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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 computationTue, 20 Oct 2009 09:39:51 -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/20/t1256053252cs9zhmwzab0oar5.htm/, Retrieved Thu, 02 May 2024 15:25:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48740, Retrieved Thu, 02 May 2024 15:25:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Ws 3 part 2 ex 3] [2009-10-20 15:39:51] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
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Dataseries X:
-16,8889
-16,8918
-16,8429
-16,838
-16,8985
-16,8175
-16,8165
-16,8093
-16,8213
-16,836
-16,7856
-16,8586
-16,8821
-16,819
-16,7909
-16,7688
-16,8056
-16,7792
-16,7548
-16,7898
-16,7724
-16,7706
-16,7724
-16,7839
-16,817
-16,7691
-16,7689
-16,7516
-16,8414
-16,7268
-16,7579
-16,7626
-16,7942
-16,8186
-16,8
-16,8331
-16,8526
-16,7894
-16,7464
-16,7392
-16,8382
-16,7205
-16,7836
-16,7576
-16,7467
-16,762
-16,7878
-16,7809
-16,8118
-16,7518
-16,7281
-16,7277
-16,8347
-16,7034
-16,7771
-16,7231
-16,7351
-16,7593
-16,7521
-16,7718
-16,8
-16,7362
-16,7295
-16,6836
-16,8168
-16,6815
-16,7085
-16,7051
-16,7306
-16,7542
-16,772
-16,7793




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=48740&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=48740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48740&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 Mean-16.78213611111110.00572225096662334-2932.78575319358
Geometric MeanNaN
Harmonic Mean-16.7819976984962
Quadratic Mean16.7822053761401
Winsorized Mean ( 1 / 24 )-16.78207222222220.00568911571737006-2949.85601558131
Winsorized Mean ( 2 / 24 )-16.78254166666670.00554481625347677-3026.70835235406
Winsorized Mean ( 3 / 24 )-16.78232916666670.00545585944995259-3076.01933675409
Winsorized Mean ( 4 / 24 )-16.78121250.00510978377324435-3284.13358464778
Winsorized Mean ( 5 / 24 )-16.78162916666670.00486501090776052-3449.45355413224
Winsorized Mean ( 6 / 24 )-16.78103750.00466826282122132-3594.70709826267
Winsorized Mean ( 7 / 24 )-16.78125138888890.0045795904448572-3664.35636351149
Winsorized Mean ( 8 / 24 )-16.78099583333330.00449813404084121-3730.65713048317
Winsorized Mean ( 9 / 24 )-16.78102083333330.0044853320925913-3741.3106737518
Winsorized Mean ( 10 / 24 )-16.78093750.00440386817693218-3810.49950311862
Winsorized Mean ( 11 / 24 )-16.78090694444440.00434151148037519-3865.2222895871
Winsorized Mean ( 12 / 24 )-16.78139027777780.00417517355056262-4019.32759789505
Winsorized Mean ( 13 / 24 )-16.77945833333330.00379134575332868-4425.72622626188
Winsorized Mean ( 14 / 24 )-16.77959444444440.00362977217524268-4622.76794088945
Winsorized Mean ( 15 / 24 )-16.78101111111110.00339120223000209-4948.39587054081
Winsorized Mean ( 16 / 24 )-16.78083333333330.00334365830501856-5018.7046051167
Winsorized Mean ( 17 / 24 )-16.78187222222220.00316404587757883-5303.92822087142
Winsorized Mean ( 18 / 24 )-16.78187222222220.00314950080639905-5328.42290058328
Winsorized Mean ( 19 / 24 )-16.78187222222220.00312651104139261-5367.60369627456
Winsorized Mean ( 20 / 24 )-16.781150.00284757948443727-5893.12786235228
Winsorized Mean ( 21 / 24 )-16.78059583333330.00271461545700697-6181.5738173962
Winsorized Mean ( 22 / 24 )-16.78032083333330.00243411455841533-6893.80899322082
Winsorized Mean ( 23 / 24 )-16.77862777777780.00216583879292205-7746.94212358291
Winsorized Mean ( 24 / 24 )-16.77909444444440.00210345297838408-7976.92870573913
Trimmed Mean ( 1 / 24 )-16.78191142857140.00545480984893345-3076.53463518122
Trimmed Mean ( 2 / 24 )-16.78174117647060.00517417874678307-3243.36324617781
Trimmed Mean ( 3 / 24 )-16.78130454545450.00493172189007219-3402.72726636029
Trimmed Mean ( 4 / 24 )-16.78092031250.00468143294124465-3584.56919561011
Trimmed Mean ( 5 / 24 )-16.78083548387100.00451465918136961-3716.96617833733
Trimmed Mean ( 6 / 24 )-16.7806450.00439223083030330-3820.52894037931
Trimmed Mean ( 7 / 24 )-16.78056379310340.00429919638115661-3903.18615512720
Trimmed Mean ( 8 / 24 )-16.78043750.00420700603238142-3988.68871849496
Trimmed Mean ( 9 / 24 )-16.78034444444440.00411209093655368-4080.7328202007
Trimmed Mean ( 10 / 24 )-16.78024038461540.00399567003539962-4199.6061326263
Trimmed Mean ( 11 / 24 )-16.780140.00386802486115729-4338.16756673572
Trimmed Mean ( 12 / 24 )-16.78003541666670.00372029784323858-4510.40108177451
Trimmed Mean ( 13 / 24 )-16.77985869565220.00357040651292075-4699.70537946546
Trimmed Mean ( 14 / 24 )-16.77990909090910.00346870457048029-4837.51462540544
Trimmed Mean ( 15 / 24 )-16.77994761904760.00337192969234518-4976.36343282626
Trimmed Mean ( 16 / 24 )-16.779820.00329713200936506-5089.21691710832
Trimmed Mean ( 17 / 24 )-16.77970.00320490600097834-5235.62937411511
Trimmed Mean ( 18 / 24 )-16.77944444444440.00311911272600577-5379.55691839699
Trimmed Mean ( 19 / 24 )-16.77915882352940.00299969433275553-5593.62287027292
Trimmed Mean ( 20 / 24 )-16.77883750.00283378504859014-5920.99866867029
Trimmed Mean ( 21 / 24 )-16.778560.00268462030963349-6249.88194412141
Trimmed Mean ( 22 / 24 )-16.77831071428570.00250898564679286-6687.28844094139
Trimmed Mean ( 23 / 24 )-16.77805769230770.00234806744154833-7145.47520885691
Trimmed Mean ( 24 / 24 )-16.77798333333330.00220990578416351-7592.17132855469
Median-16.77815
Midrange-16.79
Midmean - Weighted Average at Xnp-16.7804594594595
Midmean - Weighted Average at X(n+1)p-16.7794444444444
Midmean - Empirical Distribution Function-16.7804594594595
Midmean - Empirical Distribution Function - Averaging-16.7794444444444
Midmean - Empirical Distribution Function - Interpolation-16.7794444444444
Midmean - Closest Observation-16.7804594594595
Midmean - True Basic - Statistics Graphics Toolkit-16.7794444444444
Midmean - MS Excel (old versions)-16.7797
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -16.7821361111111 & 0.00572225096662334 & -2932.78575319358 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -16.7819976984962 &  &  \tabularnewline
Quadratic Mean & 16.7822053761401 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -16.7820722222222 & 0.00568911571737006 & -2949.85601558131 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -16.7825416666667 & 0.00554481625347677 & -3026.70835235406 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -16.7823291666667 & 0.00545585944995259 & -3076.01933675409 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -16.7812125 & 0.00510978377324435 & -3284.13358464778 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -16.7816291666667 & 0.00486501090776052 & -3449.45355413224 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -16.7810375 & 0.00466826282122132 & -3594.70709826267 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -16.7812513888889 & 0.0045795904448572 & -3664.35636351149 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -16.7809958333333 & 0.00449813404084121 & -3730.65713048317 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -16.7810208333333 & 0.0044853320925913 & -3741.3106737518 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -16.7809375 & 0.00440386817693218 & -3810.49950311862 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -16.7809069444444 & 0.00434151148037519 & -3865.2222895871 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -16.7813902777778 & 0.00417517355056262 & -4019.32759789505 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -16.7794583333333 & 0.00379134575332868 & -4425.72622626188 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -16.7795944444444 & 0.00362977217524268 & -4622.76794088945 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -16.7810111111111 & 0.00339120223000209 & -4948.39587054081 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -16.7808333333333 & 0.00334365830501856 & -5018.7046051167 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -16.7818722222222 & 0.00316404587757883 & -5303.92822087142 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -16.7818722222222 & 0.00314950080639905 & -5328.42290058328 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -16.7818722222222 & 0.00312651104139261 & -5367.60369627456 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -16.78115 & 0.00284757948443727 & -5893.12786235228 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -16.7805958333333 & 0.00271461545700697 & -6181.5738173962 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -16.7803208333333 & 0.00243411455841533 & -6893.80899322082 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -16.7786277777778 & 0.00216583879292205 & -7746.94212358291 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -16.7790944444444 & 0.00210345297838408 & -7976.92870573913 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -16.7819114285714 & 0.00545480984893345 & -3076.53463518122 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -16.7817411764706 & 0.00517417874678307 & -3243.36324617781 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -16.7813045454545 & 0.00493172189007219 & -3402.72726636029 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -16.7809203125 & 0.00468143294124465 & -3584.56919561011 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -16.7808354838710 & 0.00451465918136961 & -3716.96617833733 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -16.780645 & 0.00439223083030330 & -3820.52894037931 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -16.7805637931034 & 0.00429919638115661 & -3903.18615512720 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -16.7804375 & 0.00420700603238142 & -3988.68871849496 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -16.7803444444444 & 0.00411209093655368 & -4080.7328202007 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -16.7802403846154 & 0.00399567003539962 & -4199.6061326263 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -16.78014 & 0.00386802486115729 & -4338.16756673572 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -16.7800354166667 & 0.00372029784323858 & -4510.40108177451 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -16.7798586956522 & 0.00357040651292075 & -4699.70537946546 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -16.7799090909091 & 0.00346870457048029 & -4837.51462540544 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -16.7799476190476 & 0.00337192969234518 & -4976.36343282626 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -16.77982 & 0.00329713200936506 & -5089.21691710832 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -16.7797 & 0.00320490600097834 & -5235.62937411511 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -16.7794444444444 & 0.00311911272600577 & -5379.55691839699 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -16.7791588235294 & 0.00299969433275553 & -5593.62287027292 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -16.7788375 & 0.00283378504859014 & -5920.99866867029 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -16.77856 & 0.00268462030963349 & -6249.88194412141 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -16.7783107142857 & 0.00250898564679286 & -6687.28844094139 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -16.7780576923077 & 0.00234806744154833 & -7145.47520885691 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -16.7779833333333 & 0.00220990578416351 & -7592.17132855469 \tabularnewline
Median & -16.77815 &  &  \tabularnewline
Midrange & -16.79 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -16.7804594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -16.7794444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -16.7804594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -16.7794444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -16.7794444444444 &  &  \tabularnewline
Midmean - Closest Observation & -16.7804594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -16.7794444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -16.7797 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48740&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]-16.7821361111111[/C][C]0.00572225096662334[/C][C]-2932.78575319358[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-16.7819976984962[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.7822053761401[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-16.7820722222222[/C][C]0.00568911571737006[/C][C]-2949.85601558131[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-16.7825416666667[/C][C]0.00554481625347677[/C][C]-3026.70835235406[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-16.7823291666667[/C][C]0.00545585944995259[/C][C]-3076.01933675409[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-16.7812125[/C][C]0.00510978377324435[/C][C]-3284.13358464778[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-16.7816291666667[/C][C]0.00486501090776052[/C][C]-3449.45355413224[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-16.7810375[/C][C]0.00466826282122132[/C][C]-3594.70709826267[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-16.7812513888889[/C][C]0.0045795904448572[/C][C]-3664.35636351149[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-16.7809958333333[/C][C]0.00449813404084121[/C][C]-3730.65713048317[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-16.7810208333333[/C][C]0.0044853320925913[/C][C]-3741.3106737518[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-16.7809375[/C][C]0.00440386817693218[/C][C]-3810.49950311862[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-16.7809069444444[/C][C]0.00434151148037519[/C][C]-3865.2222895871[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-16.7813902777778[/C][C]0.00417517355056262[/C][C]-4019.32759789505[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-16.7794583333333[/C][C]0.00379134575332868[/C][C]-4425.72622626188[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-16.7795944444444[/C][C]0.00362977217524268[/C][C]-4622.76794088945[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-16.7810111111111[/C][C]0.00339120223000209[/C][C]-4948.39587054081[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-16.7808333333333[/C][C]0.00334365830501856[/C][C]-5018.7046051167[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-16.7818722222222[/C][C]0.00316404587757883[/C][C]-5303.92822087142[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-16.7818722222222[/C][C]0.00314950080639905[/C][C]-5328.42290058328[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-16.7818722222222[/C][C]0.00312651104139261[/C][C]-5367.60369627456[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-16.78115[/C][C]0.00284757948443727[/C][C]-5893.12786235228[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-16.7805958333333[/C][C]0.00271461545700697[/C][C]-6181.5738173962[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-16.7803208333333[/C][C]0.00243411455841533[/C][C]-6893.80899322082[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-16.7786277777778[/C][C]0.00216583879292205[/C][C]-7746.94212358291[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-16.7790944444444[/C][C]0.00210345297838408[/C][C]-7976.92870573913[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-16.7819114285714[/C][C]0.00545480984893345[/C][C]-3076.53463518122[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-16.7817411764706[/C][C]0.00517417874678307[/C][C]-3243.36324617781[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-16.7813045454545[/C][C]0.00493172189007219[/C][C]-3402.72726636029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-16.7809203125[/C][C]0.00468143294124465[/C][C]-3584.56919561011[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-16.7808354838710[/C][C]0.00451465918136961[/C][C]-3716.96617833733[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-16.780645[/C][C]0.00439223083030330[/C][C]-3820.52894037931[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-16.7805637931034[/C][C]0.00429919638115661[/C][C]-3903.18615512720[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-16.7804375[/C][C]0.00420700603238142[/C][C]-3988.68871849496[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-16.7803444444444[/C][C]0.00411209093655368[/C][C]-4080.7328202007[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-16.7802403846154[/C][C]0.00399567003539962[/C][C]-4199.6061326263[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-16.78014[/C][C]0.00386802486115729[/C][C]-4338.16756673572[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-16.7800354166667[/C][C]0.00372029784323858[/C][C]-4510.40108177451[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-16.7798586956522[/C][C]0.00357040651292075[/C][C]-4699.70537946546[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-16.7799090909091[/C][C]0.00346870457048029[/C][C]-4837.51462540544[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-16.7799476190476[/C][C]0.00337192969234518[/C][C]-4976.36343282626[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-16.77982[/C][C]0.00329713200936506[/C][C]-5089.21691710832[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-16.7797[/C][C]0.00320490600097834[/C][C]-5235.62937411511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-16.7794444444444[/C][C]0.00311911272600577[/C][C]-5379.55691839699[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-16.7791588235294[/C][C]0.00299969433275553[/C][C]-5593.62287027292[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-16.7788375[/C][C]0.00283378504859014[/C][C]-5920.99866867029[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-16.77856[/C][C]0.00268462030963349[/C][C]-6249.88194412141[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-16.7783107142857[/C][C]0.00250898564679286[/C][C]-6687.28844094139[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-16.7780576923077[/C][C]0.00234806744154833[/C][C]-7145.47520885691[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-16.7779833333333[/C][C]0.00220990578416351[/C][C]-7592.17132855469[/C][/ROW]
[ROW][C]Median[/C][C]-16.77815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-16.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-16.7804594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-16.7794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-16.7804594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-16.7794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-16.7794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-16.7804594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-16.7794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-16.7797[/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=48740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48740&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 Mean-16.78213611111110.00572225096662334-2932.78575319358
Geometric MeanNaN
Harmonic Mean-16.7819976984962
Quadratic Mean16.7822053761401
Winsorized Mean ( 1 / 24 )-16.78207222222220.00568911571737006-2949.85601558131
Winsorized Mean ( 2 / 24 )-16.78254166666670.00554481625347677-3026.70835235406
Winsorized Mean ( 3 / 24 )-16.78232916666670.00545585944995259-3076.01933675409
Winsorized Mean ( 4 / 24 )-16.78121250.00510978377324435-3284.13358464778
Winsorized Mean ( 5 / 24 )-16.78162916666670.00486501090776052-3449.45355413224
Winsorized Mean ( 6 / 24 )-16.78103750.00466826282122132-3594.70709826267
Winsorized Mean ( 7 / 24 )-16.78125138888890.0045795904448572-3664.35636351149
Winsorized Mean ( 8 / 24 )-16.78099583333330.00449813404084121-3730.65713048317
Winsorized Mean ( 9 / 24 )-16.78102083333330.0044853320925913-3741.3106737518
Winsorized Mean ( 10 / 24 )-16.78093750.00440386817693218-3810.49950311862
Winsorized Mean ( 11 / 24 )-16.78090694444440.00434151148037519-3865.2222895871
Winsorized Mean ( 12 / 24 )-16.78139027777780.00417517355056262-4019.32759789505
Winsorized Mean ( 13 / 24 )-16.77945833333330.00379134575332868-4425.72622626188
Winsorized Mean ( 14 / 24 )-16.77959444444440.00362977217524268-4622.76794088945
Winsorized Mean ( 15 / 24 )-16.78101111111110.00339120223000209-4948.39587054081
Winsorized Mean ( 16 / 24 )-16.78083333333330.00334365830501856-5018.7046051167
Winsorized Mean ( 17 / 24 )-16.78187222222220.00316404587757883-5303.92822087142
Winsorized Mean ( 18 / 24 )-16.78187222222220.00314950080639905-5328.42290058328
Winsorized Mean ( 19 / 24 )-16.78187222222220.00312651104139261-5367.60369627456
Winsorized Mean ( 20 / 24 )-16.781150.00284757948443727-5893.12786235228
Winsorized Mean ( 21 / 24 )-16.78059583333330.00271461545700697-6181.5738173962
Winsorized Mean ( 22 / 24 )-16.78032083333330.00243411455841533-6893.80899322082
Winsorized Mean ( 23 / 24 )-16.77862777777780.00216583879292205-7746.94212358291
Winsorized Mean ( 24 / 24 )-16.77909444444440.00210345297838408-7976.92870573913
Trimmed Mean ( 1 / 24 )-16.78191142857140.00545480984893345-3076.53463518122
Trimmed Mean ( 2 / 24 )-16.78174117647060.00517417874678307-3243.36324617781
Trimmed Mean ( 3 / 24 )-16.78130454545450.00493172189007219-3402.72726636029
Trimmed Mean ( 4 / 24 )-16.78092031250.00468143294124465-3584.56919561011
Trimmed Mean ( 5 / 24 )-16.78083548387100.00451465918136961-3716.96617833733
Trimmed Mean ( 6 / 24 )-16.7806450.00439223083030330-3820.52894037931
Trimmed Mean ( 7 / 24 )-16.78056379310340.00429919638115661-3903.18615512720
Trimmed Mean ( 8 / 24 )-16.78043750.00420700603238142-3988.68871849496
Trimmed Mean ( 9 / 24 )-16.78034444444440.00411209093655368-4080.7328202007
Trimmed Mean ( 10 / 24 )-16.78024038461540.00399567003539962-4199.6061326263
Trimmed Mean ( 11 / 24 )-16.780140.00386802486115729-4338.16756673572
Trimmed Mean ( 12 / 24 )-16.78003541666670.00372029784323858-4510.40108177451
Trimmed Mean ( 13 / 24 )-16.77985869565220.00357040651292075-4699.70537946546
Trimmed Mean ( 14 / 24 )-16.77990909090910.00346870457048029-4837.51462540544
Trimmed Mean ( 15 / 24 )-16.77994761904760.00337192969234518-4976.36343282626
Trimmed Mean ( 16 / 24 )-16.779820.00329713200936506-5089.21691710832
Trimmed Mean ( 17 / 24 )-16.77970.00320490600097834-5235.62937411511
Trimmed Mean ( 18 / 24 )-16.77944444444440.00311911272600577-5379.55691839699
Trimmed Mean ( 19 / 24 )-16.77915882352940.00299969433275553-5593.62287027292
Trimmed Mean ( 20 / 24 )-16.77883750.00283378504859014-5920.99866867029
Trimmed Mean ( 21 / 24 )-16.778560.00268462030963349-6249.88194412141
Trimmed Mean ( 22 / 24 )-16.77831071428570.00250898564679286-6687.28844094139
Trimmed Mean ( 23 / 24 )-16.77805769230770.00234806744154833-7145.47520885691
Trimmed Mean ( 24 / 24 )-16.77798333333330.00220990578416351-7592.17132855469
Median-16.77815
Midrange-16.79
Midmean - Weighted Average at Xnp-16.7804594594595
Midmean - Weighted Average at X(n+1)p-16.7794444444444
Midmean - Empirical Distribution Function-16.7804594594595
Midmean - Empirical Distribution Function - Averaging-16.7794444444444
Midmean - Empirical Distribution Function - Interpolation-16.7794444444444
Midmean - Closest Observation-16.7804594594595
Midmean - True Basic - Statistics Graphics Toolkit-16.7794444444444
Midmean - MS Excel (old versions)-16.7797
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')