Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 18:27:03 +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/11/t1476206848hzhjjwmsni11y5p.htm/, Retrieved Mon, 29 Apr 2024 03:21:57 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 03:21:57 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
480
548
634
489
399
658
497
495
445
525
565
427
477
511
538
444
559
433
459
492
526
523
636
519
671
599
579
593
684
599
721
516
556
700
579
552
734
760
714
698
800
712
782
610
596
748
581
641
598
609
526
716
552
464
631
465
539
537
488
520
477
480
645
455
379
477
424
316
381
376
389
472




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]'Gwilym Jenkins' @ jenkins.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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean554.44444444444412.793363292063843.3384428931511
Geometric Mean543.950079271976
Harmonic Mean533.421746548224
Quadratic Mean564.826718757374
Winsorized Mean ( 1 / 24 )555.02777777777812.534209404974744.2810359907897
Winsorized Mean ( 2 / 24 )554.512.368019996056344.8333686537384
Winsorized Mean ( 3 / 24 )554.08333333333312.237074398231645.2790687791686
Winsorized Mean ( 4 / 24 )553.7511.980499772729946.2209432414872
Winsorized Mean ( 5 / 24 )553.54166666666711.661399506857247.4678589256093
Winsorized Mean ( 6 / 24 )555.20833333333311.210584534032149.525368784106
Winsorized Mean ( 7 / 24 )555.30555555555611.123675896460149.9210477475591
Winsorized Mean ( 8 / 24 )555.7510.972378715628950.6499105074087
Winsorized Mean ( 9 / 24 )555.62510.464363803883753.0968733898364
Winsorized Mean ( 10 / 24 )555.48611111111110.389706765484453.4650422432025
Winsorized Mean ( 11 / 24 )554.8759.7589078424276256.8583092451839
Winsorized Mean ( 12 / 24 )553.3759.2672762469648459.7127985886077
Winsorized Mean ( 13 / 24 )551.9305555555568.727493441973563.2404434589584
Winsorized Mean ( 14 / 24 )549.5972222222228.2779062742754966.3932646749283
Winsorized Mean ( 15 / 24 )550.2222222222227.936889718069769.3246651732537
Winsorized Mean ( 16 / 24 )550.2222222222227.6066548529897672.3343220977037
Winsorized Mean ( 17 / 24 )549.757.5319546185294372.9890218201202
Winsorized Mean ( 18 / 24 )5497.4144573910540474.0445282836745
Winsorized Mean ( 19 / 24 )544.256.4747840611481184.0568573191139
Winsorized Mean ( 20 / 24 )543.9722222222226.4351517845888784.5313739957069
Winsorized Mean ( 21 / 24 )543.3888888888895.7037435046609895.2688157251186
Winsorized Mean ( 22 / 24 )543.6944444444445.6620610560588996.024122499111
Winsorized Mean ( 23 / 24 )544.3333333333335.4885354976745199.1764257631143
Winsorized Mean ( 24 / 24 )544.6666666666675.26322018330656103.485441934235
Trimmed Mean ( 1 / 24 )554.34285714285712.20534936373445.4180245581489
Trimmed Mean ( 2 / 24 )553.61764705882411.81376240587746.8620942286273
Trimmed Mean ( 3 / 24 )553.13636363636411.453338727274948.2947703554011
Trimmed Mean ( 4 / 24 )552.7812511.081710155711549.8823053691852
Trimmed Mean ( 5 / 24 )552.510.730552859698151.4884933911545
Trimmed Mean ( 6 / 24 )552.2510.408591220066353.0571321636055
Trimmed Mean ( 7 / 24 )551.63793103448310.144679295730654.3770694916535
Trimmed Mean ( 8 / 24 )550.9642857142869.8415025079557955.9837570806785
Trimmed Mean ( 9 / 24 )550.1666666666679.502500682311557.8970404801736
Trimmed Mean ( 10 / 24 )549.3269230769239.2042649122319759.6817810346698
Trimmed Mean ( 11 / 24 )548.448.8443760523341662.0100272483618
Trimmed Mean ( 12 / 24 )547.56258.5391726812254664.1236007797209
Trimmed Mean ( 13 / 24 )546.8043478260878.2647975660008466.1606462178207
Trimmed Mean ( 14 / 24 )546.1590909090918.035198937680167.9708237649156
Trimmed Mean ( 15 / 24 )545.7380952380957.8380870882525269.6264393458999
Trimmed Mean ( 16 / 24 )545.27.6488812656090271.2783975940814
Trimmed Mean ( 17 / 24 )544.6052631578957.465381409728772.9507620934382
Trimmed Mean ( 18 / 24 )5447.2256158083255375.2877006515057
Trimmed Mean ( 19 / 24 )543.4117647058826.91907869551778.5381679583972
Trimmed Mean ( 20 / 24 )543.31256.7545440947127880.4365908907584
Trimmed Mean ( 21 / 24 )543.2333333333336.5157075167969683.3728849757178
Trimmed Mean ( 22 / 24 )543.2142857142866.3802268007275985.1402783443903
Trimmed Mean ( 23 / 24 )543.1538461538466.1673313784294988.0695089700467
Trimmed Mean ( 24 / 24 )5435.8819916768860392.3156695603262
Median538.5
Midrange558
Midmean - Weighted Average at Xnp540.473684210526
Midmean - Weighted Average at X(n+1)p540.473684210526
Midmean - Empirical Distribution Function540.473684210526
Midmean - Empirical Distribution Function - Averaging540.473684210526
Midmean - Empirical Distribution Function - Interpolation540.473684210526
Midmean - Closest Observation540.473684210526
Midmean - True Basic - Statistics Graphics Toolkit540.473684210526
Midmean - MS Excel (old versions)542.871794871795
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 554.444444444444 & 12.7933632920638 & 43.3384428931511 \tabularnewline
Geometric Mean & 543.950079271976 &  &  \tabularnewline
Harmonic Mean & 533.421746548224 &  &  \tabularnewline
Quadratic Mean & 564.826718757374 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 555.027777777778 & 12.5342094049747 & 44.2810359907897 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 554.5 & 12.3680199960563 & 44.8333686537384 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 554.083333333333 & 12.2370743982316 & 45.2790687791686 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 553.75 & 11.9804997727299 & 46.2209432414872 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 553.541666666667 & 11.6613995068572 & 47.4678589256093 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 555.208333333333 & 11.2105845340321 & 49.525368784106 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 555.305555555556 & 11.1236758964601 & 49.9210477475591 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 555.75 & 10.9723787156289 & 50.6499105074087 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 555.625 & 10.4643638038837 & 53.0968733898364 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 555.486111111111 & 10.3897067654844 & 53.4650422432025 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 554.875 & 9.75890784242762 & 56.8583092451839 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 553.375 & 9.26727624696484 & 59.7127985886077 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 551.930555555556 & 8.7274934419735 & 63.2404434589584 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 549.597222222222 & 8.27790627427549 & 66.3932646749283 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 550.222222222222 & 7.9368897180697 & 69.3246651732537 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 550.222222222222 & 7.60665485298976 & 72.3343220977037 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 549.75 & 7.53195461852943 & 72.9890218201202 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 549 & 7.41445739105404 & 74.0445282836745 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 544.25 & 6.47478406114811 & 84.0568573191139 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 543.972222222222 & 6.43515178458887 & 84.5313739957069 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 543.388888888889 & 5.70374350466098 & 95.2688157251186 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 543.694444444444 & 5.66206105605889 & 96.024122499111 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 544.333333333333 & 5.48853549767451 & 99.1764257631143 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 544.666666666667 & 5.26322018330656 & 103.485441934235 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 554.342857142857 & 12.205349363734 & 45.4180245581489 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 553.617647058824 & 11.813762405877 & 46.8620942286273 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 553.136363636364 & 11.4533387272749 & 48.2947703554011 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 552.78125 & 11.0817101557115 & 49.8823053691852 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 552.5 & 10.7305528596981 & 51.4884933911545 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 552.25 & 10.4085912200663 & 53.0571321636055 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 551.637931034483 & 10.1446792957306 & 54.3770694916535 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 550.964285714286 & 9.84150250795579 & 55.9837570806785 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 550.166666666667 & 9.5025006823115 & 57.8970404801736 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 549.326923076923 & 9.20426491223197 & 59.6817810346698 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 548.44 & 8.84437605233416 & 62.0100272483618 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 547.5625 & 8.53917268122546 & 64.1236007797209 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 546.804347826087 & 8.26479756600084 & 66.1606462178207 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 546.159090909091 & 8.0351989376801 & 67.9708237649156 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 545.738095238095 & 7.83808708825252 & 69.6264393458999 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 545.2 & 7.64888126560902 & 71.2783975940814 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 544.605263157895 & 7.4653814097287 & 72.9507620934382 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 544 & 7.22561580832553 & 75.2877006515057 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 543.411764705882 & 6.919078695517 & 78.5381679583972 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 543.3125 & 6.75454409471278 & 80.4365908907584 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 543.233333333333 & 6.51570751679696 & 83.3728849757178 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 543.214285714286 & 6.38022680072759 & 85.1402783443903 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 543.153846153846 & 6.16733137842949 & 88.0695089700467 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 543 & 5.88199167688603 & 92.3156695603262 \tabularnewline
Median & 538.5 &  &  \tabularnewline
Midrange & 558 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 540.473684210526 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 540.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 540.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 540.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 540.473684210526 &  &  \tabularnewline
Midmean - Closest Observation & 540.473684210526 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 540.473684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 542.871794871795 &  &  \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]554.444444444444[/C][C]12.7933632920638[/C][C]43.3384428931511[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]543.950079271976[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]533.421746548224[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]564.826718757374[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]555.027777777778[/C][C]12.5342094049747[/C][C]44.2810359907897[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]554.5[/C][C]12.3680199960563[/C][C]44.8333686537384[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]554.083333333333[/C][C]12.2370743982316[/C][C]45.2790687791686[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]553.75[/C][C]11.9804997727299[/C][C]46.2209432414872[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]553.541666666667[/C][C]11.6613995068572[/C][C]47.4678589256093[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]555.208333333333[/C][C]11.2105845340321[/C][C]49.525368784106[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]555.305555555556[/C][C]11.1236758964601[/C][C]49.9210477475591[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]555.75[/C][C]10.9723787156289[/C][C]50.6499105074087[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]555.625[/C][C]10.4643638038837[/C][C]53.0968733898364[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]555.486111111111[/C][C]10.3897067654844[/C][C]53.4650422432025[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]554.875[/C][C]9.75890784242762[/C][C]56.8583092451839[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]553.375[/C][C]9.26727624696484[/C][C]59.7127985886077[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]551.930555555556[/C][C]8.7274934419735[/C][C]63.2404434589584[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]549.597222222222[/C][C]8.27790627427549[/C][C]66.3932646749283[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]550.222222222222[/C][C]7.9368897180697[/C][C]69.3246651732537[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]550.222222222222[/C][C]7.60665485298976[/C][C]72.3343220977037[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]549.75[/C][C]7.53195461852943[/C][C]72.9890218201202[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]549[/C][C]7.41445739105404[/C][C]74.0445282836745[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]544.25[/C][C]6.47478406114811[/C][C]84.0568573191139[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]543.972222222222[/C][C]6.43515178458887[/C][C]84.5313739957069[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]543.388888888889[/C][C]5.70374350466098[/C][C]95.2688157251186[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]543.694444444444[/C][C]5.66206105605889[/C][C]96.024122499111[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]544.333333333333[/C][C]5.48853549767451[/C][C]99.1764257631143[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]544.666666666667[/C][C]5.26322018330656[/C][C]103.485441934235[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]554.342857142857[/C][C]12.205349363734[/C][C]45.4180245581489[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]553.617647058824[/C][C]11.813762405877[/C][C]46.8620942286273[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]553.136363636364[/C][C]11.4533387272749[/C][C]48.2947703554011[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]552.78125[/C][C]11.0817101557115[/C][C]49.8823053691852[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]552.5[/C][C]10.7305528596981[/C][C]51.4884933911545[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]552.25[/C][C]10.4085912200663[/C][C]53.0571321636055[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]551.637931034483[/C][C]10.1446792957306[/C][C]54.3770694916535[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]550.964285714286[/C][C]9.84150250795579[/C][C]55.9837570806785[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]550.166666666667[/C][C]9.5025006823115[/C][C]57.8970404801736[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]549.326923076923[/C][C]9.20426491223197[/C][C]59.6817810346698[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]548.44[/C][C]8.84437605233416[/C][C]62.0100272483618[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]547.5625[/C][C]8.53917268122546[/C][C]64.1236007797209[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]546.804347826087[/C][C]8.26479756600084[/C][C]66.1606462178207[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]546.159090909091[/C][C]8.0351989376801[/C][C]67.9708237649156[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]545.738095238095[/C][C]7.83808708825252[/C][C]69.6264393458999[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]545.2[/C][C]7.64888126560902[/C][C]71.2783975940814[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]544.605263157895[/C][C]7.4653814097287[/C][C]72.9507620934382[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]544[/C][C]7.22561580832553[/C][C]75.2877006515057[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]543.411764705882[/C][C]6.919078695517[/C][C]78.5381679583972[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]543.3125[/C][C]6.75454409471278[/C][C]80.4365908907584[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]543.233333333333[/C][C]6.51570751679696[/C][C]83.3728849757178[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]543.214285714286[/C][C]6.38022680072759[/C][C]85.1402783443903[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]543.153846153846[/C][C]6.16733137842949[/C][C]88.0695089700467[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]543[/C][C]5.88199167688603[/C][C]92.3156695603262[/C][/ROW]
[ROW][C]Median[/C][C]538.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]540.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]542.871794871795[/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 Mean554.44444444444412.793363292063843.3384428931511
Geometric Mean543.950079271976
Harmonic Mean533.421746548224
Quadratic Mean564.826718757374
Winsorized Mean ( 1 / 24 )555.02777777777812.534209404974744.2810359907897
Winsorized Mean ( 2 / 24 )554.512.368019996056344.8333686537384
Winsorized Mean ( 3 / 24 )554.08333333333312.237074398231645.2790687791686
Winsorized Mean ( 4 / 24 )553.7511.980499772729946.2209432414872
Winsorized Mean ( 5 / 24 )553.54166666666711.661399506857247.4678589256093
Winsorized Mean ( 6 / 24 )555.20833333333311.210584534032149.525368784106
Winsorized Mean ( 7 / 24 )555.30555555555611.123675896460149.9210477475591
Winsorized Mean ( 8 / 24 )555.7510.972378715628950.6499105074087
Winsorized Mean ( 9 / 24 )555.62510.464363803883753.0968733898364
Winsorized Mean ( 10 / 24 )555.48611111111110.389706765484453.4650422432025
Winsorized Mean ( 11 / 24 )554.8759.7589078424276256.8583092451839
Winsorized Mean ( 12 / 24 )553.3759.2672762469648459.7127985886077
Winsorized Mean ( 13 / 24 )551.9305555555568.727493441973563.2404434589584
Winsorized Mean ( 14 / 24 )549.5972222222228.2779062742754966.3932646749283
Winsorized Mean ( 15 / 24 )550.2222222222227.936889718069769.3246651732537
Winsorized Mean ( 16 / 24 )550.2222222222227.6066548529897672.3343220977037
Winsorized Mean ( 17 / 24 )549.757.5319546185294372.9890218201202
Winsorized Mean ( 18 / 24 )5497.4144573910540474.0445282836745
Winsorized Mean ( 19 / 24 )544.256.4747840611481184.0568573191139
Winsorized Mean ( 20 / 24 )543.9722222222226.4351517845888784.5313739957069
Winsorized Mean ( 21 / 24 )543.3888888888895.7037435046609895.2688157251186
Winsorized Mean ( 22 / 24 )543.6944444444445.6620610560588996.024122499111
Winsorized Mean ( 23 / 24 )544.3333333333335.4885354976745199.1764257631143
Winsorized Mean ( 24 / 24 )544.6666666666675.26322018330656103.485441934235
Trimmed Mean ( 1 / 24 )554.34285714285712.20534936373445.4180245581489
Trimmed Mean ( 2 / 24 )553.61764705882411.81376240587746.8620942286273
Trimmed Mean ( 3 / 24 )553.13636363636411.453338727274948.2947703554011
Trimmed Mean ( 4 / 24 )552.7812511.081710155711549.8823053691852
Trimmed Mean ( 5 / 24 )552.510.730552859698151.4884933911545
Trimmed Mean ( 6 / 24 )552.2510.408591220066353.0571321636055
Trimmed Mean ( 7 / 24 )551.63793103448310.144679295730654.3770694916535
Trimmed Mean ( 8 / 24 )550.9642857142869.8415025079557955.9837570806785
Trimmed Mean ( 9 / 24 )550.1666666666679.502500682311557.8970404801736
Trimmed Mean ( 10 / 24 )549.3269230769239.2042649122319759.6817810346698
Trimmed Mean ( 11 / 24 )548.448.8443760523341662.0100272483618
Trimmed Mean ( 12 / 24 )547.56258.5391726812254664.1236007797209
Trimmed Mean ( 13 / 24 )546.8043478260878.2647975660008466.1606462178207
Trimmed Mean ( 14 / 24 )546.1590909090918.035198937680167.9708237649156
Trimmed Mean ( 15 / 24 )545.7380952380957.8380870882525269.6264393458999
Trimmed Mean ( 16 / 24 )545.27.6488812656090271.2783975940814
Trimmed Mean ( 17 / 24 )544.6052631578957.465381409728772.9507620934382
Trimmed Mean ( 18 / 24 )5447.2256158083255375.2877006515057
Trimmed Mean ( 19 / 24 )543.4117647058826.91907869551778.5381679583972
Trimmed Mean ( 20 / 24 )543.31256.7545440947127880.4365908907584
Trimmed Mean ( 21 / 24 )543.2333333333336.5157075167969683.3728849757178
Trimmed Mean ( 22 / 24 )543.2142857142866.3802268007275985.1402783443903
Trimmed Mean ( 23 / 24 )543.1538461538466.1673313784294988.0695089700467
Trimmed Mean ( 24 / 24 )5435.8819916768860392.3156695603262
Median538.5
Midrange558
Midmean - Weighted Average at Xnp540.473684210526
Midmean - Weighted Average at X(n+1)p540.473684210526
Midmean - Empirical Distribution Function540.473684210526
Midmean - Empirical Distribution Function - Averaging540.473684210526
Midmean - Empirical Distribution Function - Interpolation540.473684210526
Midmean - Closest Observation540.473684210526
Midmean - True Basic - Statistics Graphics Toolkit540.473684210526
Midmean - MS Excel (old versions)542.871794871795
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')