t1350823224peoeiioared93q2.htm/, Retrieved Sun, 28 Apr 2024 21:52:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180875, Retrieved Sun, 28 Apr 2024 21:52:17 +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] [] [2012-10-21 12:39:52] [b94d6af934ff01803109e5a51192a6cb] [Current]
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Dataseries X:
155.28
173.24
180.16
181.52
182.25
182.19
182
181.65
180.07
182.62
180.38
181.15
180.5
181.14
180.93
211.91
223.81
226.88
226.8
231.81
232.06
232.32
228.37
226.31
225.72
219.98
219.31
215.19
213.81
213.7
213.6
213.52
218.39
219.97
221.09
219.17
219.17
218.45
216.88
216.19
214.59
269.87
272.71
280.35
274.5
268.86
261.7
263.98
263.01
262.79
263.59
267
267.89
267.86
266.84
268.24
267.67
269.07
270.87
271.68
271.63
275.21
276.66
276.08
278.3
279.06
279.28
279.12
262.72
262.55
260.7
259.14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180875&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180875&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean233.0973611111114.2443229643128554.9197982978775
Geometric Mean230.226150968289
Harmonic Mean227.247213295458
Quadratic Mean235.824921189782
Winsorized Mean ( 1 / 24 )233.3319444444444.1845253508058955.760671732938
Winsorized Mean ( 2 / 24 )233.5172222222224.1474243247853156.3041550455077
Winsorized Mean ( 3 / 24 )233.5184722222224.1463572057233556.3189471230046
Winsorized Mean ( 4 / 24 )233.4884722222224.1376586800851956.4300949582954
Winsorized Mean ( 5 / 24 )233.3829166666674.1190385833629256.6595607065485
Winsorized Mean ( 6 / 24 )233.3704166666674.1054582185872756.8439390297758
Winsorized Mean ( 7 / 24 )233.306254.089487196892657.0502458541202
Winsorized Mean ( 8 / 24 )233.2284722222224.077972190370557.192266483071
Winsorized Mean ( 9 / 24 )233.0509722222224.0382322718057357.7111360952032
Winsorized Mean ( 10 / 24 )232.9259722222224.0153684549026958.0086173506254
Winsorized Mean ( 11 / 24 )232.9718055555564.0047283542299458.1741843512262
Winsorized Mean ( 12 / 24 )232.8768055555563.9819291228465658.4834130319926
Winsorized Mean ( 13 / 24 )232.7070833333333.9559072398969458.8252123271212
Winsorized Mean ( 14 / 24 )232.6234722222223.9225161002996159.3046570808095
Winsorized Mean ( 15 / 24 )238.6818055555562.9574718862563180.7046743756841
Winsorized Mean ( 16 / 24 )238.9018055555562.8928079787318982.5847437202803
Winsorized Mean ( 17 / 24 )238.8380555555562.8786992098518482.9673537055121
Winsorized Mean ( 18 / 24 )238.8555555555562.8745490419196283.0932268235189
Winsorized Mean ( 19 / 24 )238.8344444444442.8638559610984283.39610919288
Winsorized Mean ( 20 / 24 )238.8652.8110301827934784.9741854292816
Winsorized Mean ( 21 / 24 )238.9933333333332.7832700718120785.8678199265568
Winsorized Mean ( 22 / 24 )238.4252.6251053932192290.8249248262048
Winsorized Mean ( 23 / 24 )238.5208333333332.5818864398009892.3823874111673
Winsorized Mean ( 24 / 24 )238.8308333333332.496739616938295.6570848289802
Trimmed Mean ( 1 / 24 )233.5344.1650047256142756.0705246176059
Trimmed Mean ( 2 / 24 )233.7479411764714.1391541295006456.4723936010255
Trimmed Mean ( 3 / 24 )233.8737878787884.1283352315337956.6508712985252
Trimmed Mean ( 4 / 24 )234.007031254.1123549612558356.903412632099
Trimmed Mean ( 5 / 24 )234.1575806451614.0926566597259257.2140788034837
Trimmed Mean ( 6 / 24 )234.34354.0707105865411957.5682046212765
Trimmed Mean ( 7 / 24 )234.5448275862074.0438811839279557.9999304921185
Trimmed Mean ( 8 / 24 )234.7723214285714.0111170756069258.5304086126801
Trimmed Mean ( 9 / 24 )235.029629629633.9695331851621659.2083800957136
Trimmed Mean ( 10 / 24 )235.3340384615383.9227638936828559.991894704781
Trimmed Mean ( 11 / 24 )235.68083.8650797688523660.976956258261
Trimmed Mean ( 12 / 24 )236.0502083333333.790831984617862.26870757954
Trimmed Mean ( 13 / 24 )236.4641304347833.6973954349677763.954244168326
Trimmed Mean ( 14 / 24 )236.9370454545453.578879547275366.2042525669612
Trimmed Mean ( 15 / 24 )237.4652380952383.4282818951177369.2665438140942
Trimmed Mean ( 16 / 24 )237.319253.4529171314044268.7300740123682
Trimmed Mean ( 17 / 24 )237.1318421052633.4849280817178868.0449743996927
Trimmed Mean ( 18 / 24 )236.9311111111113.5157490515248867.3913603157619
Trimmed Mean ( 19 / 24 )236.7047058823533.5419809314770866.828339977438
Trimmed Mean ( 20 / 24 )236.45253.5626794238914366.3692889161856
Trimmed Mean ( 21 / 24 )236.1633.5843706432295765.8868804335518
Trimmed Mean ( 22 / 24 )235.8164285714293.5991625353907365.5198053026599
Trimmed Mean ( 23 / 24 )235.4880769230773.6399525364289664.6953702187849
Trimmed Mean ( 24 / 24 )235.09253.6792310874593863.8971824306742
Median226.84
Midrange217.815
Midmean - Weighted Average at Xnp236.300540540541
Midmean - Weighted Average at X(n+1)p236.931111111111
Midmean - Empirical Distribution Function236.300540540541
Midmean - Empirical Distribution Function - Averaging236.931111111111
Midmean - Empirical Distribution Function - Interpolation236.931111111111
Midmean - Closest Observation236.300540540541
Midmean - True Basic - Statistics Graphics Toolkit236.931111111111
Midmean - MS Excel (old versions)237.131842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 233.097361111111 & 4.24432296431285 & 54.9197982978775 \tabularnewline
Geometric Mean & 230.226150968289 &  &  \tabularnewline
Harmonic Mean & 227.247213295458 &  &  \tabularnewline
Quadratic Mean & 235.824921189782 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 233.331944444444 & 4.18452535080589 & 55.760671732938 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 233.517222222222 & 4.14742432478531 & 56.3041550455077 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 233.518472222222 & 4.14635720572335 & 56.3189471230046 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 233.488472222222 & 4.13765868008519 & 56.4300949582954 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 233.382916666667 & 4.11903858336292 & 56.6595607065485 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 233.370416666667 & 4.10545821858727 & 56.8439390297758 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 233.30625 & 4.0894871968926 & 57.0502458541202 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 233.228472222222 & 4.0779721903705 & 57.192266483071 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 233.050972222222 & 4.03823227180573 & 57.7111360952032 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 232.925972222222 & 4.01536845490269 & 58.0086173506254 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 232.971805555556 & 4.00472835422994 & 58.1741843512262 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 232.876805555556 & 3.98192912284656 & 58.4834130319926 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 232.707083333333 & 3.95590723989694 & 58.8252123271212 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 232.623472222222 & 3.92251610029961 & 59.3046570808095 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 238.681805555556 & 2.95747188625631 & 80.7046743756841 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 238.901805555556 & 2.89280797873189 & 82.5847437202803 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 238.838055555556 & 2.87869920985184 & 82.9673537055121 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 238.855555555556 & 2.87454904191962 & 83.0932268235189 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 238.834444444444 & 2.86385596109842 & 83.39610919288 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 238.865 & 2.81103018279347 & 84.9741854292816 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 238.993333333333 & 2.78327007181207 & 85.8678199265568 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 238.425 & 2.62510539321922 & 90.8249248262048 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 238.520833333333 & 2.58188643980098 & 92.3823874111673 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 238.830833333333 & 2.4967396169382 & 95.6570848289802 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 233.534 & 4.16500472561427 & 56.0705246176059 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 233.747941176471 & 4.13915412950064 & 56.4723936010255 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 233.873787878788 & 4.12833523153379 & 56.6508712985252 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 234.00703125 & 4.11235496125583 & 56.903412632099 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 234.157580645161 & 4.09265665972592 & 57.2140788034837 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 234.3435 & 4.07071058654119 & 57.5682046212765 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 234.544827586207 & 4.04388118392795 & 57.9999304921185 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 234.772321428571 & 4.01111707560692 & 58.5304086126801 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 235.02962962963 & 3.96953318516216 & 59.2083800957136 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 235.334038461538 & 3.92276389368285 & 59.991894704781 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 235.6808 & 3.86507976885236 & 60.976956258261 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 236.050208333333 & 3.7908319846178 & 62.26870757954 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 236.464130434783 & 3.69739543496777 & 63.954244168326 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 236.937045454545 & 3.5788795472753 & 66.2042525669612 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 237.465238095238 & 3.42828189511773 & 69.2665438140942 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 237.31925 & 3.45291713140442 & 68.7300740123682 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 237.131842105263 & 3.48492808171788 & 68.0449743996927 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 236.931111111111 & 3.51574905152488 & 67.3913603157619 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 236.704705882353 & 3.54198093147708 & 66.828339977438 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 236.4525 & 3.56267942389143 & 66.3692889161856 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 236.163 & 3.58437064322957 & 65.8868804335518 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 235.816428571429 & 3.59916253539073 & 65.5198053026599 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 235.488076923077 & 3.63995253642896 & 64.6953702187849 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 235.0925 & 3.67923108745938 & 63.8971824306742 \tabularnewline
Median & 226.84 &  &  \tabularnewline
Midrange & 217.815 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 236.300540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 236.931111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 236.300540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 236.931111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 236.931111111111 &  &  \tabularnewline
Midmean - Closest Observation & 236.300540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 236.931111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 237.131842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180875&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]233.097361111111[/C][C]4.24432296431285[/C][C]54.9197982978775[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]230.226150968289[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]227.247213295458[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]235.824921189782[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]233.331944444444[/C][C]4.18452535080589[/C][C]55.760671732938[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]233.517222222222[/C][C]4.14742432478531[/C][C]56.3041550455077[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]233.518472222222[/C][C]4.14635720572335[/C][C]56.3189471230046[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]233.488472222222[/C][C]4.13765868008519[/C][C]56.4300949582954[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]233.382916666667[/C][C]4.11903858336292[/C][C]56.6595607065485[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]233.370416666667[/C][C]4.10545821858727[/C][C]56.8439390297758[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]233.30625[/C][C]4.0894871968926[/C][C]57.0502458541202[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]233.228472222222[/C][C]4.0779721903705[/C][C]57.192266483071[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]233.050972222222[/C][C]4.03823227180573[/C][C]57.7111360952032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]232.925972222222[/C][C]4.01536845490269[/C][C]58.0086173506254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]232.971805555556[/C][C]4.00472835422994[/C][C]58.1741843512262[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]232.876805555556[/C][C]3.98192912284656[/C][C]58.4834130319926[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]232.707083333333[/C][C]3.95590723989694[/C][C]58.8252123271212[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]232.623472222222[/C][C]3.92251610029961[/C][C]59.3046570808095[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]238.681805555556[/C][C]2.95747188625631[/C][C]80.7046743756841[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]238.901805555556[/C][C]2.89280797873189[/C][C]82.5847437202803[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]238.838055555556[/C][C]2.87869920985184[/C][C]82.9673537055121[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]238.855555555556[/C][C]2.87454904191962[/C][C]83.0932268235189[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]238.834444444444[/C][C]2.86385596109842[/C][C]83.39610919288[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]238.865[/C][C]2.81103018279347[/C][C]84.9741854292816[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]238.993333333333[/C][C]2.78327007181207[/C][C]85.8678199265568[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]238.425[/C][C]2.62510539321922[/C][C]90.8249248262048[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]238.520833333333[/C][C]2.58188643980098[/C][C]92.3823874111673[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]238.830833333333[/C][C]2.4967396169382[/C][C]95.6570848289802[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]233.534[/C][C]4.16500472561427[/C][C]56.0705246176059[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]233.747941176471[/C][C]4.13915412950064[/C][C]56.4723936010255[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]233.873787878788[/C][C]4.12833523153379[/C][C]56.6508712985252[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]234.00703125[/C][C]4.11235496125583[/C][C]56.903412632099[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]234.157580645161[/C][C]4.09265665972592[/C][C]57.2140788034837[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]234.3435[/C][C]4.07071058654119[/C][C]57.5682046212765[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]234.544827586207[/C][C]4.04388118392795[/C][C]57.9999304921185[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]234.772321428571[/C][C]4.01111707560692[/C][C]58.5304086126801[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]235.02962962963[/C][C]3.96953318516216[/C][C]59.2083800957136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]235.334038461538[/C][C]3.92276389368285[/C][C]59.991894704781[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]235.6808[/C][C]3.86507976885236[/C][C]60.976956258261[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]236.050208333333[/C][C]3.7908319846178[/C][C]62.26870757954[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]236.464130434783[/C][C]3.69739543496777[/C][C]63.954244168326[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]236.937045454545[/C][C]3.5788795472753[/C][C]66.2042525669612[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]237.465238095238[/C][C]3.42828189511773[/C][C]69.2665438140942[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]237.31925[/C][C]3.45291713140442[/C][C]68.7300740123682[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]237.131842105263[/C][C]3.48492808171788[/C][C]68.0449743996927[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]236.931111111111[/C][C]3.51574905152488[/C][C]67.3913603157619[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]236.704705882353[/C][C]3.54198093147708[/C][C]66.828339977438[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]236.4525[/C][C]3.56267942389143[/C][C]66.3692889161856[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]236.163[/C][C]3.58437064322957[/C][C]65.8868804335518[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]235.816428571429[/C][C]3.59916253539073[/C][C]65.5198053026599[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]235.488076923077[/C][C]3.63995253642896[/C][C]64.6953702187849[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]235.0925[/C][C]3.67923108745938[/C][C]63.8971824306742[/C][/ROW]
[ROW][C]Median[/C][C]226.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]217.815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]236.300540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]236.931111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]236.300540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]236.931111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]236.931111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]236.300540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]236.931111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]237.131842105263[/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=180875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180875&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 Mean233.0973611111114.2443229643128554.9197982978775
Geometric Mean230.226150968289
Harmonic Mean227.247213295458
Quadratic Mean235.824921189782
Winsorized Mean ( 1 / 24 )233.3319444444444.1845253508058955.760671732938
Winsorized Mean ( 2 / 24 )233.5172222222224.1474243247853156.3041550455077
Winsorized Mean ( 3 / 24 )233.5184722222224.1463572057233556.3189471230046
Winsorized Mean ( 4 / 24 )233.4884722222224.1376586800851956.4300949582954
Winsorized Mean ( 5 / 24 )233.3829166666674.1190385833629256.6595607065485
Winsorized Mean ( 6 / 24 )233.3704166666674.1054582185872756.8439390297758
Winsorized Mean ( 7 / 24 )233.306254.089487196892657.0502458541202
Winsorized Mean ( 8 / 24 )233.2284722222224.077972190370557.192266483071
Winsorized Mean ( 9 / 24 )233.0509722222224.0382322718057357.7111360952032
Winsorized Mean ( 10 / 24 )232.9259722222224.0153684549026958.0086173506254
Winsorized Mean ( 11 / 24 )232.9718055555564.0047283542299458.1741843512262
Winsorized Mean ( 12 / 24 )232.8768055555563.9819291228465658.4834130319926
Winsorized Mean ( 13 / 24 )232.7070833333333.9559072398969458.8252123271212
Winsorized Mean ( 14 / 24 )232.6234722222223.9225161002996159.3046570808095
Winsorized Mean ( 15 / 24 )238.6818055555562.9574718862563180.7046743756841
Winsorized Mean ( 16 / 24 )238.9018055555562.8928079787318982.5847437202803
Winsorized Mean ( 17 / 24 )238.8380555555562.8786992098518482.9673537055121
Winsorized Mean ( 18 / 24 )238.8555555555562.8745490419196283.0932268235189
Winsorized Mean ( 19 / 24 )238.8344444444442.8638559610984283.39610919288
Winsorized Mean ( 20 / 24 )238.8652.8110301827934784.9741854292816
Winsorized Mean ( 21 / 24 )238.9933333333332.7832700718120785.8678199265568
Winsorized Mean ( 22 / 24 )238.4252.6251053932192290.8249248262048
Winsorized Mean ( 23 / 24 )238.5208333333332.5818864398009892.3823874111673
Winsorized Mean ( 24 / 24 )238.8308333333332.496739616938295.6570848289802
Trimmed Mean ( 1 / 24 )233.5344.1650047256142756.0705246176059
Trimmed Mean ( 2 / 24 )233.7479411764714.1391541295006456.4723936010255
Trimmed Mean ( 3 / 24 )233.8737878787884.1283352315337956.6508712985252
Trimmed Mean ( 4 / 24 )234.007031254.1123549612558356.903412632099
Trimmed Mean ( 5 / 24 )234.1575806451614.0926566597259257.2140788034837
Trimmed Mean ( 6 / 24 )234.34354.0707105865411957.5682046212765
Trimmed Mean ( 7 / 24 )234.5448275862074.0438811839279557.9999304921185
Trimmed Mean ( 8 / 24 )234.7723214285714.0111170756069258.5304086126801
Trimmed Mean ( 9 / 24 )235.029629629633.9695331851621659.2083800957136
Trimmed Mean ( 10 / 24 )235.3340384615383.9227638936828559.991894704781
Trimmed Mean ( 11 / 24 )235.68083.8650797688523660.976956258261
Trimmed Mean ( 12 / 24 )236.0502083333333.790831984617862.26870757954
Trimmed Mean ( 13 / 24 )236.4641304347833.6973954349677763.954244168326
Trimmed Mean ( 14 / 24 )236.9370454545453.578879547275366.2042525669612
Trimmed Mean ( 15 / 24 )237.4652380952383.4282818951177369.2665438140942
Trimmed Mean ( 16 / 24 )237.319253.4529171314044268.7300740123682
Trimmed Mean ( 17 / 24 )237.1318421052633.4849280817178868.0449743996927
Trimmed Mean ( 18 / 24 )236.9311111111113.5157490515248867.3913603157619
Trimmed Mean ( 19 / 24 )236.7047058823533.5419809314770866.828339977438
Trimmed Mean ( 20 / 24 )236.45253.5626794238914366.3692889161856
Trimmed Mean ( 21 / 24 )236.1633.5843706432295765.8868804335518
Trimmed Mean ( 22 / 24 )235.8164285714293.5991625353907365.5198053026599
Trimmed Mean ( 23 / 24 )235.4880769230773.6399525364289664.6953702187849
Trimmed Mean ( 24 / 24 )235.09253.6792310874593863.8971824306742
Median226.84
Midrange217.815
Midmean - Weighted Average at Xnp236.300540540541
Midmean - Weighted Average at X(n+1)p236.931111111111
Midmean - Empirical Distribution Function236.300540540541
Midmean - Empirical Distribution Function - Averaging236.931111111111
Midmean - Empirical Distribution Function - Interpolation236.931111111111
Midmean - Closest Observation236.300540540541
Midmean - True Basic - Statistics Graphics Toolkit236.931111111111
Midmean - MS Excel (old versions)237.131842105263
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')