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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 16:03:45 +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/2014/Oct/13/t1413212678yhhajfwdisvmmgo.htm/, Retrieved Fri, 10 May 2024 07:38:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240773, Retrieved Fri, 10 May 2024 07:38:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 15:03:45] [25af208440423f5cc2d7fa35cacd4ca5] [Current]
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Dataseries X:
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27
2513,17
2466,92
2502,66
2539,91
2482,6
2626,15
2656,32
2446,66
2467,38
2462,32
2504,58
2579,39
2649,24
2636,87
2613,94
2634,01
2711,94
2646,43
2717,79
2701,54
2572,98
2488,92
2204,91
2123,99
2149,1
2036,71
2048,32
2159,56
2267,79
2313,55
2247,3
2134,43
2114
2236,94
2345,39
2422,4
2385,96
2378,17
2457,13
2527,67
2530,03
2604,92
2596,8
2713,2
2574,82
2611,98
2768,46
2785,61
2859,27
2880,53
2824,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240773&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240773&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2535.9054166666755.22011350444345.9235821103959
Geometric Mean2496.69912551939
Harmonic Mean2460.21029315978
Quadratic Mean2578.23850888467
Winsorized Mean ( 1 / 24 )2537.6802777777854.759558831765846.3422337929005
Winsorized Mean ( 2 / 24 )2537.9138888888954.097243969612846.9139220902727
Winsorized Mean ( 3 / 24 )2534.6443055555653.010627084333547.8138902511612
Winsorized Mean ( 4 / 24 )2534.3326388888951.804319800947648.9212607872622
Winsorized Mean ( 5 / 24 )2530.0972222222247.01056427081453.8197586322741
Winsorized Mean ( 6 / 24 )2493.2480555555637.045164927010967.3029276686427
Winsorized Mean ( 7 / 24 )2492.5363888888936.630296182366468.0457612594676
Winsorized Mean ( 8 / 24 )2486.0197222222234.839483344130271.3563888897644
Winsorized Mean ( 9 / 24 )2476.2559722222232.883755740108375.3033197239673
Winsorized Mean ( 10 / 24 )2475.9156944444431.907203590343877.5973891737018
Winsorized Mean ( 11 / 24 )2477.1990277777829.86695496549382.9411311142976
Winsorized Mean ( 12 / 24 )2472.3823611111128.549033426115486.6012633145569
Winsorized Mean ( 13 / 24 )2471.1708333333327.753035783804689.0414602778482
Winsorized Mean ( 14 / 24 )2464.1708333333325.837870319261595.3705085939823
Winsorized Mean ( 15 / 24 )2465.3937525.333477517224397.3176204618483
Winsorized Mean ( 16 / 24 )2473.6159722222223.8792382195168103.588562980225
Winsorized Mean ( 17 / 24 )2472.8344444444423.2646921941985106.291302880899
Winsorized Mean ( 18 / 24 )2469.5369444444420.4606924197911120.696645733051
Winsorized Mean ( 19 / 24 )2470.402519.7856480265518124.85830621695
Winsorized Mean ( 20 / 24 )2475.3136111111118.7910541652005131.728299506219
Winsorized Mean ( 21 / 24 )2479.9977777777817.284212836834143.48340888818
Winsorized Mean ( 22 / 24 )2485.2777777777816.2457910068748152.97979499589
Winsorized Mean ( 23 / 24 )2492.9380555555614.4297334452855172.76397135181
Winsorized Mean ( 24 / 24 )2499.7947222222212.3536597790418202.352563283568
Trimmed Mean ( 1 / 24 )2529.3928571428652.055577389117548.5902372811187
Trimmed Mean ( 2 / 24 )2520.6179411764748.772089726895151.6815653233429
Trimmed Mean ( 3 / 24 )2511.1837878787945.186333708563855.5739663251959
Trimmed Mean ( 4 / 24 )2502.3860937541.285471850801460.6117837963242
Trimmed Mean ( 5 / 24 )2493.1112903225836.855420979168967.6457146353508
Trimmed Mean ( 6 / 24 )2484.2346666666733.109497922525775.0308770154
Trimmed Mean ( 7 / 24 )2482.3698275862131.866006940560377.9002475025056
Trimmed Mean ( 8 / 24 )2480.502530.448441503896981.465663839725
Trimmed Mean ( 9 / 24 )2479.5829629629629.177501000158284.9827050969692
Trimmed Mean ( 10 / 24 )2480.0948076923128.092408321751688.2834529274588
Trimmed Mean ( 11 / 24 )2480.696626.966530834986791.9916846249099
Trimmed Mean ( 12 / 24 )2481.1735416666726.033144116617995.3082551439819
Trimmed Mean ( 13 / 24 )2482.320217391325.143304806031398.7268871988479
Trimmed Mean ( 14 / 24 )2483.7236363636424.1738147127961102.744381301513
Trimmed Mean ( 15 / 24 )2486.1178571428623.3470200480939106.485446623233
Trimmed Mean ( 16 / 24 )2488.6047522.3632568553394111.28096261193
Trimmed Mean ( 17 / 24 )2490.3797368421121.4287942989057116.21651232936
Trimmed Mean ( 18 / 24 )2492.4438888888920.3030739141035122.761897997993
Trimmed Mean ( 19 / 24 )2495.1388235294119.5083535549539127.901045903272
Trimmed Mean ( 20 / 24 )2498.06812518.5557212366536134.625223840154
Trimmed Mean ( 21 / 24 )2500.7986666666717.4953962991078142.940384082308
Trimmed Mean ( 22 / 24 )2503.3457142857116.4505922235314152.173592310242
Trimmed Mean ( 23 / 24 )2505.6215.2598099494164164.197326723314
Trimmed Mean ( 24 / 24 )2507.2741666666714.1864758510088176.736928395671
Median2503.62
Midrange2763.845
Midmean - Weighted Average at Xnp2484.6727027027
Midmean - Weighted Average at X(n+1)p2492.44388888889
Midmean - Empirical Distribution Function2484.6727027027
Midmean - Empirical Distribution Function - Averaging2492.44388888889
Midmean - Empirical Distribution Function - Interpolation2492.44388888889
Midmean - Closest Observation2484.6727027027
Midmean - True Basic - Statistics Graphics Toolkit2492.44388888889
Midmean - MS Excel (old versions)2490.3797368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2535.90541666667 & 55.220113504443 & 45.9235821103959 \tabularnewline
Geometric Mean & 2496.69912551939 &  &  \tabularnewline
Harmonic Mean & 2460.21029315978 &  &  \tabularnewline
Quadratic Mean & 2578.23850888467 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2537.68027777778 & 54.7595588317658 & 46.3422337929005 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2537.91388888889 & 54.0972439696128 & 46.9139220902727 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2534.64430555556 & 53.0106270843335 & 47.8138902511612 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2534.33263888889 & 51.8043198009476 & 48.9212607872622 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2530.09722222222 & 47.010564270814 & 53.8197586322741 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2493.24805555556 & 37.0451649270109 & 67.3029276686427 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2492.53638888889 & 36.6302961823664 & 68.0457612594676 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2486.01972222222 & 34.8394833441302 & 71.3563888897644 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2476.25597222222 & 32.8837557401083 & 75.3033197239673 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2475.91569444444 & 31.9072035903438 & 77.5973891737018 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2477.19902777778 & 29.866954965493 & 82.9411311142976 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2472.38236111111 & 28.5490334261154 & 86.6012633145569 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2471.17083333333 & 27.7530357838046 & 89.0414602778482 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2464.17083333333 & 25.8378703192615 & 95.3705085939823 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2465.39375 & 25.3334775172243 & 97.3176204618483 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2473.61597222222 & 23.8792382195168 & 103.588562980225 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2472.83444444444 & 23.2646921941985 & 106.291302880899 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2469.53694444444 & 20.4606924197911 & 120.696645733051 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2470.4025 & 19.7856480265518 & 124.85830621695 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2475.31361111111 & 18.7910541652005 & 131.728299506219 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2479.99777777778 & 17.284212836834 & 143.48340888818 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2485.27777777778 & 16.2457910068748 & 152.97979499589 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2492.93805555556 & 14.4297334452855 & 172.76397135181 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2499.79472222222 & 12.3536597790418 & 202.352563283568 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2529.39285714286 & 52.0555773891175 & 48.5902372811187 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2520.61794117647 & 48.7720897268951 & 51.6815653233429 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2511.18378787879 & 45.1863337085638 & 55.5739663251959 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2502.38609375 & 41.2854718508014 & 60.6117837963242 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2493.11129032258 & 36.8554209791689 & 67.6457146353508 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2484.23466666667 & 33.1094979225257 & 75.0308770154 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2482.36982758621 & 31.8660069405603 & 77.9002475025056 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2480.5025 & 30.4484415038969 & 81.465663839725 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2479.58296296296 & 29.1775010001582 & 84.9827050969692 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2480.09480769231 & 28.0924083217516 & 88.2834529274588 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2480.6966 & 26.9665308349867 & 91.9916846249099 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2481.17354166667 & 26.0331441166179 & 95.3082551439819 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2482.3202173913 & 25.1433048060313 & 98.7268871988479 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2483.72363636364 & 24.1738147127961 & 102.744381301513 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2486.11785714286 & 23.3470200480939 & 106.485446623233 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2488.60475 & 22.3632568553394 & 111.28096261193 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2490.37973684211 & 21.4287942989057 & 116.21651232936 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2492.44388888889 & 20.3030739141035 & 122.761897997993 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2495.13882352941 & 19.5083535549539 & 127.901045903272 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2498.068125 & 18.5557212366536 & 134.625223840154 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2500.79866666667 & 17.4953962991078 & 142.940384082308 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2503.34571428571 & 16.4505922235314 & 152.173592310242 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2505.62 & 15.2598099494164 & 164.197326723314 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2507.27416666667 & 14.1864758510088 & 176.736928395671 \tabularnewline
Median & 2503.62 &  &  \tabularnewline
Midrange & 2763.845 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2484.6727027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2492.44388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2484.6727027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2492.44388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2492.44388888889 &  &  \tabularnewline
Midmean - Closest Observation & 2484.6727027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2492.44388888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2490.3797368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240773&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]2535.90541666667[/C][C]55.220113504443[/C][C]45.9235821103959[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2496.69912551939[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2460.21029315978[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2578.23850888467[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2537.68027777778[/C][C]54.7595588317658[/C][C]46.3422337929005[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2537.91388888889[/C][C]54.0972439696128[/C][C]46.9139220902727[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2534.64430555556[/C][C]53.0106270843335[/C][C]47.8138902511612[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2534.33263888889[/C][C]51.8043198009476[/C][C]48.9212607872622[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2530.09722222222[/C][C]47.010564270814[/C][C]53.8197586322741[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2493.24805555556[/C][C]37.0451649270109[/C][C]67.3029276686427[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2492.53638888889[/C][C]36.6302961823664[/C][C]68.0457612594676[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2486.01972222222[/C][C]34.8394833441302[/C][C]71.3563888897644[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2476.25597222222[/C][C]32.8837557401083[/C][C]75.3033197239673[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2475.91569444444[/C][C]31.9072035903438[/C][C]77.5973891737018[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2477.19902777778[/C][C]29.866954965493[/C][C]82.9411311142976[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2472.38236111111[/C][C]28.5490334261154[/C][C]86.6012633145569[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2471.17083333333[/C][C]27.7530357838046[/C][C]89.0414602778482[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2464.17083333333[/C][C]25.8378703192615[/C][C]95.3705085939823[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2465.39375[/C][C]25.3334775172243[/C][C]97.3176204618483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2473.61597222222[/C][C]23.8792382195168[/C][C]103.588562980225[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2472.83444444444[/C][C]23.2646921941985[/C][C]106.291302880899[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2469.53694444444[/C][C]20.4606924197911[/C][C]120.696645733051[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2470.4025[/C][C]19.7856480265518[/C][C]124.85830621695[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2475.31361111111[/C][C]18.7910541652005[/C][C]131.728299506219[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2479.99777777778[/C][C]17.284212836834[/C][C]143.48340888818[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2485.27777777778[/C][C]16.2457910068748[/C][C]152.97979499589[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2492.93805555556[/C][C]14.4297334452855[/C][C]172.76397135181[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2499.79472222222[/C][C]12.3536597790418[/C][C]202.352563283568[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2529.39285714286[/C][C]52.0555773891175[/C][C]48.5902372811187[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2520.61794117647[/C][C]48.7720897268951[/C][C]51.6815653233429[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2511.18378787879[/C][C]45.1863337085638[/C][C]55.5739663251959[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2502.38609375[/C][C]41.2854718508014[/C][C]60.6117837963242[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2493.11129032258[/C][C]36.8554209791689[/C][C]67.6457146353508[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2484.23466666667[/C][C]33.1094979225257[/C][C]75.0308770154[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2482.36982758621[/C][C]31.8660069405603[/C][C]77.9002475025056[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2480.5025[/C][C]30.4484415038969[/C][C]81.465663839725[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2479.58296296296[/C][C]29.1775010001582[/C][C]84.9827050969692[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2480.09480769231[/C][C]28.0924083217516[/C][C]88.2834529274588[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2480.6966[/C][C]26.9665308349867[/C][C]91.9916846249099[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2481.17354166667[/C][C]26.0331441166179[/C][C]95.3082551439819[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2482.3202173913[/C][C]25.1433048060313[/C][C]98.7268871988479[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2483.72363636364[/C][C]24.1738147127961[/C][C]102.744381301513[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2486.11785714286[/C][C]23.3470200480939[/C][C]106.485446623233[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2488.60475[/C][C]22.3632568553394[/C][C]111.28096261193[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2490.37973684211[/C][C]21.4287942989057[/C][C]116.21651232936[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2492.44388888889[/C][C]20.3030739141035[/C][C]122.761897997993[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2495.13882352941[/C][C]19.5083535549539[/C][C]127.901045903272[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2498.068125[/C][C]18.5557212366536[/C][C]134.625223840154[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2500.79866666667[/C][C]17.4953962991078[/C][C]142.940384082308[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2503.34571428571[/C][C]16.4505922235314[/C][C]152.173592310242[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2505.62[/C][C]15.2598099494164[/C][C]164.197326723314[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2507.27416666667[/C][C]14.1864758510088[/C][C]176.736928395671[/C][/ROW]
[ROW][C]Median[/C][C]2503.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2763.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2484.6727027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2492.44388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2484.6727027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2492.44388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2492.44388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2484.6727027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2492.44388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2490.3797368421[/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=240773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240773&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 Mean2535.9054166666755.22011350444345.9235821103959
Geometric Mean2496.69912551939
Harmonic Mean2460.21029315978
Quadratic Mean2578.23850888467
Winsorized Mean ( 1 / 24 )2537.6802777777854.759558831765846.3422337929005
Winsorized Mean ( 2 / 24 )2537.9138888888954.097243969612846.9139220902727
Winsorized Mean ( 3 / 24 )2534.6443055555653.010627084333547.8138902511612
Winsorized Mean ( 4 / 24 )2534.3326388888951.804319800947648.9212607872622
Winsorized Mean ( 5 / 24 )2530.0972222222247.01056427081453.8197586322741
Winsorized Mean ( 6 / 24 )2493.2480555555637.045164927010967.3029276686427
Winsorized Mean ( 7 / 24 )2492.5363888888936.630296182366468.0457612594676
Winsorized Mean ( 8 / 24 )2486.0197222222234.839483344130271.3563888897644
Winsorized Mean ( 9 / 24 )2476.2559722222232.883755740108375.3033197239673
Winsorized Mean ( 10 / 24 )2475.9156944444431.907203590343877.5973891737018
Winsorized Mean ( 11 / 24 )2477.1990277777829.86695496549382.9411311142976
Winsorized Mean ( 12 / 24 )2472.3823611111128.549033426115486.6012633145569
Winsorized Mean ( 13 / 24 )2471.1708333333327.753035783804689.0414602778482
Winsorized Mean ( 14 / 24 )2464.1708333333325.837870319261595.3705085939823
Winsorized Mean ( 15 / 24 )2465.3937525.333477517224397.3176204618483
Winsorized Mean ( 16 / 24 )2473.6159722222223.8792382195168103.588562980225
Winsorized Mean ( 17 / 24 )2472.8344444444423.2646921941985106.291302880899
Winsorized Mean ( 18 / 24 )2469.5369444444420.4606924197911120.696645733051
Winsorized Mean ( 19 / 24 )2470.402519.7856480265518124.85830621695
Winsorized Mean ( 20 / 24 )2475.3136111111118.7910541652005131.728299506219
Winsorized Mean ( 21 / 24 )2479.9977777777817.284212836834143.48340888818
Winsorized Mean ( 22 / 24 )2485.2777777777816.2457910068748152.97979499589
Winsorized Mean ( 23 / 24 )2492.9380555555614.4297334452855172.76397135181
Winsorized Mean ( 24 / 24 )2499.7947222222212.3536597790418202.352563283568
Trimmed Mean ( 1 / 24 )2529.3928571428652.055577389117548.5902372811187
Trimmed Mean ( 2 / 24 )2520.6179411764748.772089726895151.6815653233429
Trimmed Mean ( 3 / 24 )2511.1837878787945.186333708563855.5739663251959
Trimmed Mean ( 4 / 24 )2502.3860937541.285471850801460.6117837963242
Trimmed Mean ( 5 / 24 )2493.1112903225836.855420979168967.6457146353508
Trimmed Mean ( 6 / 24 )2484.2346666666733.109497922525775.0308770154
Trimmed Mean ( 7 / 24 )2482.3698275862131.866006940560377.9002475025056
Trimmed Mean ( 8 / 24 )2480.502530.448441503896981.465663839725
Trimmed Mean ( 9 / 24 )2479.5829629629629.177501000158284.9827050969692
Trimmed Mean ( 10 / 24 )2480.0948076923128.092408321751688.2834529274588
Trimmed Mean ( 11 / 24 )2480.696626.966530834986791.9916846249099
Trimmed Mean ( 12 / 24 )2481.1735416666726.033144116617995.3082551439819
Trimmed Mean ( 13 / 24 )2482.320217391325.143304806031398.7268871988479
Trimmed Mean ( 14 / 24 )2483.7236363636424.1738147127961102.744381301513
Trimmed Mean ( 15 / 24 )2486.1178571428623.3470200480939106.485446623233
Trimmed Mean ( 16 / 24 )2488.6047522.3632568553394111.28096261193
Trimmed Mean ( 17 / 24 )2490.3797368421121.4287942989057116.21651232936
Trimmed Mean ( 18 / 24 )2492.4438888888920.3030739141035122.761897997993
Trimmed Mean ( 19 / 24 )2495.1388235294119.5083535549539127.901045903272
Trimmed Mean ( 20 / 24 )2498.06812518.5557212366536134.625223840154
Trimmed Mean ( 21 / 24 )2500.7986666666717.4953962991078142.940384082308
Trimmed Mean ( 22 / 24 )2503.3457142857116.4505922235314152.173592310242
Trimmed Mean ( 23 / 24 )2505.6215.2598099494164164.197326723314
Trimmed Mean ( 24 / 24 )2507.2741666666714.1864758510088176.736928395671
Median2503.62
Midrange2763.845
Midmean - Weighted Average at Xnp2484.6727027027
Midmean - Weighted Average at X(n+1)p2492.44388888889
Midmean - Empirical Distribution Function2484.6727027027
Midmean - Empirical Distribution Function - Averaging2492.44388888889
Midmean - Empirical Distribution Function - Interpolation2492.44388888889
Midmean - Closest Observation2484.6727027027
Midmean - True Basic - Statistics Graphics Toolkit2492.44388888889
Midmean - MS Excel (old versions)2490.3797368421
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')