Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 11:43:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476269042ruhpr10k4hsvub3.htm/, Retrieved Sun, 05 May 2024 17:05:02 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 17:05:02 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
54854
53982
52301
51652
50338
51959
57648
57803
52599
51123
49604
51154
51765
50491
49332
48690
47496
48107
53970
54300
50246
48519
47602
49723
52010
50976
49795
49104
48354
49390
55323
56287
52831
51881
51382
53000
54365
53815
53107
53031
52419
53378
59398
60706
58531
57244
56843
58299
60654
59579
58823
57813
56487
57644
62444
62890
59758
58716
57485
57888
59676
58365
57337
56520
55189
56229
60766
61393
57919
56772
55820
56953




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean54581.2083333333475.740438848241114.72896536917
Geometric Mean54433.8026604836
Harmonic Mean54286.4216606181
Quadratic Mean54728.2163024959
Winsorized Mean ( 1 / 24 )54576.4861111111473.947377856381115.153050024151
Winsorized Mean ( 2 / 24 )54561.3194444444464.681371822261117.416627291257
Winsorized Mean ( 3 / 24 )54545.4861111111457.485598853639119.228859329759
Winsorized Mean ( 4 / 24 )54551.3194444444455.119640595768119.861492624302
Winsorized Mean ( 5 / 24 )54559.5833333333452.23915598474120.643209707331
Winsorized Mean ( 6 / 24 )54519.4166666667432.571873296557126.035510009431
Winsorized Mean ( 7 / 24 )54533.6111111111427.361783637783127.605259054544
Winsorized Mean ( 8 / 24 )54529.2777777778424.443547723737128.472391841541
Winsorized Mean ( 9 / 24 )54533.4027777778416.172472494489131.035583518802
Winsorized Mean ( 10 / 24 )54470.0694444444400.723181025975135.929419668172
Winsorized Mean ( 11 / 24 )54464.7222222222396.407710883795137.395718415246
Winsorized Mean ( 12 / 24 )54509.0555555556379.590885264151143.599484791695
Winsorized Mean ( 13 / 24 )54495.6944444444372.542458870848146.280492724554
Winsorized Mean ( 14 / 24 )54512.6111111111366.028501179734148.929962927514
Winsorized Mean ( 15 / 24 )54534.4861111111339.402025819386160.678139676549
Winsorized Mean ( 16 / 24 )54560.2638888889333.652163831149163.524381986325
Winsorized Mean ( 17 / 24 )54549.875330.114352156649165.24539040373
Winsorized Mean ( 18 / 24 )54604.375321.612680305997169.783028915548
Winsorized Mean ( 19 / 24 )54634.7222222222305.988759563093178.551402673198
Winsorized Mean ( 20 / 24 )54665301.553662075444181.277851589558
Winsorized Mean ( 21 / 24 )54652.4583333333290.578897768649188.081305122322
Winsorized Mean ( 22 / 24 )54631.0694444444281.213751846974194.268840288339
Winsorized Mean ( 23 / 24 )54617.6527777778275.024577902768198.591897474295
Winsorized Mean ( 24 / 24 )54617.6527777778249.263501336403219.116126047136
Trimmed Mean ( 1 / 24 )54563.7285714286463.521511567577117.715633923656
Trimmed Mean ( 2 / 24 )54550.2205882353451.112987023514120.923631456862
Trimmed Mean ( 3 / 24 )54544.1666666667442.186291987966123.351102589474
Trimmed Mean ( 4 / 24 )54543.671875434.667362244897125.483706881745
Trimmed Mean ( 5 / 24 )54541.4516129032426.364590433314127.922094931647
Trimmed Mean ( 6 / 24 )54537.1417.117384946802130.747607192051
Trimmed Mean ( 7 / 24 )54540.7586206897411.25151037467132.621418389443
Trimmed Mean ( 8 / 24 )54542.0714285714405.175349131212134.613498934528
Trimmed Mean ( 9 / 24 )54544.2037037037398.161314207091136.990214160621
Trimmed Mean ( 10 / 24 )54545.8653846154391.15153026621139.449449034477
Trimmed Mean ( 11 / 24 )54556.78385.552801423766141.502745664234
Trimmed Mean ( 12 / 24 )54569.3333333333379.093283367155143.946980143361
Trimmed Mean ( 13 / 24 )54577.1956521739374.18173349422145.857455794317
Trimmed Mean ( 14 / 24 )54587.4545454545368.917839868873147.966426792635
Trimmed Mean ( 15 / 24 )54596.619047619363.028514880038150.392095413388
Trimmed Mean ( 16 / 24 )54604.075360.548501996148151.447238575917
Trimmed Mean ( 17 / 24 )54609.2631578947357.692817590225152.67084065539
Trimmed Mean ( 18 / 24 )54616.25353.76091238988154.387463643262
Trimmed Mean ( 19 / 24 )54617.6470588235349.521103186663156.2642328628
Trimmed Mean ( 20 / 24 )54615.625346.48421317549157.628033033464
Trimmed Mean ( 21 / 24 )54609.7342.057211555335159.650778159857
Trimmed Mean ( 22 / 24 )54604.4642857143337.432742591564161.823253624823
Trimmed Mean ( 23 / 24 )54601.1153846154331.92511355111164.498295415083
Trimmed Mean ( 24 / 24 )54598.9583333333323.909689949772168.562287660489
Median54332.5
Midrange55193
Midmean - Weighted Average at Xnp54522.6756756757
Midmean - Weighted Average at X(n+1)p54616.25
Midmean - Empirical Distribution Function54522.6756756757
Midmean - Empirical Distribution Function - Averaging54616.25
Midmean - Empirical Distribution Function - Interpolation54616.25
Midmean - Closest Observation54522.6756756757
Midmean - True Basic - Statistics Graphics Toolkit54616.25
Midmean - MS Excel (old versions)54609.2631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 54581.2083333333 & 475.740438848241 & 114.72896536917 \tabularnewline
Geometric Mean & 54433.8026604836 &  &  \tabularnewline
Harmonic Mean & 54286.4216606181 &  &  \tabularnewline
Quadratic Mean & 54728.2163024959 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 54576.4861111111 & 473.947377856381 & 115.153050024151 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 54561.3194444444 & 464.681371822261 & 117.416627291257 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 54545.4861111111 & 457.485598853639 & 119.228859329759 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 54551.3194444444 & 455.119640595768 & 119.861492624302 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 54559.5833333333 & 452.23915598474 & 120.643209707331 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 54519.4166666667 & 432.571873296557 & 126.035510009431 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 54533.6111111111 & 427.361783637783 & 127.605259054544 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 54529.2777777778 & 424.443547723737 & 128.472391841541 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 54533.4027777778 & 416.172472494489 & 131.035583518802 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 54470.0694444444 & 400.723181025975 & 135.929419668172 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 54464.7222222222 & 396.407710883795 & 137.395718415246 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 54509.0555555556 & 379.590885264151 & 143.599484791695 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 54495.6944444444 & 372.542458870848 & 146.280492724554 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 54512.6111111111 & 366.028501179734 & 148.929962927514 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 54534.4861111111 & 339.402025819386 & 160.678139676549 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 54560.2638888889 & 333.652163831149 & 163.524381986325 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 54549.875 & 330.114352156649 & 165.24539040373 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 54604.375 & 321.612680305997 & 169.783028915548 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 54634.7222222222 & 305.988759563093 & 178.551402673198 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 54665 & 301.553662075444 & 181.277851589558 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 54652.4583333333 & 290.578897768649 & 188.081305122322 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 54631.0694444444 & 281.213751846974 & 194.268840288339 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 54617.6527777778 & 275.024577902768 & 198.591897474295 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 54617.6527777778 & 249.263501336403 & 219.116126047136 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 54563.7285714286 & 463.521511567577 & 117.715633923656 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 54550.2205882353 & 451.112987023514 & 120.923631456862 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 54544.1666666667 & 442.186291987966 & 123.351102589474 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 54543.671875 & 434.667362244897 & 125.483706881745 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 54541.4516129032 & 426.364590433314 & 127.922094931647 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 54537.1 & 417.117384946802 & 130.747607192051 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 54540.7586206897 & 411.25151037467 & 132.621418389443 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 54542.0714285714 & 405.175349131212 & 134.613498934528 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 54544.2037037037 & 398.161314207091 & 136.990214160621 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 54545.8653846154 & 391.15153026621 & 139.449449034477 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 54556.78 & 385.552801423766 & 141.502745664234 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 54569.3333333333 & 379.093283367155 & 143.946980143361 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 54577.1956521739 & 374.18173349422 & 145.857455794317 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 54587.4545454545 & 368.917839868873 & 147.966426792635 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 54596.619047619 & 363.028514880038 & 150.392095413388 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 54604.075 & 360.548501996148 & 151.447238575917 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 54609.2631578947 & 357.692817590225 & 152.67084065539 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 54616.25 & 353.76091238988 & 154.387463643262 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 54617.6470588235 & 349.521103186663 & 156.2642328628 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 54615.625 & 346.48421317549 & 157.628033033464 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 54609.7 & 342.057211555335 & 159.650778159857 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 54604.4642857143 & 337.432742591564 & 161.823253624823 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 54601.1153846154 & 331.92511355111 & 164.498295415083 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 54598.9583333333 & 323.909689949772 & 168.562287660489 \tabularnewline
Median & 54332.5 &  &  \tabularnewline
Midrange & 55193 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 54522.6756756757 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 54616.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 54522.6756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 54616.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 54616.25 &  &  \tabularnewline
Midmean - Closest Observation & 54522.6756756757 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 54616.25 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 54609.2631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]54581.2083333333[/C][C]475.740438848241[/C][C]114.72896536917[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]54433.8026604836[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]54286.4216606181[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]54728.2163024959[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]54576.4861111111[/C][C]473.947377856381[/C][C]115.153050024151[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]54561.3194444444[/C][C]464.681371822261[/C][C]117.416627291257[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]54545.4861111111[/C][C]457.485598853639[/C][C]119.228859329759[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]54551.3194444444[/C][C]455.119640595768[/C][C]119.861492624302[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]54559.5833333333[/C][C]452.23915598474[/C][C]120.643209707331[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]54519.4166666667[/C][C]432.571873296557[/C][C]126.035510009431[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]54533.6111111111[/C][C]427.361783637783[/C][C]127.605259054544[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]54529.2777777778[/C][C]424.443547723737[/C][C]128.472391841541[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]54533.4027777778[/C][C]416.172472494489[/C][C]131.035583518802[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]54470.0694444444[/C][C]400.723181025975[/C][C]135.929419668172[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]54464.7222222222[/C][C]396.407710883795[/C][C]137.395718415246[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]54509.0555555556[/C][C]379.590885264151[/C][C]143.599484791695[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]54495.6944444444[/C][C]372.542458870848[/C][C]146.280492724554[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]54512.6111111111[/C][C]366.028501179734[/C][C]148.929962927514[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]54534.4861111111[/C][C]339.402025819386[/C][C]160.678139676549[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]54560.2638888889[/C][C]333.652163831149[/C][C]163.524381986325[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]54549.875[/C][C]330.114352156649[/C][C]165.24539040373[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]54604.375[/C][C]321.612680305997[/C][C]169.783028915548[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]54634.7222222222[/C][C]305.988759563093[/C][C]178.551402673198[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]54665[/C][C]301.553662075444[/C][C]181.277851589558[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]54652.4583333333[/C][C]290.578897768649[/C][C]188.081305122322[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]54631.0694444444[/C][C]281.213751846974[/C][C]194.268840288339[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]54617.6527777778[/C][C]275.024577902768[/C][C]198.591897474295[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]54617.6527777778[/C][C]249.263501336403[/C][C]219.116126047136[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]54563.7285714286[/C][C]463.521511567577[/C][C]117.715633923656[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]54550.2205882353[/C][C]451.112987023514[/C][C]120.923631456862[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]54544.1666666667[/C][C]442.186291987966[/C][C]123.351102589474[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]54543.671875[/C][C]434.667362244897[/C][C]125.483706881745[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]54541.4516129032[/C][C]426.364590433314[/C][C]127.922094931647[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]54537.1[/C][C]417.117384946802[/C][C]130.747607192051[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]54540.7586206897[/C][C]411.25151037467[/C][C]132.621418389443[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]54542.0714285714[/C][C]405.175349131212[/C][C]134.613498934528[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]54544.2037037037[/C][C]398.161314207091[/C][C]136.990214160621[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]54545.8653846154[/C][C]391.15153026621[/C][C]139.449449034477[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]54556.78[/C][C]385.552801423766[/C][C]141.502745664234[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]54569.3333333333[/C][C]379.093283367155[/C][C]143.946980143361[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]54577.1956521739[/C][C]374.18173349422[/C][C]145.857455794317[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]54587.4545454545[/C][C]368.917839868873[/C][C]147.966426792635[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]54596.619047619[/C][C]363.028514880038[/C][C]150.392095413388[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]54604.075[/C][C]360.548501996148[/C][C]151.447238575917[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]54609.2631578947[/C][C]357.692817590225[/C][C]152.67084065539[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]54616.25[/C][C]353.76091238988[/C][C]154.387463643262[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]54617.6470588235[/C][C]349.521103186663[/C][C]156.2642328628[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]54615.625[/C][C]346.48421317549[/C][C]157.628033033464[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]54609.7[/C][C]342.057211555335[/C][C]159.650778159857[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]54604.4642857143[/C][C]337.432742591564[/C][C]161.823253624823[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]54601.1153846154[/C][C]331.92511355111[/C][C]164.498295415083[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]54598.9583333333[/C][C]323.909689949772[/C][C]168.562287660489[/C][/ROW]
[ROW][C]Median[/C][C]54332.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]55193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]54522.6756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]54616.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]54522.6756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]54616.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]54616.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]54522.6756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]54616.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]54609.2631578947[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean54581.2083333333475.740438848241114.72896536917
Geometric Mean54433.8026604836
Harmonic Mean54286.4216606181
Quadratic Mean54728.2163024959
Winsorized Mean ( 1 / 24 )54576.4861111111473.947377856381115.153050024151
Winsorized Mean ( 2 / 24 )54561.3194444444464.681371822261117.416627291257
Winsorized Mean ( 3 / 24 )54545.4861111111457.485598853639119.228859329759
Winsorized Mean ( 4 / 24 )54551.3194444444455.119640595768119.861492624302
Winsorized Mean ( 5 / 24 )54559.5833333333452.23915598474120.643209707331
Winsorized Mean ( 6 / 24 )54519.4166666667432.571873296557126.035510009431
Winsorized Mean ( 7 / 24 )54533.6111111111427.361783637783127.605259054544
Winsorized Mean ( 8 / 24 )54529.2777777778424.443547723737128.472391841541
Winsorized Mean ( 9 / 24 )54533.4027777778416.172472494489131.035583518802
Winsorized Mean ( 10 / 24 )54470.0694444444400.723181025975135.929419668172
Winsorized Mean ( 11 / 24 )54464.7222222222396.407710883795137.395718415246
Winsorized Mean ( 12 / 24 )54509.0555555556379.590885264151143.599484791695
Winsorized Mean ( 13 / 24 )54495.6944444444372.542458870848146.280492724554
Winsorized Mean ( 14 / 24 )54512.6111111111366.028501179734148.929962927514
Winsorized Mean ( 15 / 24 )54534.4861111111339.402025819386160.678139676549
Winsorized Mean ( 16 / 24 )54560.2638888889333.652163831149163.524381986325
Winsorized Mean ( 17 / 24 )54549.875330.114352156649165.24539040373
Winsorized Mean ( 18 / 24 )54604.375321.612680305997169.783028915548
Winsorized Mean ( 19 / 24 )54634.7222222222305.988759563093178.551402673198
Winsorized Mean ( 20 / 24 )54665301.553662075444181.277851589558
Winsorized Mean ( 21 / 24 )54652.4583333333290.578897768649188.081305122322
Winsorized Mean ( 22 / 24 )54631.0694444444281.213751846974194.268840288339
Winsorized Mean ( 23 / 24 )54617.6527777778275.024577902768198.591897474295
Winsorized Mean ( 24 / 24 )54617.6527777778249.263501336403219.116126047136
Trimmed Mean ( 1 / 24 )54563.7285714286463.521511567577117.715633923656
Trimmed Mean ( 2 / 24 )54550.2205882353451.112987023514120.923631456862
Trimmed Mean ( 3 / 24 )54544.1666666667442.186291987966123.351102589474
Trimmed Mean ( 4 / 24 )54543.671875434.667362244897125.483706881745
Trimmed Mean ( 5 / 24 )54541.4516129032426.364590433314127.922094931647
Trimmed Mean ( 6 / 24 )54537.1417.117384946802130.747607192051
Trimmed Mean ( 7 / 24 )54540.7586206897411.25151037467132.621418389443
Trimmed Mean ( 8 / 24 )54542.0714285714405.175349131212134.613498934528
Trimmed Mean ( 9 / 24 )54544.2037037037398.161314207091136.990214160621
Trimmed Mean ( 10 / 24 )54545.8653846154391.15153026621139.449449034477
Trimmed Mean ( 11 / 24 )54556.78385.552801423766141.502745664234
Trimmed Mean ( 12 / 24 )54569.3333333333379.093283367155143.946980143361
Trimmed Mean ( 13 / 24 )54577.1956521739374.18173349422145.857455794317
Trimmed Mean ( 14 / 24 )54587.4545454545368.917839868873147.966426792635
Trimmed Mean ( 15 / 24 )54596.619047619363.028514880038150.392095413388
Trimmed Mean ( 16 / 24 )54604.075360.548501996148151.447238575917
Trimmed Mean ( 17 / 24 )54609.2631578947357.692817590225152.67084065539
Trimmed Mean ( 18 / 24 )54616.25353.76091238988154.387463643262
Trimmed Mean ( 19 / 24 )54617.6470588235349.521103186663156.2642328628
Trimmed Mean ( 20 / 24 )54615.625346.48421317549157.628033033464
Trimmed Mean ( 21 / 24 )54609.7342.057211555335159.650778159857
Trimmed Mean ( 22 / 24 )54604.4642857143337.432742591564161.823253624823
Trimmed Mean ( 23 / 24 )54601.1153846154331.92511355111164.498295415083
Trimmed Mean ( 24 / 24 )54598.9583333333323.909689949772168.562287660489
Median54332.5
Midrange55193
Midmean - Weighted Average at Xnp54522.6756756757
Midmean - Weighted Average at X(n+1)p54616.25
Midmean - Empirical Distribution Function54522.6756756757
Midmean - Empirical Distribution Function - Averaging54616.25
Midmean - Empirical Distribution Function - Interpolation54616.25
Midmean - Closest Observation54522.6756756757
Midmean - True Basic - Statistics Graphics Toolkit54616.25
Midmean - MS Excel (old versions)54609.2631578947
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')