Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 12:45:51 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/21/t1350837986ut989egwkyr2xq7.htm/, Retrieved Mon, 29 Apr 2024 03:47:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181094, Retrieved Mon, 29 Apr 2024 03:47:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-21 16:45:51] [9de610bc675449a09d9ad0dc935d1f26] [Current]
Feedback Forum

Post a new message
Dataseries X:
246,24
247,57
247,84
248,27
248,3
248,31
248,31
248,38
248,37
248,41
248,68
248,75
248,75
247,95
248,13
247,86
246,23
245,98
245,98
246,27
246,31
246,3
246,67
246,78
246,78
247,91
247,99
248,6
248,68
248,75
248,75
249,03
249,05
249,57
249,35
249,46
249,46
250,82
254,19
255,18
256,68
256,73
256,73
257,39
257,78
258,67
258,71
258,91
258,91
261,38
262,42
262,77
263,24
262,83
262,83
263,09
263,6
265,68
266,08
266,28
266,28
269,14
270,96
272,97
273,13
274,73
274,73
274,59
275,15
275,16
275,38
275,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181094&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181094&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean256.00751.15325540711395221.98681958983
Geometric Mean255.826376141524
Harmonic Mean255.648602569637
Quadratic Mean256.191861534801
Winsorized Mean ( 1 / 24 )256.0072222222221.15318965057639221.999236720747
Winsorized Mean ( 2 / 24 )256.0080555555561.15090978571511222.439724410272
Winsorized Mean ( 3 / 24 )256.0080555555561.15076231178949222.468230782994
Winsorized Mean ( 4 / 24 )255.9863888888891.14514010708279223.541545096177
Winsorized Mean ( 5 / 24 )255.9884722222221.14489146795016223.591911887116
Winsorized Mean ( 6 / 24 )255.9776388888891.14210828121478224.127294319784
Winsorized Mean ( 7 / 24 )255.8706944444441.10607177443555231.332812533816
Winsorized Mean ( 8 / 24 )255.8651388888891.10074633226335232.446960202702
Winsorized Mean ( 9 / 24 )255.6138888888891.04728562549085244.072755958133
Winsorized Mean ( 10 / 24 )255.4708333333330.983688957536867259.706923998645
Winsorized Mean ( 11 / 24 )255.0751388888890.897647900051552284.159455922796
Winsorized Mean ( 12 / 24 )255.0784722222220.897269847468062284.282897661176
Winsorized Mean ( 13 / 24 )255.0513888888890.889921843941236286.599762243538
Winsorized Mean ( 14 / 24 )254.9813888888890.875560949312327291.220604446959
Winsorized Mean ( 15 / 24 )254.5563888888890.802819130661061317.078130262393
Winsorized Mean ( 16 / 24 )254.50750.786649427628013323.533572975979
Winsorized Mean ( 17 / 24 )254.5051388888890.777371780737701327.391790125661
Winsorized Mean ( 18 / 24 )254.4476388888890.766462962656538331.976431068477
Winsorized Mean ( 19 / 24 )254.4502777777780.766164970881926332.108994078498
Winsorized Mean ( 20 / 24 )254.4336111111110.763599890559257333.20278624551
Winsorized Mean ( 21 / 24 )254.3490277777780.745996884780231340.951863160539
Winsorized Mean ( 22 / 24 )254.0343055555560.697860771747832364.018606346524
Winsorized Mean ( 23 / 24 )253.2548611111110.584049124654767433.619109113143
Winsorized Mean ( 24 / 24 )253.3181944444440.576700056239417439.254672691205
Trimmed Mean ( 1 / 24 )255.8737142857141.14398935428144223.667915551919
Trimmed Mean ( 2 / 24 )255.7323529411761.13230727249047225.850667176853
Trimmed Mean ( 3 / 24 )255.581969696971.11903605329049228.394758994081
Trimmed Mean ( 4 / 24 )255.42218751.10243042893075231.690073855939
Trimmed Mean ( 5 / 24 )255.2583870967741.08375888736435235.530605629035
Trimmed Mean ( 6 / 24 )255.0831666666671.06043996017394240.544657167414
Trimmed Mean ( 7 / 24 )254.8981034482761.03205946078932246.980056026354
Trimmed Mean ( 8 / 24 )254.7194642857141.00638937430007253.102298961442
Trimmed Mean ( 9 / 24 )254.5285185185190.975127127385839261.020857045449
Trimmed Mean ( 10 / 24 )254.3615384615380.949302211963697267.945797719542
Trimmed Mean ( 11 / 24 )254.20180.931119917746629273.006510928458
Trimmed Mean ( 12 / 24 )254.0827083333330.926624351978391274.202494021287
Trimmed Mean ( 13 / 24 )253.9528260869570.919147718177164276.291635245084
Trimmed Mean ( 14 / 24 )253.8145454545450.909306443794244279.129821620376
Trimmed Mean ( 15 / 24 )253.6716666666670.897906515797224282.514562711954
Trimmed Mean ( 16 / 24 )253.56550.897658846024565282.474239654584
Trimmed Mean ( 17 / 24 )253.4539473684210.8978483478217282.290375633406
Trimmed Mean ( 18 / 24 )253.3302777777780.896706361850252282.511966632041
Trimmed Mean ( 19 / 24 )253.1988235294120.894132065509038283.17832823193
Trimmed Mean ( 20 / 24 )253.0506250.886528197782625285.440018301648
Trimmed Mean ( 21 / 24 )252.8846666666670.872227131303754289.92983317163
Trimmed Mean ( 22 / 24 )252.7053571428570.852690805059197296.362240150242
Trimmed Mean ( 23 / 24 )252.5380769230770.836648997118086301.844713605069
Trimmed Mean ( 24 / 24 )252.4445833333330.848203339709983297.622717943611
Median249.515
Midrange260.69
Midmean - Weighted Average at Xnp253.193513513514
Midmean - Weighted Average at X(n+1)p253.330277777778
Midmean - Empirical Distribution Function253.193513513514
Midmean - Empirical Distribution Function - Averaging253.330277777778
Midmean - Empirical Distribution Function - Interpolation253.330277777778
Midmean - Closest Observation253.193513513514
Midmean - True Basic - Statistics Graphics Toolkit253.330277777778
Midmean - MS Excel (old versions)253.453947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 256.0075 & 1.15325540711395 & 221.98681958983 \tabularnewline
Geometric Mean & 255.826376141524 &  &  \tabularnewline
Harmonic Mean & 255.648602569637 &  &  \tabularnewline
Quadratic Mean & 256.191861534801 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 256.007222222222 & 1.15318965057639 & 221.999236720747 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 256.008055555556 & 1.15090978571511 & 222.439724410272 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 256.008055555556 & 1.15076231178949 & 222.468230782994 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 255.986388888889 & 1.14514010708279 & 223.541545096177 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 255.988472222222 & 1.14489146795016 & 223.591911887116 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 255.977638888889 & 1.14210828121478 & 224.127294319784 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 255.870694444444 & 1.10607177443555 & 231.332812533816 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 255.865138888889 & 1.10074633226335 & 232.446960202702 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 255.613888888889 & 1.04728562549085 & 244.072755958133 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 255.470833333333 & 0.983688957536867 & 259.706923998645 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 255.075138888889 & 0.897647900051552 & 284.159455922796 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 255.078472222222 & 0.897269847468062 & 284.282897661176 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 255.051388888889 & 0.889921843941236 & 286.599762243538 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 254.981388888889 & 0.875560949312327 & 291.220604446959 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 254.556388888889 & 0.802819130661061 & 317.078130262393 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 254.5075 & 0.786649427628013 & 323.533572975979 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 254.505138888889 & 0.777371780737701 & 327.391790125661 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 254.447638888889 & 0.766462962656538 & 331.976431068477 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 254.450277777778 & 0.766164970881926 & 332.108994078498 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 254.433611111111 & 0.763599890559257 & 333.20278624551 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 254.349027777778 & 0.745996884780231 & 340.951863160539 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 254.034305555556 & 0.697860771747832 & 364.018606346524 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 253.254861111111 & 0.584049124654767 & 433.619109113143 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 253.318194444444 & 0.576700056239417 & 439.254672691205 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 255.873714285714 & 1.14398935428144 & 223.667915551919 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 255.732352941176 & 1.13230727249047 & 225.850667176853 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 255.58196969697 & 1.11903605329049 & 228.394758994081 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 255.4221875 & 1.10243042893075 & 231.690073855939 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 255.258387096774 & 1.08375888736435 & 235.530605629035 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 255.083166666667 & 1.06043996017394 & 240.544657167414 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 254.898103448276 & 1.03205946078932 & 246.980056026354 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 254.719464285714 & 1.00638937430007 & 253.102298961442 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 254.528518518519 & 0.975127127385839 & 261.020857045449 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 254.361538461538 & 0.949302211963697 & 267.945797719542 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 254.2018 & 0.931119917746629 & 273.006510928458 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 254.082708333333 & 0.926624351978391 & 274.202494021287 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 253.952826086957 & 0.919147718177164 & 276.291635245084 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 253.814545454545 & 0.909306443794244 & 279.129821620376 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 253.671666666667 & 0.897906515797224 & 282.514562711954 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 253.5655 & 0.897658846024565 & 282.474239654584 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 253.453947368421 & 0.8978483478217 & 282.290375633406 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 253.330277777778 & 0.896706361850252 & 282.511966632041 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 253.198823529412 & 0.894132065509038 & 283.17832823193 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 253.050625 & 0.886528197782625 & 285.440018301648 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 252.884666666667 & 0.872227131303754 & 289.92983317163 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 252.705357142857 & 0.852690805059197 & 296.362240150242 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 252.538076923077 & 0.836648997118086 & 301.844713605069 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 252.444583333333 & 0.848203339709983 & 297.622717943611 \tabularnewline
Median & 249.515 &  &  \tabularnewline
Midrange & 260.69 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 253.193513513514 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 253.330277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 253.193513513514 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 253.330277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 253.330277777778 &  &  \tabularnewline
Midmean - Closest Observation & 253.193513513514 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 253.330277777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 253.453947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181094&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]256.0075[/C][C]1.15325540711395[/C][C]221.98681958983[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]255.826376141524[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]255.648602569637[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]256.191861534801[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]256.007222222222[/C][C]1.15318965057639[/C][C]221.999236720747[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]256.008055555556[/C][C]1.15090978571511[/C][C]222.439724410272[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]256.008055555556[/C][C]1.15076231178949[/C][C]222.468230782994[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]255.986388888889[/C][C]1.14514010708279[/C][C]223.541545096177[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]255.988472222222[/C][C]1.14489146795016[/C][C]223.591911887116[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]255.977638888889[/C][C]1.14210828121478[/C][C]224.127294319784[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]255.870694444444[/C][C]1.10607177443555[/C][C]231.332812533816[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]255.865138888889[/C][C]1.10074633226335[/C][C]232.446960202702[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]255.613888888889[/C][C]1.04728562549085[/C][C]244.072755958133[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]255.470833333333[/C][C]0.983688957536867[/C][C]259.706923998645[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]255.075138888889[/C][C]0.897647900051552[/C][C]284.159455922796[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]255.078472222222[/C][C]0.897269847468062[/C][C]284.282897661176[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]255.051388888889[/C][C]0.889921843941236[/C][C]286.599762243538[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]254.981388888889[/C][C]0.875560949312327[/C][C]291.220604446959[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]254.556388888889[/C][C]0.802819130661061[/C][C]317.078130262393[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]254.5075[/C][C]0.786649427628013[/C][C]323.533572975979[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]254.505138888889[/C][C]0.777371780737701[/C][C]327.391790125661[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]254.447638888889[/C][C]0.766462962656538[/C][C]331.976431068477[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]254.450277777778[/C][C]0.766164970881926[/C][C]332.108994078498[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]254.433611111111[/C][C]0.763599890559257[/C][C]333.20278624551[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]254.349027777778[/C][C]0.745996884780231[/C][C]340.951863160539[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]254.034305555556[/C][C]0.697860771747832[/C][C]364.018606346524[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]253.254861111111[/C][C]0.584049124654767[/C][C]433.619109113143[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]253.318194444444[/C][C]0.576700056239417[/C][C]439.254672691205[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]255.873714285714[/C][C]1.14398935428144[/C][C]223.667915551919[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]255.732352941176[/C][C]1.13230727249047[/C][C]225.850667176853[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]255.58196969697[/C][C]1.11903605329049[/C][C]228.394758994081[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]255.4221875[/C][C]1.10243042893075[/C][C]231.690073855939[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]255.258387096774[/C][C]1.08375888736435[/C][C]235.530605629035[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]255.083166666667[/C][C]1.06043996017394[/C][C]240.544657167414[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]254.898103448276[/C][C]1.03205946078932[/C][C]246.980056026354[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]254.719464285714[/C][C]1.00638937430007[/C][C]253.102298961442[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]254.528518518519[/C][C]0.975127127385839[/C][C]261.020857045449[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]254.361538461538[/C][C]0.949302211963697[/C][C]267.945797719542[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]254.2018[/C][C]0.931119917746629[/C][C]273.006510928458[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]254.082708333333[/C][C]0.926624351978391[/C][C]274.202494021287[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]253.952826086957[/C][C]0.919147718177164[/C][C]276.291635245084[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]253.814545454545[/C][C]0.909306443794244[/C][C]279.129821620376[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]253.671666666667[/C][C]0.897906515797224[/C][C]282.514562711954[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]253.5655[/C][C]0.897658846024565[/C][C]282.474239654584[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]253.453947368421[/C][C]0.8978483478217[/C][C]282.290375633406[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]253.330277777778[/C][C]0.896706361850252[/C][C]282.511966632041[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]253.198823529412[/C][C]0.894132065509038[/C][C]283.17832823193[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]253.050625[/C][C]0.886528197782625[/C][C]285.440018301648[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]252.884666666667[/C][C]0.872227131303754[/C][C]289.92983317163[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]252.705357142857[/C][C]0.852690805059197[/C][C]296.362240150242[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]252.538076923077[/C][C]0.836648997118086[/C][C]301.844713605069[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]252.444583333333[/C][C]0.848203339709983[/C][C]297.622717943611[/C][/ROW]
[ROW][C]Median[/C][C]249.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]260.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]253.193513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]253.330277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]253.193513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]253.330277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]253.330277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]253.193513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]253.330277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]253.453947368421[/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=181094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181094&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 Mean256.00751.15325540711395221.98681958983
Geometric Mean255.826376141524
Harmonic Mean255.648602569637
Quadratic Mean256.191861534801
Winsorized Mean ( 1 / 24 )256.0072222222221.15318965057639221.999236720747
Winsorized Mean ( 2 / 24 )256.0080555555561.15090978571511222.439724410272
Winsorized Mean ( 3 / 24 )256.0080555555561.15076231178949222.468230782994
Winsorized Mean ( 4 / 24 )255.9863888888891.14514010708279223.541545096177
Winsorized Mean ( 5 / 24 )255.9884722222221.14489146795016223.591911887116
Winsorized Mean ( 6 / 24 )255.9776388888891.14210828121478224.127294319784
Winsorized Mean ( 7 / 24 )255.8706944444441.10607177443555231.332812533816
Winsorized Mean ( 8 / 24 )255.8651388888891.10074633226335232.446960202702
Winsorized Mean ( 9 / 24 )255.6138888888891.04728562549085244.072755958133
Winsorized Mean ( 10 / 24 )255.4708333333330.983688957536867259.706923998645
Winsorized Mean ( 11 / 24 )255.0751388888890.897647900051552284.159455922796
Winsorized Mean ( 12 / 24 )255.0784722222220.897269847468062284.282897661176
Winsorized Mean ( 13 / 24 )255.0513888888890.889921843941236286.599762243538
Winsorized Mean ( 14 / 24 )254.9813888888890.875560949312327291.220604446959
Winsorized Mean ( 15 / 24 )254.5563888888890.802819130661061317.078130262393
Winsorized Mean ( 16 / 24 )254.50750.786649427628013323.533572975979
Winsorized Mean ( 17 / 24 )254.5051388888890.777371780737701327.391790125661
Winsorized Mean ( 18 / 24 )254.4476388888890.766462962656538331.976431068477
Winsorized Mean ( 19 / 24 )254.4502777777780.766164970881926332.108994078498
Winsorized Mean ( 20 / 24 )254.4336111111110.763599890559257333.20278624551
Winsorized Mean ( 21 / 24 )254.3490277777780.745996884780231340.951863160539
Winsorized Mean ( 22 / 24 )254.0343055555560.697860771747832364.018606346524
Winsorized Mean ( 23 / 24 )253.2548611111110.584049124654767433.619109113143
Winsorized Mean ( 24 / 24 )253.3181944444440.576700056239417439.254672691205
Trimmed Mean ( 1 / 24 )255.8737142857141.14398935428144223.667915551919
Trimmed Mean ( 2 / 24 )255.7323529411761.13230727249047225.850667176853
Trimmed Mean ( 3 / 24 )255.581969696971.11903605329049228.394758994081
Trimmed Mean ( 4 / 24 )255.42218751.10243042893075231.690073855939
Trimmed Mean ( 5 / 24 )255.2583870967741.08375888736435235.530605629035
Trimmed Mean ( 6 / 24 )255.0831666666671.06043996017394240.544657167414
Trimmed Mean ( 7 / 24 )254.8981034482761.03205946078932246.980056026354
Trimmed Mean ( 8 / 24 )254.7194642857141.00638937430007253.102298961442
Trimmed Mean ( 9 / 24 )254.5285185185190.975127127385839261.020857045449
Trimmed Mean ( 10 / 24 )254.3615384615380.949302211963697267.945797719542
Trimmed Mean ( 11 / 24 )254.20180.931119917746629273.006510928458
Trimmed Mean ( 12 / 24 )254.0827083333330.926624351978391274.202494021287
Trimmed Mean ( 13 / 24 )253.9528260869570.919147718177164276.291635245084
Trimmed Mean ( 14 / 24 )253.8145454545450.909306443794244279.129821620376
Trimmed Mean ( 15 / 24 )253.6716666666670.897906515797224282.514562711954
Trimmed Mean ( 16 / 24 )253.56550.897658846024565282.474239654584
Trimmed Mean ( 17 / 24 )253.4539473684210.8978483478217282.290375633406
Trimmed Mean ( 18 / 24 )253.3302777777780.896706361850252282.511966632041
Trimmed Mean ( 19 / 24 )253.1988235294120.894132065509038283.17832823193
Trimmed Mean ( 20 / 24 )253.0506250.886528197782625285.440018301648
Trimmed Mean ( 21 / 24 )252.8846666666670.872227131303754289.92983317163
Trimmed Mean ( 22 / 24 )252.7053571428570.852690805059197296.362240150242
Trimmed Mean ( 23 / 24 )252.5380769230770.836648997118086301.844713605069
Trimmed Mean ( 24 / 24 )252.4445833333330.848203339709983297.622717943611
Median249.515
Midrange260.69
Midmean - Weighted Average at Xnp253.193513513514
Midmean - Weighted Average at X(n+1)p253.330277777778
Midmean - Empirical Distribution Function253.193513513514
Midmean - Empirical Distribution Function - Averaging253.330277777778
Midmean - Empirical Distribution Function - Interpolation253.330277777778
Midmean - Closest Observation253.193513513514
Midmean - True Basic - Statistics Graphics Toolkit253.330277777778
Midmean - MS Excel (old versions)253.453947368421
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')