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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 25 Nov 2010 20:52:57 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t1290718422vwzlsd0dm52y18y.htm/, Retrieved Fri, 19 Apr 2024 22:03:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101520, Retrieved Fri, 19 Apr 2024 22:03:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
-496,9
112,3
-85,1
2,2
358,6
-158,3
441,9
-488,9
239,2
-154,9
-235,7
139,1
-552
130,3
97,2
-217,1
-213,5
115,1
190,6
-141,7
34,9
-347,3
-862,5
56,9
-1248,1
175,4
-425,1
-602,2
-121,9
-316,4
101,4
-1080,8
-644
-533
-735,4
-578,2
-1369,7
-217,1
-242,6
221,1
167,8
541,2
186,5
-711,8
127,7
-464,2
239,1
417,7
-77
486,6
261,4
101,9
-97,1
821
994,7
-73,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101520&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101520&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-120.17857142857162.2111156766146-1.93178614659931
Geometric MeanNaN
Harmonic Mean113.134169584326
Quadratic Mean476.765297904235
Winsorized Mean ( 1 / 18 )-121.10892857142960.50116432693-2.00176194819975
Winsorized Mean ( 2 / 18 )-125.12678571428656.0526880787274-2.23230660300434
Winsorized Mean ( 3 / 18 )-116.35714285714352.082089853307-2.23411048183495
Winsorized Mean ( 4 / 18 )-110.47142857142949.1849488456571-2.24604134321841
Winsorized Mean ( 5 / 18 )-110.52548.2672690481203-2.28985401866866
Winsorized Mean ( 6 / 18 )-109.59285714285745.4424170275539-2.41168635630463
Winsorized Mean ( 7 / 18 )-116.51785714285742.2041613405831-2.76081441833592
Winsorized Mean ( 8 / 18 )-116.26071428571440.9857341889066-2.83661416798975
Winsorized Mean ( 9 / 18 )-112.06607142857140.132006146986-2.79243631674236
Winsorized Mean ( 10 / 18 )-111.887538.9548253235753-2.87223724071704
Winsorized Mean ( 11 / 18 )-110.787536.6647308379433-3.02163680103575
Winsorized Mean ( 12 / 18 )-109.95178571428636.2064433340678-3.03680161842433
Winsorized Mean ( 13 / 18 )-106.79464285714334.7423276048148-3.07390581517464
Winsorized Mean ( 14 / 18 )-98.919642857142932.6584599945934-3.02891327005373
Winsorized Mean ( 15 / 18 )-85.767857142857127.8420995470751-3.08050967915842
Winsorized Mean ( 16 / 18 )-79.453571428571425.9865076085681-3.05749324323883
Winsorized Mean ( 17 / 18 )-57.839285714285722.3125226441111-2.59223426399754
Winsorized Mean ( 18 / 18 )-59.671428571428621.3721310392225-2.79202052719583
Trimmed Mean ( 1 / 18 )-117.68518518518556.43649402199-2.08526747142248
Trimmed Mean ( 2 / 18 )-113.99807692307751.2145782008353-2.22589116083392
Trimmed Mean ( 3 / 18 )-107.76647.7668057922218-2.25608554335338
Trimmed Mean ( 4 / 18 )-104.42545.4813490045041-2.29599610138342
Trimmed Mean ( 5 / 18 )-102.58478260869643.7929889793208-2.34249328487573
Trimmed Mean ( 6 / 18 )-100.56363636363641.9395039107045-2.39782608248661
Trimmed Mean ( 7 / 18 )-98.557142857142940.4788195634504-2.43478302776727
Trimmed Mean ( 8 / 18 )-94.96539.5310294465318-2.40229008274237
Trimmed Mean ( 9 / 18 )-91.042105263157938.5738698752026-2.36020149281638
Trimmed Mean ( 10 / 18 )-87.408333333333337.4811818127359-2.33205915891458
Trimmed Mean ( 11 / 18 )-83.376470588235336.2676609037585-2.29892053996774
Trimmed Mean ( 12 / 18 )-79.01562535.2002013572684-2.24474923305188
Trimmed Mean ( 13 / 18 )-74.203333333333333.7322665146379-2.19977312526964
Trimmed Mean ( 14 / 18 )-69.189285714285732.0143834817501-2.16119375697887
Trimmed Mean ( 15 / 18 )-64.615384615384630.165180993634-2.14205194489040
Trimmed Mean ( 16 / 18 )-61.32529.1730657059069-2.10211023476984
Trimmed Mean ( 17 / 18 )-58.440909090909128.2161958489403-2.071183139066
Trimmed Mean ( 18 / 18 )-58.5428.0628902739243-2.08602889540550
Median-81.05
Midrange-187.5
Midmean - Weighted Average at Xnp-82.8103448275862
Midmean - Weighted Average at X(n+1)p-69.1892857142857
Midmean - Empirical Distribution Function-82.8103448275862
Midmean - Empirical Distribution Function - Averaging-69.1892857142857
Midmean - Empirical Distribution Function - Interpolation-69.1892857142857
Midmean - Closest Observation-82.8103448275862
Midmean - True Basic - Statistics Graphics Toolkit-69.1892857142857
Midmean - MS Excel (old versions)-74.2033333333333
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -120.178571428571 & 62.2111156766146 & -1.93178614659931 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 113.134169584326 &  &  \tabularnewline
Quadratic Mean & 476.765297904235 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & -121.108928571429 & 60.50116432693 & -2.00176194819975 \tabularnewline
Winsorized Mean ( 2 / 18 ) & -125.126785714286 & 56.0526880787274 & -2.23230660300434 \tabularnewline
Winsorized Mean ( 3 / 18 ) & -116.357142857143 & 52.082089853307 & -2.23411048183495 \tabularnewline
Winsorized Mean ( 4 / 18 ) & -110.471428571429 & 49.1849488456571 & -2.24604134321841 \tabularnewline
Winsorized Mean ( 5 / 18 ) & -110.525 & 48.2672690481203 & -2.28985401866866 \tabularnewline
Winsorized Mean ( 6 / 18 ) & -109.592857142857 & 45.4424170275539 & -2.41168635630463 \tabularnewline
Winsorized Mean ( 7 / 18 ) & -116.517857142857 & 42.2041613405831 & -2.76081441833592 \tabularnewline
Winsorized Mean ( 8 / 18 ) & -116.260714285714 & 40.9857341889066 & -2.83661416798975 \tabularnewline
Winsorized Mean ( 9 / 18 ) & -112.066071428571 & 40.132006146986 & -2.79243631674236 \tabularnewline
Winsorized Mean ( 10 / 18 ) & -111.8875 & 38.9548253235753 & -2.87223724071704 \tabularnewline
Winsorized Mean ( 11 / 18 ) & -110.7875 & 36.6647308379433 & -3.02163680103575 \tabularnewline
Winsorized Mean ( 12 / 18 ) & -109.951785714286 & 36.2064433340678 & -3.03680161842433 \tabularnewline
Winsorized Mean ( 13 / 18 ) & -106.794642857143 & 34.7423276048148 & -3.07390581517464 \tabularnewline
Winsorized Mean ( 14 / 18 ) & -98.9196428571429 & 32.6584599945934 & -3.02891327005373 \tabularnewline
Winsorized Mean ( 15 / 18 ) & -85.7678571428571 & 27.8420995470751 & -3.08050967915842 \tabularnewline
Winsorized Mean ( 16 / 18 ) & -79.4535714285714 & 25.9865076085681 & -3.05749324323883 \tabularnewline
Winsorized Mean ( 17 / 18 ) & -57.8392857142857 & 22.3125226441111 & -2.59223426399754 \tabularnewline
Winsorized Mean ( 18 / 18 ) & -59.6714285714286 & 21.3721310392225 & -2.79202052719583 \tabularnewline
Trimmed Mean ( 1 / 18 ) & -117.685185185185 & 56.43649402199 & -2.08526747142248 \tabularnewline
Trimmed Mean ( 2 / 18 ) & -113.998076923077 & 51.2145782008353 & -2.22589116083392 \tabularnewline
Trimmed Mean ( 3 / 18 ) & -107.766 & 47.7668057922218 & -2.25608554335338 \tabularnewline
Trimmed Mean ( 4 / 18 ) & -104.425 & 45.4813490045041 & -2.29599610138342 \tabularnewline
Trimmed Mean ( 5 / 18 ) & -102.584782608696 & 43.7929889793208 & -2.34249328487573 \tabularnewline
Trimmed Mean ( 6 / 18 ) & -100.563636363636 & 41.9395039107045 & -2.39782608248661 \tabularnewline
Trimmed Mean ( 7 / 18 ) & -98.5571428571429 & 40.4788195634504 & -2.43478302776727 \tabularnewline
Trimmed Mean ( 8 / 18 ) & -94.965 & 39.5310294465318 & -2.40229008274237 \tabularnewline
Trimmed Mean ( 9 / 18 ) & -91.0421052631579 & 38.5738698752026 & -2.36020149281638 \tabularnewline
Trimmed Mean ( 10 / 18 ) & -87.4083333333333 & 37.4811818127359 & -2.33205915891458 \tabularnewline
Trimmed Mean ( 11 / 18 ) & -83.3764705882353 & 36.2676609037585 & -2.29892053996774 \tabularnewline
Trimmed Mean ( 12 / 18 ) & -79.015625 & 35.2002013572684 & -2.24474923305188 \tabularnewline
Trimmed Mean ( 13 / 18 ) & -74.2033333333333 & 33.7322665146379 & -2.19977312526964 \tabularnewline
Trimmed Mean ( 14 / 18 ) & -69.1892857142857 & 32.0143834817501 & -2.16119375697887 \tabularnewline
Trimmed Mean ( 15 / 18 ) & -64.6153846153846 & 30.165180993634 & -2.14205194489040 \tabularnewline
Trimmed Mean ( 16 / 18 ) & -61.325 & 29.1730657059069 & -2.10211023476984 \tabularnewline
Trimmed Mean ( 17 / 18 ) & -58.4409090909091 & 28.2161958489403 & -2.071183139066 \tabularnewline
Trimmed Mean ( 18 / 18 ) & -58.54 & 28.0628902739243 & -2.08602889540550 \tabularnewline
Median & -81.05 &  &  \tabularnewline
Midrange & -187.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -82.8103448275862 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -69.1892857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -82.8103448275862 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -69.1892857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -69.1892857142857 &  &  \tabularnewline
Midmean - Closest Observation & -82.8103448275862 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -69.1892857142857 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -74.2033333333333 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101520&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]-120.178571428571[/C][C]62.2111156766146[/C][C]-1.93178614659931[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.134169584326[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]476.765297904235[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]-121.108928571429[/C][C]60.50116432693[/C][C]-2.00176194819975[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]-125.126785714286[/C][C]56.0526880787274[/C][C]-2.23230660300434[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]-116.357142857143[/C][C]52.082089853307[/C][C]-2.23411048183495[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]-110.471428571429[/C][C]49.1849488456571[/C][C]-2.24604134321841[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]-110.525[/C][C]48.2672690481203[/C][C]-2.28985401866866[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]-109.592857142857[/C][C]45.4424170275539[/C][C]-2.41168635630463[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]-116.517857142857[/C][C]42.2041613405831[/C][C]-2.76081441833592[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]-116.260714285714[/C][C]40.9857341889066[/C][C]-2.83661416798975[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]-112.066071428571[/C][C]40.132006146986[/C][C]-2.79243631674236[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]-111.8875[/C][C]38.9548253235753[/C][C]-2.87223724071704[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]-110.7875[/C][C]36.6647308379433[/C][C]-3.02163680103575[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]-109.951785714286[/C][C]36.2064433340678[/C][C]-3.03680161842433[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]-106.794642857143[/C][C]34.7423276048148[/C][C]-3.07390581517464[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]-98.9196428571429[/C][C]32.6584599945934[/C][C]-3.02891327005373[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]-85.7678571428571[/C][C]27.8420995470751[/C][C]-3.08050967915842[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]-79.4535714285714[/C][C]25.9865076085681[/C][C]-3.05749324323883[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]-57.8392857142857[/C][C]22.3125226441111[/C][C]-2.59223426399754[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]-59.6714285714286[/C][C]21.3721310392225[/C][C]-2.79202052719583[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]-117.685185185185[/C][C]56.43649402199[/C][C]-2.08526747142248[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]-113.998076923077[/C][C]51.2145782008353[/C][C]-2.22589116083392[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]-107.766[/C][C]47.7668057922218[/C][C]-2.25608554335338[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]-104.425[/C][C]45.4813490045041[/C][C]-2.29599610138342[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]-102.584782608696[/C][C]43.7929889793208[/C][C]-2.34249328487573[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]-100.563636363636[/C][C]41.9395039107045[/C][C]-2.39782608248661[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]-98.5571428571429[/C][C]40.4788195634504[/C][C]-2.43478302776727[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]-94.965[/C][C]39.5310294465318[/C][C]-2.40229008274237[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]-91.0421052631579[/C][C]38.5738698752026[/C][C]-2.36020149281638[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]-87.4083333333333[/C][C]37.4811818127359[/C][C]-2.33205915891458[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]-83.3764705882353[/C][C]36.2676609037585[/C][C]-2.29892053996774[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]-79.015625[/C][C]35.2002013572684[/C][C]-2.24474923305188[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]-74.2033333333333[/C][C]33.7322665146379[/C][C]-2.19977312526964[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]-69.1892857142857[/C][C]32.0143834817501[/C][C]-2.16119375697887[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]-64.6153846153846[/C][C]30.165180993634[/C][C]-2.14205194489040[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]-61.325[/C][C]29.1730657059069[/C][C]-2.10211023476984[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]-58.4409090909091[/C][C]28.2161958489403[/C][C]-2.071183139066[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]-58.54[/C][C]28.0628902739243[/C][C]-2.08602889540550[/C][/ROW]
[ROW][C]Median[/C][C]-81.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-187.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-82.8103448275862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-69.1892857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-82.8103448275862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-69.1892857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-69.1892857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-82.8103448275862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-69.1892857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-74.2033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101520&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-120.17857142857162.2111156766146-1.93178614659931
Geometric MeanNaN
Harmonic Mean113.134169584326
Quadratic Mean476.765297904235
Winsorized Mean ( 1 / 18 )-121.10892857142960.50116432693-2.00176194819975
Winsorized Mean ( 2 / 18 )-125.12678571428656.0526880787274-2.23230660300434
Winsorized Mean ( 3 / 18 )-116.35714285714352.082089853307-2.23411048183495
Winsorized Mean ( 4 / 18 )-110.47142857142949.1849488456571-2.24604134321841
Winsorized Mean ( 5 / 18 )-110.52548.2672690481203-2.28985401866866
Winsorized Mean ( 6 / 18 )-109.59285714285745.4424170275539-2.41168635630463
Winsorized Mean ( 7 / 18 )-116.51785714285742.2041613405831-2.76081441833592
Winsorized Mean ( 8 / 18 )-116.26071428571440.9857341889066-2.83661416798975
Winsorized Mean ( 9 / 18 )-112.06607142857140.132006146986-2.79243631674236
Winsorized Mean ( 10 / 18 )-111.887538.9548253235753-2.87223724071704
Winsorized Mean ( 11 / 18 )-110.787536.6647308379433-3.02163680103575
Winsorized Mean ( 12 / 18 )-109.95178571428636.2064433340678-3.03680161842433
Winsorized Mean ( 13 / 18 )-106.79464285714334.7423276048148-3.07390581517464
Winsorized Mean ( 14 / 18 )-98.919642857142932.6584599945934-3.02891327005373
Winsorized Mean ( 15 / 18 )-85.767857142857127.8420995470751-3.08050967915842
Winsorized Mean ( 16 / 18 )-79.453571428571425.9865076085681-3.05749324323883
Winsorized Mean ( 17 / 18 )-57.839285714285722.3125226441111-2.59223426399754
Winsorized Mean ( 18 / 18 )-59.671428571428621.3721310392225-2.79202052719583
Trimmed Mean ( 1 / 18 )-117.68518518518556.43649402199-2.08526747142248
Trimmed Mean ( 2 / 18 )-113.99807692307751.2145782008353-2.22589116083392
Trimmed Mean ( 3 / 18 )-107.76647.7668057922218-2.25608554335338
Trimmed Mean ( 4 / 18 )-104.42545.4813490045041-2.29599610138342
Trimmed Mean ( 5 / 18 )-102.58478260869643.7929889793208-2.34249328487573
Trimmed Mean ( 6 / 18 )-100.56363636363641.9395039107045-2.39782608248661
Trimmed Mean ( 7 / 18 )-98.557142857142940.4788195634504-2.43478302776727
Trimmed Mean ( 8 / 18 )-94.96539.5310294465318-2.40229008274237
Trimmed Mean ( 9 / 18 )-91.042105263157938.5738698752026-2.36020149281638
Trimmed Mean ( 10 / 18 )-87.408333333333337.4811818127359-2.33205915891458
Trimmed Mean ( 11 / 18 )-83.376470588235336.2676609037585-2.29892053996774
Trimmed Mean ( 12 / 18 )-79.01562535.2002013572684-2.24474923305188
Trimmed Mean ( 13 / 18 )-74.203333333333333.7322665146379-2.19977312526964
Trimmed Mean ( 14 / 18 )-69.189285714285732.0143834817501-2.16119375697887
Trimmed Mean ( 15 / 18 )-64.615384615384630.165180993634-2.14205194489040
Trimmed Mean ( 16 / 18 )-61.32529.1730657059069-2.10211023476984
Trimmed Mean ( 17 / 18 )-58.440909090909128.2161958489403-2.071183139066
Trimmed Mean ( 18 / 18 )-58.5428.0628902739243-2.08602889540550
Median-81.05
Midrange-187.5
Midmean - Weighted Average at Xnp-82.8103448275862
Midmean - Weighted Average at X(n+1)p-69.1892857142857
Midmean - Empirical Distribution Function-82.8103448275862
Midmean - Empirical Distribution Function - Averaging-69.1892857142857
Midmean - Empirical Distribution Function - Interpolation-69.1892857142857
Midmean - Closest Observation-82.8103448275862
Midmean - True Basic - Statistics Graphics Toolkit-69.1892857142857
Midmean - MS Excel (old versions)-74.2033333333333
Number of observations56



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')