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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 05:27:24 -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/18/t1255865299oga95djpc2bzn4v.htm/, Retrieved Mon, 29 Apr 2024 10:23:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47276, Retrieved Mon, 29 Apr 2024 10:23:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHSWWS3V2
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-18 11:27:24] [4563e36d4b7005634fe3557528d9fcab] [Current]
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Dataseries X:
14271
14013
15912
14290
14744
14721
13918
13263
15660
15629
15113
14526
15132
14908
16167
14122
13985
14236
13921
12394
15454
16146
15107
14593
14695
14513
17071
15179
15460
17173
15938
15003
18216
17847
18029
17281
16706
16750
18912
17763
16736
18061
16713
16769
19514
19251
19951
19052
19555
19083
22534
18854
19801
20346
18169
19087
20842
21602
22360
20334
21215
20530
23152
20134
21193
21628
20823
20493
22106
24178
24958
21620




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47276&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47276&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17630.625350.29775253258750.330397133678
Geometric Mean17389.5747994799
Harmonic Mean17156.0991801814
Quadratic Mean17875.9962655543
Winsorized Mean ( 1 / 24 )17631.8611111111344.90405512264651.1210606231965
Winsorized Mean ( 2 / 24 )17621.5555555556334.72754429239352.6444741582505
Winsorized Mean ( 3 / 24 )17595.9305555556328.98762785646653.485082919995
Winsorized Mean ( 4 / 24 )17589.8194444444326.41464680018953.8879600436921
Winsorized Mean ( 5 / 24 )17574.125322.55125876291154.4847509428501
Winsorized Mean ( 6 / 24 )17543.375313.54724333318455.9512972064561
Winsorized Mean ( 7 / 24 )17553.6805555556311.72198288100156.3119751559408
Winsorized Mean ( 8 / 24 )17555.5694444444310.77393850739056.4898380113911
Winsorized Mean ( 9 / 24 )17509.5694444444301.7966783533258.0177672596701
Winsorized Mean ( 10 / 24 )17537.4861111111296.71638753112559.1052157820957
Winsorized Mean ( 11 / 24 )17485.8472222222287.36288739692860.8493580386023
Winsorized Mean ( 12 / 24 )17493.8472222222285.2323714717861.3319138075217
Winsorized Mean ( 13 / 24 )17459.3611111111274.07930119462163.7018594071553
Winsorized Mean ( 14 / 24 )17457.2222222222272.22973720903664.1268011393532
Winsorized Mean ( 15 / 24 )17431.3888888889266.78900036946065.3377345570814
Winsorized Mean ( 16 / 24 )17465.1666666667261.2797564127666.8446989788059
Winsorized Mean ( 17 / 24 )17440.375250.97732631560769.4898429911096
Winsorized Mean ( 18 / 24 )17420.625240.59020448377572.4078731192683
Winsorized Mean ( 19 / 24 )17382.625234.56865020258874.1046383861924
Winsorized Mean ( 20 / 24 )17319.5694444444224.0805922556977.2916979114449
Winsorized Mean ( 21 / 24 )17321.3194444444220.52279594511678.5466163269372
Winsorized Mean ( 22 / 24 )17324.9861111111198.0375388185887.4833438875562
Winsorized Mean ( 23 / 24 )17274.5138888889190.68519168790190.5917954927644
Winsorized Mean ( 24 / 24 )17329.5138888889183.04359306266294.6742445279493
Trimmed Mean ( 1 / 24 )17600.7571428571336.25350872011752.3437129618393
Trimmed Mean ( 2 / 24 )17567.8235294118325.92167004497653.901980580142
Trimmed Mean ( 3 / 24 )17538.5151515152320.03783010830354.8013812791444
Trimmed Mean ( 4 / 24 )17516.984375315.49317299812755.5225465214868
Trimmed Mean ( 5 / 24 )17495.8387096774310.81828610463456.2896055085628
Trimmed Mean ( 6 / 24 )17477.05306.22844619182957.0719350776836
Trimmed Mean ( 7 / 24 )17463.3275862069302.9742066012557.6396511838735
Trimmed Mean ( 8 / 24 )17446.7321428571299.21970437741758.3074305856908
Trimmed Mean ( 9 / 24 )17428.5925925926294.60001133674159.1601898231801
Trimmed Mean ( 10 / 24 )17416.1346153846290.75425919054159.8998434756246
Trimmed Mean ( 11 / 24 )17398.66286.7742546865460.6702300351812
Trimmed Mean ( 12 / 24 )17386.7708333333283.54015069539761.3203131573832
Trimmed Mean ( 13 / 24 )17372.8043478261279.53494785454662.1489530420572
Trimmed Mean ( 14 / 24 )17361.9090909091276.45981517412662.8008417063212
Trimmed Mean ( 15 / 24 )17350.2380952381272.44938327226963.6824274911253
Trimmed Mean ( 16 / 24 )17340.5268.00653455485564.7017806069605
Trimmed Mean ( 17 / 24 )17325.7368421053262.8822129248765.9068434084463
Trimmed Mean ( 18 / 24 )17312.25258.00905415083767.099389426384
Trimmed Mean ( 19 / 24 )17299.5253.39912100800468.269771146734
Trimmed Mean ( 20 / 24 )17289.65625247.98275909672469.7212028488493
Trimmed Mean ( 21 / 24 )17286.0666666667242.62888710587971.2448829686273
Trimmed Mean ( 22 / 24 )17281.75235.17385567741173.4849966643632
Trimmed Mean ( 23 / 24 )17276.3076923077230.69297458030774.8887464984055
Trimmed Mean ( 24 / 24 )17276.5416666667225.28134567053276.6887361012712
Median17122
Midrange18676
Midmean - Weighted Average at Xnp17249.8378378378
Midmean - Weighted Average at X(n+1)p17312.25
Midmean - Empirical Distribution Function17249.8378378378
Midmean - Empirical Distribution Function - Averaging17312.25
Midmean - Empirical Distribution Function - Interpolation17312.25
Midmean - Closest Observation17249.8378378378
Midmean - True Basic - Statistics Graphics Toolkit17312.25
Midmean - MS Excel (old versions)17325.7368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17630.625 & 350.297752532587 & 50.330397133678 \tabularnewline
Geometric Mean & 17389.5747994799 &  &  \tabularnewline
Harmonic Mean & 17156.0991801814 &  &  \tabularnewline
Quadratic Mean & 17875.9962655543 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17631.8611111111 & 344.904055122646 & 51.1210606231965 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17621.5555555556 & 334.727544292393 & 52.6444741582505 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17595.9305555556 & 328.987627856466 & 53.485082919995 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17589.8194444444 & 326.414646800189 & 53.8879600436921 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17574.125 & 322.551258762911 & 54.4847509428501 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17543.375 & 313.547243333184 & 55.9512972064561 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17553.6805555556 & 311.721982881001 & 56.3119751559408 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17555.5694444444 & 310.773938507390 & 56.4898380113911 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17509.5694444444 & 301.79667835332 & 58.0177672596701 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17537.4861111111 & 296.716387531125 & 59.1052157820957 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17485.8472222222 & 287.362887396928 & 60.8493580386023 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17493.8472222222 & 285.23237147178 & 61.3319138075217 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17459.3611111111 & 274.079301194621 & 63.7018594071553 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17457.2222222222 & 272.229737209036 & 64.1268011393532 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17431.3888888889 & 266.789000369460 & 65.3377345570814 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17465.1666666667 & 261.27975641276 & 66.8446989788059 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17440.375 & 250.977326315607 & 69.4898429911096 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17420.625 & 240.590204483775 & 72.4078731192683 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17382.625 & 234.568650202588 & 74.1046383861924 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17319.5694444444 & 224.08059225569 & 77.2916979114449 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17321.3194444444 & 220.522795945116 & 78.5466163269372 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17324.9861111111 & 198.03753881858 & 87.4833438875562 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17274.5138888889 & 190.685191687901 & 90.5917954927644 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 17329.5138888889 & 183.043593062662 & 94.6742445279493 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17600.7571428571 & 336.253508720117 & 52.3437129618393 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17567.8235294118 & 325.921670044976 & 53.901980580142 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17538.5151515152 & 320.037830108303 & 54.8013812791444 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17516.984375 & 315.493172998127 & 55.5225465214868 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17495.8387096774 & 310.818286104634 & 56.2896055085628 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17477.05 & 306.228446191829 & 57.0719350776836 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17463.3275862069 & 302.97420660125 & 57.6396511838735 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17446.7321428571 & 299.219704377417 & 58.3074305856908 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17428.5925925926 & 294.600011336741 & 59.1601898231801 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17416.1346153846 & 290.754259190541 & 59.8998434756246 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17398.66 & 286.77425468654 & 60.6702300351812 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17386.7708333333 & 283.540150695397 & 61.3203131573832 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17372.8043478261 & 279.534947854546 & 62.1489530420572 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17361.9090909091 & 276.459815174126 & 62.8008417063212 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17350.2380952381 & 272.449383272269 & 63.6824274911253 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17340.5 & 268.006534554855 & 64.7017806069605 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17325.7368421053 & 262.88221292487 & 65.9068434084463 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17312.25 & 258.009054150837 & 67.099389426384 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17299.5 & 253.399121008004 & 68.269771146734 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17289.65625 & 247.982759096724 & 69.7212028488493 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17286.0666666667 & 242.628887105879 & 71.2448829686273 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17281.75 & 235.173855677411 & 73.4849966643632 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17276.3076923077 & 230.692974580307 & 74.8887464984055 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17276.5416666667 & 225.281345670532 & 76.6887361012712 \tabularnewline
Median & 17122 &  &  \tabularnewline
Midrange & 18676 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17249.8378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17312.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17249.8378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17312.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17312.25 &  &  \tabularnewline
Midmean - Closest Observation & 17249.8378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17312.25 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17325.7368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47276&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]17630.625[/C][C]350.297752532587[/C][C]50.330397133678[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17389.5747994799[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17156.0991801814[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17875.9962655543[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17631.8611111111[/C][C]344.904055122646[/C][C]51.1210606231965[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17621.5555555556[/C][C]334.727544292393[/C][C]52.6444741582505[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17595.9305555556[/C][C]328.987627856466[/C][C]53.485082919995[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17589.8194444444[/C][C]326.414646800189[/C][C]53.8879600436921[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17574.125[/C][C]322.551258762911[/C][C]54.4847509428501[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17543.375[/C][C]313.547243333184[/C][C]55.9512972064561[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17553.6805555556[/C][C]311.721982881001[/C][C]56.3119751559408[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17555.5694444444[/C][C]310.773938507390[/C][C]56.4898380113911[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17509.5694444444[/C][C]301.79667835332[/C][C]58.0177672596701[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17537.4861111111[/C][C]296.716387531125[/C][C]59.1052157820957[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17485.8472222222[/C][C]287.362887396928[/C][C]60.8493580386023[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17493.8472222222[/C][C]285.23237147178[/C][C]61.3319138075217[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17459.3611111111[/C][C]274.079301194621[/C][C]63.7018594071553[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17457.2222222222[/C][C]272.229737209036[/C][C]64.1268011393532[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17431.3888888889[/C][C]266.789000369460[/C][C]65.3377345570814[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17465.1666666667[/C][C]261.27975641276[/C][C]66.8446989788059[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17440.375[/C][C]250.977326315607[/C][C]69.4898429911096[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17420.625[/C][C]240.590204483775[/C][C]72.4078731192683[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17382.625[/C][C]234.568650202588[/C][C]74.1046383861924[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17319.5694444444[/C][C]224.08059225569[/C][C]77.2916979114449[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17321.3194444444[/C][C]220.522795945116[/C][C]78.5466163269372[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17324.9861111111[/C][C]198.03753881858[/C][C]87.4833438875562[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17274.5138888889[/C][C]190.685191687901[/C][C]90.5917954927644[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]17329.5138888889[/C][C]183.043593062662[/C][C]94.6742445279493[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17600.7571428571[/C][C]336.253508720117[/C][C]52.3437129618393[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17567.8235294118[/C][C]325.921670044976[/C][C]53.901980580142[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17538.5151515152[/C][C]320.037830108303[/C][C]54.8013812791444[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17516.984375[/C][C]315.493172998127[/C][C]55.5225465214868[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17495.8387096774[/C][C]310.818286104634[/C][C]56.2896055085628[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17477.05[/C][C]306.228446191829[/C][C]57.0719350776836[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17463.3275862069[/C][C]302.97420660125[/C][C]57.6396511838735[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17446.7321428571[/C][C]299.219704377417[/C][C]58.3074305856908[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17428.5925925926[/C][C]294.600011336741[/C][C]59.1601898231801[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17416.1346153846[/C][C]290.754259190541[/C][C]59.8998434756246[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17398.66[/C][C]286.77425468654[/C][C]60.6702300351812[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17386.7708333333[/C][C]283.540150695397[/C][C]61.3203131573832[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17372.8043478261[/C][C]279.534947854546[/C][C]62.1489530420572[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17361.9090909091[/C][C]276.459815174126[/C][C]62.8008417063212[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17350.2380952381[/C][C]272.449383272269[/C][C]63.6824274911253[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17340.5[/C][C]268.006534554855[/C][C]64.7017806069605[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17325.7368421053[/C][C]262.88221292487[/C][C]65.9068434084463[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17312.25[/C][C]258.009054150837[/C][C]67.099389426384[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17299.5[/C][C]253.399121008004[/C][C]68.269771146734[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17289.65625[/C][C]247.982759096724[/C][C]69.7212028488493[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17286.0666666667[/C][C]242.628887105879[/C][C]71.2448829686273[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17281.75[/C][C]235.173855677411[/C][C]73.4849966643632[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17276.3076923077[/C][C]230.692974580307[/C][C]74.8887464984055[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17276.5416666667[/C][C]225.281345670532[/C][C]76.6887361012712[/C][/ROW]
[ROW][C]Median[/C][C]17122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17249.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17312.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17249.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17312.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17312.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17249.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17312.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17325.7368421053[/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=47276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47276&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 Mean17630.625350.29775253258750.330397133678
Geometric Mean17389.5747994799
Harmonic Mean17156.0991801814
Quadratic Mean17875.9962655543
Winsorized Mean ( 1 / 24 )17631.8611111111344.90405512264651.1210606231965
Winsorized Mean ( 2 / 24 )17621.5555555556334.72754429239352.6444741582505
Winsorized Mean ( 3 / 24 )17595.9305555556328.98762785646653.485082919995
Winsorized Mean ( 4 / 24 )17589.8194444444326.41464680018953.8879600436921
Winsorized Mean ( 5 / 24 )17574.125322.55125876291154.4847509428501
Winsorized Mean ( 6 / 24 )17543.375313.54724333318455.9512972064561
Winsorized Mean ( 7 / 24 )17553.6805555556311.72198288100156.3119751559408
Winsorized Mean ( 8 / 24 )17555.5694444444310.77393850739056.4898380113911
Winsorized Mean ( 9 / 24 )17509.5694444444301.7966783533258.0177672596701
Winsorized Mean ( 10 / 24 )17537.4861111111296.71638753112559.1052157820957
Winsorized Mean ( 11 / 24 )17485.8472222222287.36288739692860.8493580386023
Winsorized Mean ( 12 / 24 )17493.8472222222285.2323714717861.3319138075217
Winsorized Mean ( 13 / 24 )17459.3611111111274.07930119462163.7018594071553
Winsorized Mean ( 14 / 24 )17457.2222222222272.22973720903664.1268011393532
Winsorized Mean ( 15 / 24 )17431.3888888889266.78900036946065.3377345570814
Winsorized Mean ( 16 / 24 )17465.1666666667261.2797564127666.8446989788059
Winsorized Mean ( 17 / 24 )17440.375250.97732631560769.4898429911096
Winsorized Mean ( 18 / 24 )17420.625240.59020448377572.4078731192683
Winsorized Mean ( 19 / 24 )17382.625234.56865020258874.1046383861924
Winsorized Mean ( 20 / 24 )17319.5694444444224.0805922556977.2916979114449
Winsorized Mean ( 21 / 24 )17321.3194444444220.52279594511678.5466163269372
Winsorized Mean ( 22 / 24 )17324.9861111111198.0375388185887.4833438875562
Winsorized Mean ( 23 / 24 )17274.5138888889190.68519168790190.5917954927644
Winsorized Mean ( 24 / 24 )17329.5138888889183.04359306266294.6742445279493
Trimmed Mean ( 1 / 24 )17600.7571428571336.25350872011752.3437129618393
Trimmed Mean ( 2 / 24 )17567.8235294118325.92167004497653.901980580142
Trimmed Mean ( 3 / 24 )17538.5151515152320.03783010830354.8013812791444
Trimmed Mean ( 4 / 24 )17516.984375315.49317299812755.5225465214868
Trimmed Mean ( 5 / 24 )17495.8387096774310.81828610463456.2896055085628
Trimmed Mean ( 6 / 24 )17477.05306.22844619182957.0719350776836
Trimmed Mean ( 7 / 24 )17463.3275862069302.9742066012557.6396511838735
Trimmed Mean ( 8 / 24 )17446.7321428571299.21970437741758.3074305856908
Trimmed Mean ( 9 / 24 )17428.5925925926294.60001133674159.1601898231801
Trimmed Mean ( 10 / 24 )17416.1346153846290.75425919054159.8998434756246
Trimmed Mean ( 11 / 24 )17398.66286.7742546865460.6702300351812
Trimmed Mean ( 12 / 24 )17386.7708333333283.54015069539761.3203131573832
Trimmed Mean ( 13 / 24 )17372.8043478261279.53494785454662.1489530420572
Trimmed Mean ( 14 / 24 )17361.9090909091276.45981517412662.8008417063212
Trimmed Mean ( 15 / 24 )17350.2380952381272.44938327226963.6824274911253
Trimmed Mean ( 16 / 24 )17340.5268.00653455485564.7017806069605
Trimmed Mean ( 17 / 24 )17325.7368421053262.8822129248765.9068434084463
Trimmed Mean ( 18 / 24 )17312.25258.00905415083767.099389426384
Trimmed Mean ( 19 / 24 )17299.5253.39912100800468.269771146734
Trimmed Mean ( 20 / 24 )17289.65625247.98275909672469.7212028488493
Trimmed Mean ( 21 / 24 )17286.0666666667242.62888710587971.2448829686273
Trimmed Mean ( 22 / 24 )17281.75235.17385567741173.4849966643632
Trimmed Mean ( 23 / 24 )17276.3076923077230.69297458030774.8887464984055
Trimmed Mean ( 24 / 24 )17276.5416666667225.28134567053276.6887361012712
Median17122
Midrange18676
Midmean - Weighted Average at Xnp17249.8378378378
Midmean - Weighted Average at X(n+1)p17312.25
Midmean - Empirical Distribution Function17249.8378378378
Midmean - Empirical Distribution Function - Averaging17312.25
Midmean - Empirical Distribution Function - Interpolation17312.25
Midmean - Closest Observation17249.8378378378
Midmean - True Basic - Statistics Graphics Toolkit17312.25
Midmean - MS Excel (old versions)17325.7368421053
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')