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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 16:33:38 -0500
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/Mar/05/t1330983252vonqf19bj2dzs44.htm/, Retrieved Fri, 03 May 2024 01:24:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163502, Retrieved Fri, 03 May 2024 01:24:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - bo...] [2012-03-05 21:33:38] [1924da7ecb4a93ab5e2de1fdfa2878e4] [Current]
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Dataseries X:
3440
2678
2981
2260
2844
2546
2456
2295
2379
2479
2057
2280
2351
2276
2548
2311
2201
2725
2408
2139
1898
2539
2070
2063
2565
2442
2194
2798
2074
2628
2289
2154
2468
2137
1850
2078
1791
1755
2232
1954
1822
2522
2074
2366
2173
2094
1833
1858
2040
2133
2921
3252
3318
3556
2305
1618
1314
1501
1414
1661




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163502&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163502&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2290.1333333333359.64461354280438.396314391237
Geometric Mean2245.11658039437
Harmonic Mean2200.12940689463
Quadratic Mean2335.50893811178
Winsorized Mean ( 1 / 20 )2289.8666666666758.532001323273839.1216191980123
Winsorized Mean ( 2 / 20 )2288.756.515536087071140.4968289865267
Winsorized Mean ( 3 / 20 )2291.2554.201854498471242.272538849471
Winsorized Mean ( 4 / 20 )2276.0548.633155932267146.8003763352296
Winsorized Mean ( 5 / 20 )2278.8833333333345.823698576436549.7315451203056
Winsorized Mean ( 6 / 20 )2274.7833333333343.361703609575552.4606540788909
Winsorized Mean ( 7 / 20 )2273.0333333333341.513927733435154.7535118317086
Winsorized Mean ( 8 / 20 )2264.7666666666739.229207430572557.731644736255
Winsorized Mean ( 9 / 20 )2260.2666666666737.384865564262860.4594033588639
Winsorized Mean ( 10 / 20 )2253.2666666666735.601877899644163.2906689084845
Winsorized Mean ( 11 / 20 )2249.0532.241605792326769.7561410088097
Winsorized Mean ( 12 / 20 )2256.8529.671628719156276.0608735489791
Winsorized Mean ( 13 / 20 )2275.0526.578148547744885.5985132264995
Winsorized Mean ( 14 / 20 )2277.3833333333325.71060248297788.5775949762821
Winsorized Mean ( 15 / 20 )2274.6333333333324.766662104310291.8425472012827
Winsorized Mean ( 16 / 20 )2265.0333333333322.6022343611591100.212806271299
Winsorized Mean ( 17 / 20 )2263.0521.9397792247182103.148257638361
Winsorized Mean ( 18 / 20 )2259.4521.3741808578629105.709314196657
Winsorized Mean ( 19 / 20 )2256.2833333333320.5017718907204110.053089331005
Winsorized Mean ( 20 / 20 )2250.2833333333318.0030300598844124.99469955047
Trimmed Mean ( 1 / 20 )2285.1379310344855.099252952358341.4731200259708
Trimmed Mean ( 2 / 20 )2280.0714285714350.782039065512244.8991704651715
Trimmed Mean ( 3 / 20 )2275.2777777777846.758156922196748.6605531001517
Trimmed Mean ( 4 / 20 )2269.1346153846242.849574030612552.9558266731777
Trimmed Mean ( 5 / 20 )2267.0640.368227655937956.1595128555645
Trimmed Mean ( 6 / 20 )2264.1041666666738.259116092372359.1781619104906
Trimmed Mean ( 7 / 20 )2261.7826086956536.394827803731562.1457153443039
Trimmed Mean ( 8 / 20 )2259.5909090909134.567232620166865.3680013647563
Trimmed Mean ( 9 / 20 )2258.6666666666732.884174778035268.6855206771171
Trimmed Mean ( 10 / 20 )2258.431.207181947881972.3679569584874
Trimmed Mean ( 11 / 20 )2259.2105263157929.484865030267876.6227189439933
Trimmed Mean ( 12 / 20 )2260.7528.14715793823680.3189439218276
Trimmed Mean ( 13 / 20 )2261.3235294117627.060891283468183.5642664435537
Trimmed Mean ( 14 / 20 )2259.3437526.401849938811785.5752061024587
Trimmed Mean ( 15 / 20 )2256.7666666666725.644146711021688.003188099713
Trimmed Mean ( 16 / 20 )2254.2142857142924.775572387947390.9853564800346
Trimmed Mean ( 17 / 20 )2252.6538461538524.163796333656693.2243350775237
Trimmed Mean ( 18 / 20 )2251.12523.358447599859196.3730569155452
Trimmed Mean ( 19 / 20 )2249.8636363636422.2051918049196101.321513280744
Trimmed Mean ( 20 / 20 )2248.8520.6043269599782109.144550286363
Median2268
Midrange2435
Midmean - Weighted Average at Xnp2250.32258064516
Midmean - Weighted Average at X(n+1)p2256.76666666667
Midmean - Empirical Distribution Function2250.32258064516
Midmean - Empirical Distribution Function - Averaging2256.76666666667
Midmean - Empirical Distribution Function - Interpolation2256.76666666667
Midmean - Closest Observation2250.32258064516
Midmean - True Basic - Statistics Graphics Toolkit2256.76666666667
Midmean - MS Excel (old versions)2259.34375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2290.13333333333 & 59.644613542804 & 38.396314391237 \tabularnewline
Geometric Mean & 2245.11658039437 &  &  \tabularnewline
Harmonic Mean & 2200.12940689463 &  &  \tabularnewline
Quadratic Mean & 2335.50893811178 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2289.86666666667 & 58.5320013232738 & 39.1216191980123 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2288.7 & 56.5155360870711 & 40.4968289865267 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2291.25 & 54.2018544984712 & 42.272538849471 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2276.05 & 48.6331559322671 & 46.8003763352296 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2278.88333333333 & 45.8236985764365 & 49.7315451203056 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2274.78333333333 & 43.3617036095755 & 52.4606540788909 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2273.03333333333 & 41.5139277334351 & 54.7535118317086 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2264.76666666667 & 39.2292074305725 & 57.731644736255 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2260.26666666667 & 37.3848655642628 & 60.4594033588639 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2253.26666666667 & 35.6018778996441 & 63.2906689084845 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2249.05 & 32.2416057923267 & 69.7561410088097 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2256.85 & 29.6716287191562 & 76.0608735489791 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2275.05 & 26.5781485477448 & 85.5985132264995 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2277.38333333333 & 25.710602482977 & 88.5775949762821 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2274.63333333333 & 24.7666621043102 & 91.8425472012827 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2265.03333333333 & 22.6022343611591 & 100.212806271299 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2263.05 & 21.9397792247182 & 103.148257638361 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2259.45 & 21.3741808578629 & 105.709314196657 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2256.28333333333 & 20.5017718907204 & 110.053089331005 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2250.28333333333 & 18.0030300598844 & 124.99469955047 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2285.13793103448 & 55.0992529523583 & 41.4731200259708 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2280.07142857143 & 50.7820390655122 & 44.8991704651715 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2275.27777777778 & 46.7581569221967 & 48.6605531001517 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2269.13461538462 & 42.8495740306125 & 52.9558266731777 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2267.06 & 40.3682276559379 & 56.1595128555645 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2264.10416666667 & 38.2591160923723 & 59.1781619104906 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2261.78260869565 & 36.3948278037315 & 62.1457153443039 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2259.59090909091 & 34.5672326201668 & 65.3680013647563 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2258.66666666667 & 32.8841747780352 & 68.6855206771171 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2258.4 & 31.2071819478819 & 72.3679569584874 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2259.21052631579 & 29.4848650302678 & 76.6227189439933 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2260.75 & 28.147157938236 & 80.3189439218276 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2261.32352941176 & 27.0608912834681 & 83.5642664435537 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2259.34375 & 26.4018499388117 & 85.5752061024587 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2256.76666666667 & 25.6441467110216 & 88.003188099713 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2254.21428571429 & 24.7755723879473 & 90.9853564800346 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2252.65384615385 & 24.1637963336566 & 93.2243350775237 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2251.125 & 23.3584475998591 & 96.3730569155452 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2249.86363636364 & 22.2051918049196 & 101.321513280744 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2248.85 & 20.6043269599782 & 109.144550286363 \tabularnewline
Median & 2268 &  &  \tabularnewline
Midrange & 2435 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2250.32258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2256.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2250.32258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2256.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2256.76666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2250.32258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2256.76666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2259.34375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163502&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]2290.13333333333[/C][C]59.644613542804[/C][C]38.396314391237[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2245.11658039437[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2200.12940689463[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2335.50893811178[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2289.86666666667[/C][C]58.5320013232738[/C][C]39.1216191980123[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2288.7[/C][C]56.5155360870711[/C][C]40.4968289865267[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2291.25[/C][C]54.2018544984712[/C][C]42.272538849471[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2276.05[/C][C]48.6331559322671[/C][C]46.8003763352296[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2278.88333333333[/C][C]45.8236985764365[/C][C]49.7315451203056[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2274.78333333333[/C][C]43.3617036095755[/C][C]52.4606540788909[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2273.03333333333[/C][C]41.5139277334351[/C][C]54.7535118317086[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2264.76666666667[/C][C]39.2292074305725[/C][C]57.731644736255[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2260.26666666667[/C][C]37.3848655642628[/C][C]60.4594033588639[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2253.26666666667[/C][C]35.6018778996441[/C][C]63.2906689084845[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2249.05[/C][C]32.2416057923267[/C][C]69.7561410088097[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2256.85[/C][C]29.6716287191562[/C][C]76.0608735489791[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2275.05[/C][C]26.5781485477448[/C][C]85.5985132264995[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2277.38333333333[/C][C]25.710602482977[/C][C]88.5775949762821[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2274.63333333333[/C][C]24.7666621043102[/C][C]91.8425472012827[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2265.03333333333[/C][C]22.6022343611591[/C][C]100.212806271299[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2263.05[/C][C]21.9397792247182[/C][C]103.148257638361[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2259.45[/C][C]21.3741808578629[/C][C]105.709314196657[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2256.28333333333[/C][C]20.5017718907204[/C][C]110.053089331005[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2250.28333333333[/C][C]18.0030300598844[/C][C]124.99469955047[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2285.13793103448[/C][C]55.0992529523583[/C][C]41.4731200259708[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2280.07142857143[/C][C]50.7820390655122[/C][C]44.8991704651715[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2275.27777777778[/C][C]46.7581569221967[/C][C]48.6605531001517[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2269.13461538462[/C][C]42.8495740306125[/C][C]52.9558266731777[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2267.06[/C][C]40.3682276559379[/C][C]56.1595128555645[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2264.10416666667[/C][C]38.2591160923723[/C][C]59.1781619104906[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2261.78260869565[/C][C]36.3948278037315[/C][C]62.1457153443039[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2259.59090909091[/C][C]34.5672326201668[/C][C]65.3680013647563[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2258.66666666667[/C][C]32.8841747780352[/C][C]68.6855206771171[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2258.4[/C][C]31.2071819478819[/C][C]72.3679569584874[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2259.21052631579[/C][C]29.4848650302678[/C][C]76.6227189439933[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2260.75[/C][C]28.147157938236[/C][C]80.3189439218276[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2261.32352941176[/C][C]27.0608912834681[/C][C]83.5642664435537[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2259.34375[/C][C]26.4018499388117[/C][C]85.5752061024587[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2256.76666666667[/C][C]25.6441467110216[/C][C]88.003188099713[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2254.21428571429[/C][C]24.7755723879473[/C][C]90.9853564800346[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2252.65384615385[/C][C]24.1637963336566[/C][C]93.2243350775237[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2251.125[/C][C]23.3584475998591[/C][C]96.3730569155452[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2249.86363636364[/C][C]22.2051918049196[/C][C]101.321513280744[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2248.85[/C][C]20.6043269599782[/C][C]109.144550286363[/C][/ROW]
[ROW][C]Median[/C][C]2268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2250.32258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2256.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2250.32258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2256.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2256.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2250.32258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2256.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2259.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163502&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 Mean2290.1333333333359.64461354280438.396314391237
Geometric Mean2245.11658039437
Harmonic Mean2200.12940689463
Quadratic Mean2335.50893811178
Winsorized Mean ( 1 / 20 )2289.8666666666758.532001323273839.1216191980123
Winsorized Mean ( 2 / 20 )2288.756.515536087071140.4968289865267
Winsorized Mean ( 3 / 20 )2291.2554.201854498471242.272538849471
Winsorized Mean ( 4 / 20 )2276.0548.633155932267146.8003763352296
Winsorized Mean ( 5 / 20 )2278.8833333333345.823698576436549.7315451203056
Winsorized Mean ( 6 / 20 )2274.7833333333343.361703609575552.4606540788909
Winsorized Mean ( 7 / 20 )2273.0333333333341.513927733435154.7535118317086
Winsorized Mean ( 8 / 20 )2264.7666666666739.229207430572557.731644736255
Winsorized Mean ( 9 / 20 )2260.2666666666737.384865564262860.4594033588639
Winsorized Mean ( 10 / 20 )2253.2666666666735.601877899644163.2906689084845
Winsorized Mean ( 11 / 20 )2249.0532.241605792326769.7561410088097
Winsorized Mean ( 12 / 20 )2256.8529.671628719156276.0608735489791
Winsorized Mean ( 13 / 20 )2275.0526.578148547744885.5985132264995
Winsorized Mean ( 14 / 20 )2277.3833333333325.71060248297788.5775949762821
Winsorized Mean ( 15 / 20 )2274.6333333333324.766662104310291.8425472012827
Winsorized Mean ( 16 / 20 )2265.0333333333322.6022343611591100.212806271299
Winsorized Mean ( 17 / 20 )2263.0521.9397792247182103.148257638361
Winsorized Mean ( 18 / 20 )2259.4521.3741808578629105.709314196657
Winsorized Mean ( 19 / 20 )2256.2833333333320.5017718907204110.053089331005
Winsorized Mean ( 20 / 20 )2250.2833333333318.0030300598844124.99469955047
Trimmed Mean ( 1 / 20 )2285.1379310344855.099252952358341.4731200259708
Trimmed Mean ( 2 / 20 )2280.0714285714350.782039065512244.8991704651715
Trimmed Mean ( 3 / 20 )2275.2777777777846.758156922196748.6605531001517
Trimmed Mean ( 4 / 20 )2269.1346153846242.849574030612552.9558266731777
Trimmed Mean ( 5 / 20 )2267.0640.368227655937956.1595128555645
Trimmed Mean ( 6 / 20 )2264.1041666666738.259116092372359.1781619104906
Trimmed Mean ( 7 / 20 )2261.7826086956536.394827803731562.1457153443039
Trimmed Mean ( 8 / 20 )2259.5909090909134.567232620166865.3680013647563
Trimmed Mean ( 9 / 20 )2258.6666666666732.884174778035268.6855206771171
Trimmed Mean ( 10 / 20 )2258.431.207181947881972.3679569584874
Trimmed Mean ( 11 / 20 )2259.2105263157929.484865030267876.6227189439933
Trimmed Mean ( 12 / 20 )2260.7528.14715793823680.3189439218276
Trimmed Mean ( 13 / 20 )2261.3235294117627.060891283468183.5642664435537
Trimmed Mean ( 14 / 20 )2259.3437526.401849938811785.5752061024587
Trimmed Mean ( 15 / 20 )2256.7666666666725.644146711021688.003188099713
Trimmed Mean ( 16 / 20 )2254.2142857142924.775572387947390.9853564800346
Trimmed Mean ( 17 / 20 )2252.6538461538524.163796333656693.2243350775237
Trimmed Mean ( 18 / 20 )2251.12523.358447599859196.3730569155452
Trimmed Mean ( 19 / 20 )2249.8636363636422.2051918049196101.321513280744
Trimmed Mean ( 20 / 20 )2248.8520.6043269599782109.144550286363
Median2268
Midrange2435
Midmean - Weighted Average at Xnp2250.32258064516
Midmean - Weighted Average at X(n+1)p2256.76666666667
Midmean - Empirical Distribution Function2250.32258064516
Midmean - Empirical Distribution Function - Averaging2256.76666666667
Midmean - Empirical Distribution Function - Interpolation2256.76666666667
Midmean - Closest Observation2250.32258064516
Midmean - True Basic - Statistics Graphics Toolkit2256.76666666667
Midmean - MS Excel (old versions)2259.34375
Number of observations60



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')