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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 23 Oct 2009 00:57:10 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t1256281136iy9fsxsni1f940s.htm/, Retrieved Thu, 02 May 2024 09:50:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49840, Retrieved Thu, 02 May 2024 09:50:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKVN WS3
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [] [2009-10-20 15:12:09] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D        [Central Tendency] [] [2009-10-20 15:25:16] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D            [Central Tendency] [WS3 Q2 Yt Central...] [2009-10-23 06:57:10] [f1100e00818182135823a11ccbd0f3b9] [Current]
-    D              [Central Tendency] [WS3 Q2 Central Te...] [2009-10-23 07:40:09] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
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Dataseries X:
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49840&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49840&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9639.666.9555683688311143.970101887558
Geometric Mean9625.8296850747
Harmonic Mean9612.0099657583
Quadratic Mean9653.3096914996
Winsorized Mean ( 1 / 20 )9639.7666666666766.1909511569815145.635717543997
Winsorized Mean ( 2 / 20 )9641.2333333333365.5614016193793147.056546919270
Winsorized Mean ( 3 / 20 )9635.7833333333363.401028755607151.981498131151
Winsorized Mean ( 4 / 20 )9640.3166666666761.7009669075437156.242554206845
Winsorized Mean ( 5 / 20 )9649.959.5664500990375162.002267785905
Winsorized Mean ( 6 / 20 )9653.157.316125554573168.418571677684
Winsorized Mean ( 7 / 20 )9650.0666666666755.3118680712303174.466475336529
Winsorized Mean ( 8 / 20 )9636.4666666666751.6863228511003186.441327900763
Winsorized Mean ( 9 / 20 )9640.3666666666749.8858072649761193.248685251506
Winsorized Mean ( 10 / 20 )9638.8666666666749.1420256169053196.143047537520
Winsorized Mean ( 11 / 20 )9642.7166666666745.8484921516514210.316985666002
Winsorized Mean ( 12 / 20 )9645.5166666666744.9018357536634214.813414747296
Winsorized Mean ( 13 / 20 )9645.5166666666744.3150348265245217.657883028299
Winsorized Mean ( 14 / 20 )9652.0541.3869873992865233.214606970074
Winsorized Mean ( 15 / 20 )9635.337.6045307704175256.227103559017
Winsorized Mean ( 16 / 20 )9624.135.4051665609560271.827558936362
Winsorized Mean ( 17 / 20 )9627.2166666666734.8086625661226276.575310768657
Winsorized Mean ( 18 / 20 )9618.2166666666731.2685026956621307.600807121507
Winsorized Mean ( 19 / 20 )9643.8666666666724.3171310504249396.587354267606
Winsorized Mean ( 20 / 20 )9631.221.9221375097035439.336720506241
Trimmed Mean ( 1 / 20 )9640.564.1236151646067150.342428062620
Trimmed Mean ( 2 / 20 )9641.2857142857161.5751294575821156.577595519753
Trimmed Mean ( 3 / 20 )9641.3148148148258.8401987553542163.855918551558
Trimmed Mean ( 4 / 20 )9643.4423076923156.5056986238511170.663181635663
Trimmed Mean ( 5 / 20 )9644.3854.2671012451469177.720566949621
Trimmed Mean ( 6 / 20 )964352.1926328324776184.757876287849
Trimmed Mean ( 7 / 20 )9640.8043478260950.2663497045827191.794399324508
Trimmed Mean ( 8 / 20 )963948.3851378470913199.214065080512
Trimmed Mean ( 9 / 20 )9639.4523809523846.9814281440450205.175805882227
Trimmed Mean ( 10 / 20 )9639.345.6039275186711211.369952643958
Trimmed Mean ( 11 / 20 )9639.3684210526343.9344109142171219.403611439646
Trimmed Mean ( 12 / 20 )9638.8611111111142.5764140828605226.3896882521
Trimmed Mean ( 13 / 20 )9637.8823529411840.9270853903477235.489096304283
Trimmed Mean ( 14 / 20 )9636.7812538.7412251868969248.747457095378
Trimmed Mean ( 15 / 20 )9634.636.5300569048457263.744456382765
Trimmed Mean ( 16 / 20 )9634.534.5920098123417278.518075482351
Trimmed Mean ( 17 / 20 )963632.4243023766956297.184497234572
Trimmed Mean ( 18 / 20 )9637.2916666666729.2089845696384329.942714841387
Trimmed Mean ( 19 / 20 )9640.1818181818225.6275889929486376.164211968372
Trimmed Mean ( 20 / 20 )9639.623.4619961460634410.860181716354
Median9655.5
Midrange9613.5
Midmean - Weighted Average at Xnp9622.70967741935
Midmean - Weighted Average at X(n+1)p9634.6
Midmean - Empirical Distribution Function9622.70967741935
Midmean - Empirical Distribution Function - Averaging9634.6
Midmean - Empirical Distribution Function - Interpolation9634.6
Midmean - Closest Observation9622.70967741935
Midmean - True Basic - Statistics Graphics Toolkit9634.6
Midmean - MS Excel (old versions)9636.78125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9639.6 & 66.9555683688311 & 143.970101887558 \tabularnewline
Geometric Mean & 9625.8296850747 &  &  \tabularnewline
Harmonic Mean & 9612.0099657583 &  &  \tabularnewline
Quadratic Mean & 9653.3096914996 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 9639.76666666667 & 66.1909511569815 & 145.635717543997 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 9641.23333333333 & 65.5614016193793 & 147.056546919270 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 9635.78333333333 & 63.401028755607 & 151.981498131151 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 9640.31666666667 & 61.7009669075437 & 156.242554206845 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 9649.9 & 59.5664500990375 & 162.002267785905 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9653.1 & 57.316125554573 & 168.418571677684 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9650.06666666667 & 55.3118680712303 & 174.466475336529 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9636.46666666667 & 51.6863228511003 & 186.441327900763 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9640.36666666667 & 49.8858072649761 & 193.248685251506 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9638.86666666667 & 49.1420256169053 & 196.143047537520 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9642.71666666667 & 45.8484921516514 & 210.316985666002 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 9645.51666666667 & 44.9018357536634 & 214.813414747296 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9645.51666666667 & 44.3150348265245 & 217.657883028299 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9652.05 & 41.3869873992865 & 233.214606970074 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9635.3 & 37.6045307704175 & 256.227103559017 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9624.1 & 35.4051665609560 & 271.827558936362 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9627.21666666667 & 34.8086625661226 & 276.575310768657 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9618.21666666667 & 31.2685026956621 & 307.600807121507 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9643.86666666667 & 24.3171310504249 & 396.587354267606 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9631.2 & 21.9221375097035 & 439.336720506241 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 9640.5 & 64.1236151646067 & 150.342428062620 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 9641.28571428571 & 61.5751294575821 & 156.577595519753 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9641.31481481482 & 58.8401987553542 & 163.855918551558 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9643.44230769231 & 56.5056986238511 & 170.663181635663 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9644.38 & 54.2671012451469 & 177.720566949621 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9643 & 52.1926328324776 & 184.757876287849 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9640.80434782609 & 50.2663497045827 & 191.794399324508 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9639 & 48.3851378470913 & 199.214065080512 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9639.45238095238 & 46.9814281440450 & 205.175805882227 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9639.3 & 45.6039275186711 & 211.369952643958 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9639.36842105263 & 43.9344109142171 & 219.403611439646 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9638.86111111111 & 42.5764140828605 & 226.3896882521 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9637.88235294118 & 40.9270853903477 & 235.489096304283 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9636.78125 & 38.7412251868969 & 248.747457095378 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9634.6 & 36.5300569048457 & 263.744456382765 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9634.5 & 34.5920098123417 & 278.518075482351 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9636 & 32.4243023766956 & 297.184497234572 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9637.29166666667 & 29.2089845696384 & 329.942714841387 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9640.18181818182 & 25.6275889929486 & 376.164211968372 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9639.6 & 23.4619961460634 & 410.860181716354 \tabularnewline
Median & 9655.5 &  &  \tabularnewline
Midrange & 9613.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9622.70967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9634.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9622.70967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9634.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9634.6 &  &  \tabularnewline
Midmean - Closest Observation & 9622.70967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9634.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9636.78125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49840&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]9639.6[/C][C]66.9555683688311[/C][C]143.970101887558[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9625.8296850747[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9612.0099657583[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9653.3096914996[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]9639.76666666667[/C][C]66.1909511569815[/C][C]145.635717543997[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]9641.23333333333[/C][C]65.5614016193793[/C][C]147.056546919270[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]9635.78333333333[/C][C]63.401028755607[/C][C]151.981498131151[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]9640.31666666667[/C][C]61.7009669075437[/C][C]156.242554206845[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]9649.9[/C][C]59.5664500990375[/C][C]162.002267785905[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9653.1[/C][C]57.316125554573[/C][C]168.418571677684[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9650.06666666667[/C][C]55.3118680712303[/C][C]174.466475336529[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9636.46666666667[/C][C]51.6863228511003[/C][C]186.441327900763[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9640.36666666667[/C][C]49.8858072649761[/C][C]193.248685251506[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9638.86666666667[/C][C]49.1420256169053[/C][C]196.143047537520[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9642.71666666667[/C][C]45.8484921516514[/C][C]210.316985666002[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]9645.51666666667[/C][C]44.9018357536634[/C][C]214.813414747296[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9645.51666666667[/C][C]44.3150348265245[/C][C]217.657883028299[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9652.05[/C][C]41.3869873992865[/C][C]233.214606970074[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9635.3[/C][C]37.6045307704175[/C][C]256.227103559017[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9624.1[/C][C]35.4051665609560[/C][C]271.827558936362[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9627.21666666667[/C][C]34.8086625661226[/C][C]276.575310768657[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9618.21666666667[/C][C]31.2685026956621[/C][C]307.600807121507[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9643.86666666667[/C][C]24.3171310504249[/C][C]396.587354267606[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9631.2[/C][C]21.9221375097035[/C][C]439.336720506241[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]9640.5[/C][C]64.1236151646067[/C][C]150.342428062620[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]9641.28571428571[/C][C]61.5751294575821[/C][C]156.577595519753[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9641.31481481482[/C][C]58.8401987553542[/C][C]163.855918551558[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9643.44230769231[/C][C]56.5056986238511[/C][C]170.663181635663[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9644.38[/C][C]54.2671012451469[/C][C]177.720566949621[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9643[/C][C]52.1926328324776[/C][C]184.757876287849[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9640.80434782609[/C][C]50.2663497045827[/C][C]191.794399324508[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9639[/C][C]48.3851378470913[/C][C]199.214065080512[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9639.45238095238[/C][C]46.9814281440450[/C][C]205.175805882227[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9639.3[/C][C]45.6039275186711[/C][C]211.369952643958[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9639.36842105263[/C][C]43.9344109142171[/C][C]219.403611439646[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9638.86111111111[/C][C]42.5764140828605[/C][C]226.3896882521[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9637.88235294118[/C][C]40.9270853903477[/C][C]235.489096304283[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9636.78125[/C][C]38.7412251868969[/C][C]248.747457095378[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9634.6[/C][C]36.5300569048457[/C][C]263.744456382765[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9634.5[/C][C]34.5920098123417[/C][C]278.518075482351[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9636[/C][C]32.4243023766956[/C][C]297.184497234572[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9637.29166666667[/C][C]29.2089845696384[/C][C]329.942714841387[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9640.18181818182[/C][C]25.6275889929486[/C][C]376.164211968372[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9639.6[/C][C]23.4619961460634[/C][C]410.860181716354[/C][/ROW]
[ROW][C]Median[/C][C]9655.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9613.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9622.70967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9634.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9622.70967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9634.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9634.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9622.70967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9634.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9636.78125[/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=49840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49840&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 Mean9639.666.9555683688311143.970101887558
Geometric Mean9625.8296850747
Harmonic Mean9612.0099657583
Quadratic Mean9653.3096914996
Winsorized Mean ( 1 / 20 )9639.7666666666766.1909511569815145.635717543997
Winsorized Mean ( 2 / 20 )9641.2333333333365.5614016193793147.056546919270
Winsorized Mean ( 3 / 20 )9635.7833333333363.401028755607151.981498131151
Winsorized Mean ( 4 / 20 )9640.3166666666761.7009669075437156.242554206845
Winsorized Mean ( 5 / 20 )9649.959.5664500990375162.002267785905
Winsorized Mean ( 6 / 20 )9653.157.316125554573168.418571677684
Winsorized Mean ( 7 / 20 )9650.0666666666755.3118680712303174.466475336529
Winsorized Mean ( 8 / 20 )9636.4666666666751.6863228511003186.441327900763
Winsorized Mean ( 9 / 20 )9640.3666666666749.8858072649761193.248685251506
Winsorized Mean ( 10 / 20 )9638.8666666666749.1420256169053196.143047537520
Winsorized Mean ( 11 / 20 )9642.7166666666745.8484921516514210.316985666002
Winsorized Mean ( 12 / 20 )9645.5166666666744.9018357536634214.813414747296
Winsorized Mean ( 13 / 20 )9645.5166666666744.3150348265245217.657883028299
Winsorized Mean ( 14 / 20 )9652.0541.3869873992865233.214606970074
Winsorized Mean ( 15 / 20 )9635.337.6045307704175256.227103559017
Winsorized Mean ( 16 / 20 )9624.135.4051665609560271.827558936362
Winsorized Mean ( 17 / 20 )9627.2166666666734.8086625661226276.575310768657
Winsorized Mean ( 18 / 20 )9618.2166666666731.2685026956621307.600807121507
Winsorized Mean ( 19 / 20 )9643.8666666666724.3171310504249396.587354267606
Winsorized Mean ( 20 / 20 )9631.221.9221375097035439.336720506241
Trimmed Mean ( 1 / 20 )9640.564.1236151646067150.342428062620
Trimmed Mean ( 2 / 20 )9641.2857142857161.5751294575821156.577595519753
Trimmed Mean ( 3 / 20 )9641.3148148148258.8401987553542163.855918551558
Trimmed Mean ( 4 / 20 )9643.4423076923156.5056986238511170.663181635663
Trimmed Mean ( 5 / 20 )9644.3854.2671012451469177.720566949621
Trimmed Mean ( 6 / 20 )964352.1926328324776184.757876287849
Trimmed Mean ( 7 / 20 )9640.8043478260950.2663497045827191.794399324508
Trimmed Mean ( 8 / 20 )963948.3851378470913199.214065080512
Trimmed Mean ( 9 / 20 )9639.4523809523846.9814281440450205.175805882227
Trimmed Mean ( 10 / 20 )9639.345.6039275186711211.369952643958
Trimmed Mean ( 11 / 20 )9639.3684210526343.9344109142171219.403611439646
Trimmed Mean ( 12 / 20 )9638.8611111111142.5764140828605226.3896882521
Trimmed Mean ( 13 / 20 )9637.8823529411840.9270853903477235.489096304283
Trimmed Mean ( 14 / 20 )9636.7812538.7412251868969248.747457095378
Trimmed Mean ( 15 / 20 )9634.636.5300569048457263.744456382765
Trimmed Mean ( 16 / 20 )9634.534.5920098123417278.518075482351
Trimmed Mean ( 17 / 20 )963632.4243023766956297.184497234572
Trimmed Mean ( 18 / 20 )9637.2916666666729.2089845696384329.942714841387
Trimmed Mean ( 19 / 20 )9640.1818181818225.6275889929486376.164211968372
Trimmed Mean ( 20 / 20 )9639.623.4619961460634410.860181716354
Median9655.5
Midrange9613.5
Midmean - Weighted Average at Xnp9622.70967741935
Midmean - Weighted Average at X(n+1)p9634.6
Midmean - Empirical Distribution Function9622.70967741935
Midmean - Empirical Distribution Function - Averaging9634.6
Midmean - Empirical Distribution Function - Interpolation9634.6
Midmean - Closest Observation9622.70967741935
Midmean - True Basic - Statistics Graphics Toolkit9634.6
Midmean - MS Excel (old versions)9636.78125
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')