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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 05:38:54 -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/t1255866026bx0pcya2h0apjhf.htm/, Retrieved Mon, 29 Apr 2024 12:04:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47280, Retrieved Mon, 29 Apr 2024 12:04:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHSWWS3V2c
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-18 11:38:54] [4563e36d4b7005634fe3557528d9fcab] [Current]
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Dataseries X:
1.5253
1.5008
1.5678
1.4600
1.5091
1.4853
1.4761
1.5115
1.5370
1.4844
1.5244
1.4838
1.5722
1.5323
1.5268
1.4694
1.4897
1.4970
1.4366
1.4695
1.5699
1.5231
1.5195
1.4266
1.5665
1.5063
1.5204
1.5181
1.5324
1.4776
1.5131
1.5056
1.5748
1.5765
1.5428
1.4711
1.5768
1.5580
1.5503
1.5195
1.5245
1.5367
1.5419
1.5943
1.6017
1.6087
1.6138
1.5415
1.6079
1.5776
1.5731
1.4881
1.4281
1.5001
1.4268
1.5314
1.5567
1.5473
1.5872
1.5471
1.5817
1.5119
1.5045
1.4688
1.4428
1.4532
1.4883
1.4792
1.5390
1.5428
1.5693
1.5425




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=47280&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=47280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47280&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 Mean1.523144444444440.0054586204414649279.034686653481
Geometric Mean1.52244739060972
Harmonic Mean1.52174776967675
Quadratic Mean1.52383875550459
Winsorized Mean ( 1 / 24 )1.523076388888890.00544179454840984279.884948860105
Winsorized Mean ( 2 / 24 )1.523090277777780.00542793741095588280.602033970314
Winsorized Mean ( 3 / 24 )1.523186111111110.00528795813102224288.048065693867
Winsorized Mean ( 4 / 24 )1.523119444444440.00512698857900392297.078766799273
Winsorized Mean ( 5 / 24 )1.523348611111110.00488033885381675312.139926497061
Winsorized Mean ( 6 / 24 )1.523456944444440.00468649160312087325.074079601451
Winsorized Mean ( 7 / 24 )1.523913888888890.00446161612085147341.560960784331
Winsorized Mean ( 8 / 24 )1.523891666666670.00443504800668451343.602067975331
Winsorized Mean ( 9 / 24 )1.523866666666670.00442659482944142344.252574582020
Winsorized Mean ( 10 / 24 )1.523852777777780.00434913918246041350.380319839683
Winsorized Mean ( 11 / 24 )1.524356944444440.00417894427105864364.770823818209
Winsorized Mean ( 12 / 24 )1.524456944444440.00411397900631886370.555353370292
Winsorized Mean ( 13 / 24 )1.524330555555560.00400059445841391381.026012859074
Winsorized Mean ( 14 / 24 )1.525108333333330.0038429572750882396.857998713590
Winsorized Mean ( 15 / 24 )1.524920833333330.00377372771702436404.088728090789
Winsorized Mean ( 16 / 24 )1.524831944444440.00369750043852793412.395338363102
Winsorized Mean ( 17 / 24 )1.523486111111110.00328945195331848463.142837387906
Winsorized Mean ( 18 / 24 )1.523211111111110.00323414729817691470.977655213709
Winsorized Mean ( 19 / 24 )1.521891666666670.00293907871372068517.812489866953
Winsorized Mean ( 20 / 24 )1.523086111111110.00252113546713471604.127041551683
Winsorized Mean ( 21 / 24 )1.523931944444440.00238359007973018639.343130936739
Winsorized Mean ( 22 / 24 )1.522831944444440.00217832079372959699.085253571464
Winsorized Mean ( 23 / 24 )1.524013888888890.00201332154331066756.964973604183
Winsorized Mean ( 24 / 24 )1.524280555555560.00195040888824207781.518462484761
Trimmed Mean ( 1 / 24 )1.523228571428570.00528249860215884288.353804922175
Trimmed Mean ( 2 / 24 )1.523389705882350.00509295815199318299.116870867309
Trimmed Mean ( 3 / 24 )1.523553030303030.00487490755142607312.529625276143
Trimmed Mean ( 4 / 24 )1.5236906250.00467923674774195325.628025924374
Trimmed Mean ( 5 / 24 )1.523856451612900.00450485936639397338.269483611585
Trimmed Mean ( 6 / 24 )1.523978333333330.00437459802296434348.369913151619
Trimmed Mean ( 7 / 24 )1.524086206896550.00427147678252677356.805452655413
Trimmed Mean ( 8 / 24 )1.524117857142860.00420263222026978362.657919432460
Trimmed Mean ( 9 / 24 )1.524155555555560.00412207982033219369.75401301975
Trimmed Mean ( 10 / 24 )1.52420.00402211645958687378.954715835492
Trimmed Mean ( 11 / 24 )1.524250.00391347358624076389.487744432224
Trimmed Mean ( 12 / 24 )1.524235416666670.00381403191474072399.638873176625
Trimmed Mean ( 13 / 24 )1.524206521739130.00370025250760510411.919597002216
Trimmed Mean ( 14 / 24 )1.524190909090910.00357852683583879425.926918816482
Trimmed Mean ( 15 / 24 )1.524078571428570.00345553224353536441.054652081407
Trimmed Mean ( 16 / 24 )1.52397750.00330845166261291460.631635402649
Trimmed Mean ( 17 / 24 )1.523876315789470.00312961223610396486.921765645491
Trimmed Mean ( 18 / 24 )1.523922222222220.00299822463635026508.274864980529
Trimmed Mean ( 19 / 24 )1.524005882352940.00282953275929864538.606905095771
Trimmed Mean ( 20 / 24 )1.524256250.00267770415587140569.239976215358
Trimmed Mean ( 21 / 24 )1.524396666666670.00259048428141545588.460110568102
Trimmed Mean ( 22 / 24 )1.524453571428570.0025019488813398609.306442189267
Trimmed Mean ( 23 / 24 )1.524657692307690.00242905599312809627.674988399206
Trimmed Mean ( 24 / 24 )1.524741666666670.00236962906553168643.451622384854
Median1.52445
Midrange1.5202
Midmean - Weighted Average at Xnp1.52295405405405
Midmean - Weighted Average at X(n+1)p1.52392222222222
Midmean - Empirical Distribution Function1.52295405405405
Midmean - Empirical Distribution Function - Averaging1.52392222222222
Midmean - Empirical Distribution Function - Interpolation1.52392222222222
Midmean - Closest Observation1.52295405405405
Midmean - True Basic - Statistics Graphics Toolkit1.52392222222222
Midmean - MS Excel (old versions)1.52387631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.52314444444444 & 0.0054586204414649 & 279.034686653481 \tabularnewline
Geometric Mean & 1.52244739060972 &  &  \tabularnewline
Harmonic Mean & 1.52174776967675 &  &  \tabularnewline
Quadratic Mean & 1.52383875550459 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.52307638888889 & 0.00544179454840984 & 279.884948860105 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.52309027777778 & 0.00542793741095588 & 280.602033970314 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.52318611111111 & 0.00528795813102224 & 288.048065693867 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.52311944444444 & 0.00512698857900392 & 297.078766799273 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.52334861111111 & 0.00488033885381675 & 312.139926497061 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.52345694444444 & 0.00468649160312087 & 325.074079601451 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.52391388888889 & 0.00446161612085147 & 341.560960784331 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.52389166666667 & 0.00443504800668451 & 343.602067975331 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.52386666666667 & 0.00442659482944142 & 344.252574582020 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.52385277777778 & 0.00434913918246041 & 350.380319839683 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.52435694444444 & 0.00417894427105864 & 364.770823818209 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.52445694444444 & 0.00411397900631886 & 370.555353370292 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.52433055555556 & 0.00400059445841391 & 381.026012859074 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.52510833333333 & 0.0038429572750882 & 396.857998713590 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.52492083333333 & 0.00377372771702436 & 404.088728090789 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.52483194444444 & 0.00369750043852793 & 412.395338363102 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.52348611111111 & 0.00328945195331848 & 463.142837387906 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.52321111111111 & 0.00323414729817691 & 470.977655213709 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.52189166666667 & 0.00293907871372068 & 517.812489866953 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.52308611111111 & 0.00252113546713471 & 604.127041551683 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.52393194444444 & 0.00238359007973018 & 639.343130936739 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.52283194444444 & 0.00217832079372959 & 699.085253571464 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.52401388888889 & 0.00201332154331066 & 756.964973604183 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.52428055555556 & 0.00195040888824207 & 781.518462484761 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.52322857142857 & 0.00528249860215884 & 288.353804922175 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.52338970588235 & 0.00509295815199318 & 299.116870867309 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.52355303030303 & 0.00487490755142607 & 312.529625276143 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.523690625 & 0.00467923674774195 & 325.628025924374 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.52385645161290 & 0.00450485936639397 & 338.269483611585 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.52397833333333 & 0.00437459802296434 & 348.369913151619 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.52408620689655 & 0.00427147678252677 & 356.805452655413 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.52411785714286 & 0.00420263222026978 & 362.657919432460 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.52415555555556 & 0.00412207982033219 & 369.75401301975 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.5242 & 0.00402211645958687 & 378.954715835492 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.52425 & 0.00391347358624076 & 389.487744432224 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.52423541666667 & 0.00381403191474072 & 399.638873176625 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.52420652173913 & 0.00370025250760510 & 411.919597002216 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.52419090909091 & 0.00357852683583879 & 425.926918816482 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.52407857142857 & 0.00345553224353536 & 441.054652081407 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.5239775 & 0.00330845166261291 & 460.631635402649 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.52387631578947 & 0.00312961223610396 & 486.921765645491 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.52392222222222 & 0.00299822463635026 & 508.274864980529 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.52400588235294 & 0.00282953275929864 & 538.606905095771 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.52425625 & 0.00267770415587140 & 569.239976215358 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.52439666666667 & 0.00259048428141545 & 588.460110568102 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.52445357142857 & 0.0025019488813398 & 609.306442189267 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.52465769230769 & 0.00242905599312809 & 627.674988399206 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.52474166666667 & 0.00236962906553168 & 643.451622384854 \tabularnewline
Median & 1.52445 &  &  \tabularnewline
Midrange & 1.5202 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.52295405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.52392222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.52295405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.52392222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.52392222222222 &  &  \tabularnewline
Midmean - Closest Observation & 1.52295405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.52392222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.52387631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47280&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]1.52314444444444[/C][C]0.0054586204414649[/C][C]279.034686653481[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.52244739060972[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.52174776967675[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.52383875550459[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.52307638888889[/C][C]0.00544179454840984[/C][C]279.884948860105[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.52309027777778[/C][C]0.00542793741095588[/C][C]280.602033970314[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.52318611111111[/C][C]0.00528795813102224[/C][C]288.048065693867[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.52311944444444[/C][C]0.00512698857900392[/C][C]297.078766799273[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.52334861111111[/C][C]0.00488033885381675[/C][C]312.139926497061[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.52345694444444[/C][C]0.00468649160312087[/C][C]325.074079601451[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.52391388888889[/C][C]0.00446161612085147[/C][C]341.560960784331[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.52389166666667[/C][C]0.00443504800668451[/C][C]343.602067975331[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.52386666666667[/C][C]0.00442659482944142[/C][C]344.252574582020[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.52385277777778[/C][C]0.00434913918246041[/C][C]350.380319839683[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.52435694444444[/C][C]0.00417894427105864[/C][C]364.770823818209[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.52445694444444[/C][C]0.00411397900631886[/C][C]370.555353370292[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.52433055555556[/C][C]0.00400059445841391[/C][C]381.026012859074[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.52510833333333[/C][C]0.0038429572750882[/C][C]396.857998713590[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.52492083333333[/C][C]0.00377372771702436[/C][C]404.088728090789[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.52483194444444[/C][C]0.00369750043852793[/C][C]412.395338363102[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.52348611111111[/C][C]0.00328945195331848[/C][C]463.142837387906[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.52321111111111[/C][C]0.00323414729817691[/C][C]470.977655213709[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.52189166666667[/C][C]0.00293907871372068[/C][C]517.812489866953[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.52308611111111[/C][C]0.00252113546713471[/C][C]604.127041551683[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.52393194444444[/C][C]0.00238359007973018[/C][C]639.343130936739[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.52283194444444[/C][C]0.00217832079372959[/C][C]699.085253571464[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.52401388888889[/C][C]0.00201332154331066[/C][C]756.964973604183[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.52428055555556[/C][C]0.00195040888824207[/C][C]781.518462484761[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.52322857142857[/C][C]0.00528249860215884[/C][C]288.353804922175[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.52338970588235[/C][C]0.00509295815199318[/C][C]299.116870867309[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.52355303030303[/C][C]0.00487490755142607[/C][C]312.529625276143[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.523690625[/C][C]0.00467923674774195[/C][C]325.628025924374[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.52385645161290[/C][C]0.00450485936639397[/C][C]338.269483611585[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.52397833333333[/C][C]0.00437459802296434[/C][C]348.369913151619[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.52408620689655[/C][C]0.00427147678252677[/C][C]356.805452655413[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.52411785714286[/C][C]0.00420263222026978[/C][C]362.657919432460[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.52415555555556[/C][C]0.00412207982033219[/C][C]369.75401301975[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.5242[/C][C]0.00402211645958687[/C][C]378.954715835492[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.52425[/C][C]0.00391347358624076[/C][C]389.487744432224[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.52423541666667[/C][C]0.00381403191474072[/C][C]399.638873176625[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.52420652173913[/C][C]0.00370025250760510[/C][C]411.919597002216[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.52419090909091[/C][C]0.00357852683583879[/C][C]425.926918816482[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.52407857142857[/C][C]0.00345553224353536[/C][C]441.054652081407[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.5239775[/C][C]0.00330845166261291[/C][C]460.631635402649[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.52387631578947[/C][C]0.00312961223610396[/C][C]486.921765645491[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.52392222222222[/C][C]0.00299822463635026[/C][C]508.274864980529[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.52400588235294[/C][C]0.00282953275929864[/C][C]538.606905095771[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.52425625[/C][C]0.00267770415587140[/C][C]569.239976215358[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.52439666666667[/C][C]0.00259048428141545[/C][C]588.460110568102[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.52445357142857[/C][C]0.0025019488813398[/C][C]609.306442189267[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.52465769230769[/C][C]0.00242905599312809[/C][C]627.674988399206[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.52474166666667[/C][C]0.00236962906553168[/C][C]643.451622384854[/C][/ROW]
[ROW][C]Median[/C][C]1.52445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5202[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.52295405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.52392222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.52295405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.52392222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.52392222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.52295405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.52392222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.52387631578947[/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=47280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47280&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 Mean1.523144444444440.0054586204414649279.034686653481
Geometric Mean1.52244739060972
Harmonic Mean1.52174776967675
Quadratic Mean1.52383875550459
Winsorized Mean ( 1 / 24 )1.523076388888890.00544179454840984279.884948860105
Winsorized Mean ( 2 / 24 )1.523090277777780.00542793741095588280.602033970314
Winsorized Mean ( 3 / 24 )1.523186111111110.00528795813102224288.048065693867
Winsorized Mean ( 4 / 24 )1.523119444444440.00512698857900392297.078766799273
Winsorized Mean ( 5 / 24 )1.523348611111110.00488033885381675312.139926497061
Winsorized Mean ( 6 / 24 )1.523456944444440.00468649160312087325.074079601451
Winsorized Mean ( 7 / 24 )1.523913888888890.00446161612085147341.560960784331
Winsorized Mean ( 8 / 24 )1.523891666666670.00443504800668451343.602067975331
Winsorized Mean ( 9 / 24 )1.523866666666670.00442659482944142344.252574582020
Winsorized Mean ( 10 / 24 )1.523852777777780.00434913918246041350.380319839683
Winsorized Mean ( 11 / 24 )1.524356944444440.00417894427105864364.770823818209
Winsorized Mean ( 12 / 24 )1.524456944444440.00411397900631886370.555353370292
Winsorized Mean ( 13 / 24 )1.524330555555560.00400059445841391381.026012859074
Winsorized Mean ( 14 / 24 )1.525108333333330.0038429572750882396.857998713590
Winsorized Mean ( 15 / 24 )1.524920833333330.00377372771702436404.088728090789
Winsorized Mean ( 16 / 24 )1.524831944444440.00369750043852793412.395338363102
Winsorized Mean ( 17 / 24 )1.523486111111110.00328945195331848463.142837387906
Winsorized Mean ( 18 / 24 )1.523211111111110.00323414729817691470.977655213709
Winsorized Mean ( 19 / 24 )1.521891666666670.00293907871372068517.812489866953
Winsorized Mean ( 20 / 24 )1.523086111111110.00252113546713471604.127041551683
Winsorized Mean ( 21 / 24 )1.523931944444440.00238359007973018639.343130936739
Winsorized Mean ( 22 / 24 )1.522831944444440.00217832079372959699.085253571464
Winsorized Mean ( 23 / 24 )1.524013888888890.00201332154331066756.964973604183
Winsorized Mean ( 24 / 24 )1.524280555555560.00195040888824207781.518462484761
Trimmed Mean ( 1 / 24 )1.523228571428570.00528249860215884288.353804922175
Trimmed Mean ( 2 / 24 )1.523389705882350.00509295815199318299.116870867309
Trimmed Mean ( 3 / 24 )1.523553030303030.00487490755142607312.529625276143
Trimmed Mean ( 4 / 24 )1.5236906250.00467923674774195325.628025924374
Trimmed Mean ( 5 / 24 )1.523856451612900.00450485936639397338.269483611585
Trimmed Mean ( 6 / 24 )1.523978333333330.00437459802296434348.369913151619
Trimmed Mean ( 7 / 24 )1.524086206896550.00427147678252677356.805452655413
Trimmed Mean ( 8 / 24 )1.524117857142860.00420263222026978362.657919432460
Trimmed Mean ( 9 / 24 )1.524155555555560.00412207982033219369.75401301975
Trimmed Mean ( 10 / 24 )1.52420.00402211645958687378.954715835492
Trimmed Mean ( 11 / 24 )1.524250.00391347358624076389.487744432224
Trimmed Mean ( 12 / 24 )1.524235416666670.00381403191474072399.638873176625
Trimmed Mean ( 13 / 24 )1.524206521739130.00370025250760510411.919597002216
Trimmed Mean ( 14 / 24 )1.524190909090910.00357852683583879425.926918816482
Trimmed Mean ( 15 / 24 )1.524078571428570.00345553224353536441.054652081407
Trimmed Mean ( 16 / 24 )1.52397750.00330845166261291460.631635402649
Trimmed Mean ( 17 / 24 )1.523876315789470.00312961223610396486.921765645491
Trimmed Mean ( 18 / 24 )1.523922222222220.00299822463635026508.274864980529
Trimmed Mean ( 19 / 24 )1.524005882352940.00282953275929864538.606905095771
Trimmed Mean ( 20 / 24 )1.524256250.00267770415587140569.239976215358
Trimmed Mean ( 21 / 24 )1.524396666666670.00259048428141545588.460110568102
Trimmed Mean ( 22 / 24 )1.524453571428570.0025019488813398609.306442189267
Trimmed Mean ( 23 / 24 )1.524657692307690.00242905599312809627.674988399206
Trimmed Mean ( 24 / 24 )1.524741666666670.00236962906553168643.451622384854
Median1.52445
Midrange1.5202
Midmean - Weighted Average at Xnp1.52295405405405
Midmean - Weighted Average at X(n+1)p1.52392222222222
Midmean - Empirical Distribution Function1.52295405405405
Midmean - Empirical Distribution Function - Averaging1.52392222222222
Midmean - Empirical Distribution Function - Interpolation1.52392222222222
Midmean - Closest Observation1.52295405405405
Midmean - True Basic - Statistics Graphics Toolkit1.52392222222222
Midmean - MS Excel (old versions)1.52387631578947
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')