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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, 03 Dec 2009 10:29:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259861412dhd0v18zuqwio5s.htm/, Retrieved Thu, 28 Mar 2024 23:36:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62953, Retrieved Thu, 28 Mar 2024 23:36:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [prijsindex graan] [2009-11-29 09:59:12] [757146c69eaf0537be37c7b0c18216d8]
- RMP   [Univariate Explorative Data Analysis] [paper - prijsinde...] [2009-12-03 15:14:25] [757146c69eaf0537be37c7b0c18216d8]
- RMPD      [Central Tendency] [central tendency ...] [2009-12-03 17:29:28] [a931a0a30926b49d162330b43e89b999] [Current]
-             [Central Tendency] [central tendency ...] [2009-12-21 15:24:47] [03c44f58d7d4de05d4cfabfda8c46d2c]
-   P         [Central Tendency] [central tendency ...] [2009-12-21 15:54:33] [12f02da0296cb21dc23d82ae014a8b71]
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Dataseries X:
108.2
108.8
110.2
109.5
109.5
116
111.2
112.1
114
119.1
114.1
115.1
115.4
110.8
116
119.2
126.5
127.8
131.3
140.3
137.3
143
134.5
139.9
159.3
170.4
175
175.8
180.9
180.3
169.6
172.3
184.8
177.7
184.6
211.4
215.3
215.9
244.7
259.3
289
310.9
321
315.1
333.2
314.1
284.7
273.9
216
196.4
190.9
206.4
196.3
199.5
198.9
214.4
214.2
187.6
180.6
172.2
187.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62953&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62953&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean179.8295081967218.0524273719586122.3323353182856
Geometric Mean169.989168012488
Harmonic Mean161.251193241253
Quadratic Mean190.339557667645
Winsorized Mean ( 1 / 20 )179.6393442622957.9897305256569822.4837801081562
Winsorized Mean ( 2 / 20 )179.4688524590167.9302521480125722.6309137602887
Winsorized Mean ( 3 / 20 )179.4196721311487.9162701032705522.6646728560994
Winsorized Mean ( 4 / 20 )179.2557377049187.8504524684574122.8338096976137
Winsorized Mean ( 5 / 20 )177.5098360655747.3650673429891524.1015903587829
Winsorized Mean ( 6 / 20 )177.1262295081977.2534833921663924.4194712983681
Winsorized Mean ( 7 / 20 )175.9901639344266.9386707223354225.3636713683383
Winsorized Mean ( 8 / 20 )174.3245901639346.4647466260061126.9654172466201
Winsorized Mean ( 9 / 20 )172.1852459016396.0091327743537128.6539260101734
Winsorized Mean ( 10 / 20 )167.6442622950825.1312098321957932.6714883580082
Winsorized Mean ( 11 / 20 )167.6803278688525.1191576427070532.755453059301
Winsorized Mean ( 12 / 20 )167.6803278688525.0806225790308533.0038937670584
Winsorized Mean ( 13 / 20 )167.4885245901645.0507955865007733.16082025529
Winsorized Mean ( 14 / 20 )168.1540983606564.9241440263449334.1488992728493
Winsorized Mean ( 15 / 20 )167.4901639344264.8140440635139334.79198813402
Winsorized Mean ( 16 / 20 )168.0934426229514.3022696188768439.0708759593811
Winsorized Mean ( 17 / 20 )166.5327868852463.9673956174433441.9753417463728
Winsorized Mean ( 18 / 20 )167.3885245901643.7765136279773544.3235589963474
Winsorized Mean ( 19 / 20 )167.6065573770493.5114013120202047.7320996615511
Winsorized Mean ( 20 / 20 )168.4918032786893.3638087434845350.0895907370018
Trimmed Mean ( 1 / 20 )178.444067796617.806725536066922.8577355476637
Trimmed Mean ( 2 / 20 )177.1649122807027.5776661566163123.3798782658184
Trimmed Mean ( 3 / 20 )175.8872727272737.3304287427472223.9941317076845
Trimmed Mean ( 4 / 20 )174.5320754716987.0243753362781124.8466329198426
Trimmed Mean ( 5 / 20 )173.1196078431376.6612593872611825.9890206608988
Trimmed Mean ( 6 / 20 )172.0265306122456.3814081941255526.957456000167
Trimmed Mean ( 7 / 20 )170.9234042553196.0573364457859228.2175847065966
Trimmed Mean ( 8 / 20 )169.9422222222225.7392389324831429.6105849959265
Trimmed Mean ( 9 / 20 )169.1651162790705.4720996592985130.914114656449
Trimmed Mean ( 10 / 20 )168.6658536585375.2574414274321032.0813566801672
Trimmed Mean ( 11 / 20 )168.8256410256415.2095051168091732.4072320191993
Trimmed Mean ( 12 / 20 )168.9972972972975.1369042313809732.8986661392100
Trimmed Mean ( 13 / 20 )169.1885714285715.0372224096064633.5876714726578
Trimmed Mean ( 14 / 20 )169.4303030303034.8966177350639234.6014968285229
Trimmed Mean ( 15 / 20 )169.6096774193554.7270790609153435.8804401690104
Trimmed Mean ( 16 / 20 )169.9068965517244.5065604368845137.7021231449821
Trimmed Mean ( 17 / 20 )170.1629629629634.3483144985821539.1330854790857
Trimmed Mean ( 18 / 20 )170.6844.2054000206084240.5868643086433
Trimmed Mean ( 19 / 20 )171.1695652173914.0399606442659542.3691170012604
Trimmed Mean ( 20 / 20 )171.7142857142863.8640916243837544.4384611976355
Median175.8
Midrange220.7
Midmean - Weighted Average at Xnp168.216666666667
Midmean - Weighted Average at X(n+1)p169.609677419355
Midmean - Empirical Distribution Function169.609677419355
Midmean - Empirical Distribution Function - Averaging169.609677419355
Midmean - Empirical Distribution Function - Interpolation169.609677419355
Midmean - Closest Observation168.03125
Midmean - True Basic - Statistics Graphics Toolkit169.609677419355
Midmean - MS Excel (old versions)169.609677419355
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 179.829508196721 & 8.05242737195861 & 22.3323353182856 \tabularnewline
Geometric Mean & 169.989168012488 &  &  \tabularnewline
Harmonic Mean & 161.251193241253 &  &  \tabularnewline
Quadratic Mean & 190.339557667645 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 179.639344262295 & 7.98973052565698 & 22.4837801081562 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 179.468852459016 & 7.93025214801257 & 22.6309137602887 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 179.419672131148 & 7.91627010327055 & 22.6646728560994 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 179.255737704918 & 7.85045246845741 & 22.8338096976137 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 177.509836065574 & 7.36506734298915 & 24.1015903587829 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 177.126229508197 & 7.25348339216639 & 24.4194712983681 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 175.990163934426 & 6.93867072233542 & 25.3636713683383 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 174.324590163934 & 6.46474662600611 & 26.9654172466201 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 172.185245901639 & 6.00913277435371 & 28.6539260101734 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 167.644262295082 & 5.13120983219579 & 32.6714883580082 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 167.680327868852 & 5.11915764270705 & 32.755453059301 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 167.680327868852 & 5.08062257903085 & 33.0038937670584 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 167.488524590164 & 5.05079558650077 & 33.16082025529 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 168.154098360656 & 4.92414402634493 & 34.1488992728493 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 167.490163934426 & 4.81404406351393 & 34.79198813402 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 168.093442622951 & 4.30226961887684 & 39.0708759593811 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 166.532786885246 & 3.96739561744334 & 41.9753417463728 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 167.388524590164 & 3.77651362797735 & 44.3235589963474 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 167.606557377049 & 3.51140131202020 & 47.7320996615511 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 168.491803278689 & 3.36380874348453 & 50.0895907370018 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 178.44406779661 & 7.8067255360669 & 22.8577355476637 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 177.164912280702 & 7.57766615661631 & 23.3798782658184 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 175.887272727273 & 7.33042874274722 & 23.9941317076845 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 174.532075471698 & 7.02437533627811 & 24.8466329198426 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 173.119607843137 & 6.66125938726118 & 25.9890206608988 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 172.026530612245 & 6.38140819412555 & 26.957456000167 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 170.923404255319 & 6.05733644578592 & 28.2175847065966 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 169.942222222222 & 5.73923893248314 & 29.6105849959265 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 169.165116279070 & 5.47209965929851 & 30.914114656449 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 168.665853658537 & 5.25744142743210 & 32.0813566801672 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 168.825641025641 & 5.20950511680917 & 32.4072320191993 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 168.997297297297 & 5.13690423138097 & 32.8986661392100 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 169.188571428571 & 5.03722240960646 & 33.5876714726578 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 169.430303030303 & 4.89661773506392 & 34.6014968285229 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 169.609677419355 & 4.72707906091534 & 35.8804401690104 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 169.906896551724 & 4.50656043688451 & 37.7021231449821 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 170.162962962963 & 4.34831449858215 & 39.1330854790857 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 170.684 & 4.20540002060842 & 40.5868643086433 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 171.169565217391 & 4.03996064426595 & 42.3691170012604 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 171.714285714286 & 3.86409162438375 & 44.4384611976355 \tabularnewline
Median & 175.8 &  &  \tabularnewline
Midrange & 220.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 168.216666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 169.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 169.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 169.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 169.609677419355 &  &  \tabularnewline
Midmean - Closest Observation & 168.03125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 169.609677419355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 169.609677419355 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62953&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]179.829508196721[/C][C]8.05242737195861[/C][C]22.3323353182856[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]169.989168012488[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]161.251193241253[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]190.339557667645[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]179.639344262295[/C][C]7.98973052565698[/C][C]22.4837801081562[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]179.468852459016[/C][C]7.93025214801257[/C][C]22.6309137602887[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]179.419672131148[/C][C]7.91627010327055[/C][C]22.6646728560994[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]179.255737704918[/C][C]7.85045246845741[/C][C]22.8338096976137[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]177.509836065574[/C][C]7.36506734298915[/C][C]24.1015903587829[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]177.126229508197[/C][C]7.25348339216639[/C][C]24.4194712983681[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]175.990163934426[/C][C]6.93867072233542[/C][C]25.3636713683383[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]174.324590163934[/C][C]6.46474662600611[/C][C]26.9654172466201[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]172.185245901639[/C][C]6.00913277435371[/C][C]28.6539260101734[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]167.644262295082[/C][C]5.13120983219579[/C][C]32.6714883580082[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]167.680327868852[/C][C]5.11915764270705[/C][C]32.755453059301[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]167.680327868852[/C][C]5.08062257903085[/C][C]33.0038937670584[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]167.488524590164[/C][C]5.05079558650077[/C][C]33.16082025529[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]168.154098360656[/C][C]4.92414402634493[/C][C]34.1488992728493[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]167.490163934426[/C][C]4.81404406351393[/C][C]34.79198813402[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]168.093442622951[/C][C]4.30226961887684[/C][C]39.0708759593811[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]166.532786885246[/C][C]3.96739561744334[/C][C]41.9753417463728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]167.388524590164[/C][C]3.77651362797735[/C][C]44.3235589963474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]167.606557377049[/C][C]3.51140131202020[/C][C]47.7320996615511[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]168.491803278689[/C][C]3.36380874348453[/C][C]50.0895907370018[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]178.44406779661[/C][C]7.8067255360669[/C][C]22.8577355476637[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]177.164912280702[/C][C]7.57766615661631[/C][C]23.3798782658184[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]175.887272727273[/C][C]7.33042874274722[/C][C]23.9941317076845[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]174.532075471698[/C][C]7.02437533627811[/C][C]24.8466329198426[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]173.119607843137[/C][C]6.66125938726118[/C][C]25.9890206608988[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]172.026530612245[/C][C]6.38140819412555[/C][C]26.957456000167[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]170.923404255319[/C][C]6.05733644578592[/C][C]28.2175847065966[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]169.942222222222[/C][C]5.73923893248314[/C][C]29.6105849959265[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]169.165116279070[/C][C]5.47209965929851[/C][C]30.914114656449[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]168.665853658537[/C][C]5.25744142743210[/C][C]32.0813566801672[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]168.825641025641[/C][C]5.20950511680917[/C][C]32.4072320191993[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]168.997297297297[/C][C]5.13690423138097[/C][C]32.8986661392100[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]169.188571428571[/C][C]5.03722240960646[/C][C]33.5876714726578[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]169.430303030303[/C][C]4.89661773506392[/C][C]34.6014968285229[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]169.609677419355[/C][C]4.72707906091534[/C][C]35.8804401690104[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]169.906896551724[/C][C]4.50656043688451[/C][C]37.7021231449821[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]170.162962962963[/C][C]4.34831449858215[/C][C]39.1330854790857[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]170.684[/C][C]4.20540002060842[/C][C]40.5868643086433[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]171.169565217391[/C][C]4.03996064426595[/C][C]42.3691170012604[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]171.714285714286[/C][C]3.86409162438375[/C][C]44.4384611976355[/C][/ROW]
[ROW][C]Median[/C][C]175.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]220.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]168.216666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]168.03125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]169.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62953&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 Mean179.8295081967218.0524273719586122.3323353182856
Geometric Mean169.989168012488
Harmonic Mean161.251193241253
Quadratic Mean190.339557667645
Winsorized Mean ( 1 / 20 )179.6393442622957.9897305256569822.4837801081562
Winsorized Mean ( 2 / 20 )179.4688524590167.9302521480125722.6309137602887
Winsorized Mean ( 3 / 20 )179.4196721311487.9162701032705522.6646728560994
Winsorized Mean ( 4 / 20 )179.2557377049187.8504524684574122.8338096976137
Winsorized Mean ( 5 / 20 )177.5098360655747.3650673429891524.1015903587829
Winsorized Mean ( 6 / 20 )177.1262295081977.2534833921663924.4194712983681
Winsorized Mean ( 7 / 20 )175.9901639344266.9386707223354225.3636713683383
Winsorized Mean ( 8 / 20 )174.3245901639346.4647466260061126.9654172466201
Winsorized Mean ( 9 / 20 )172.1852459016396.0091327743537128.6539260101734
Winsorized Mean ( 10 / 20 )167.6442622950825.1312098321957932.6714883580082
Winsorized Mean ( 11 / 20 )167.6803278688525.1191576427070532.755453059301
Winsorized Mean ( 12 / 20 )167.6803278688525.0806225790308533.0038937670584
Winsorized Mean ( 13 / 20 )167.4885245901645.0507955865007733.16082025529
Winsorized Mean ( 14 / 20 )168.1540983606564.9241440263449334.1488992728493
Winsorized Mean ( 15 / 20 )167.4901639344264.8140440635139334.79198813402
Winsorized Mean ( 16 / 20 )168.0934426229514.3022696188768439.0708759593811
Winsorized Mean ( 17 / 20 )166.5327868852463.9673956174433441.9753417463728
Winsorized Mean ( 18 / 20 )167.3885245901643.7765136279773544.3235589963474
Winsorized Mean ( 19 / 20 )167.6065573770493.5114013120202047.7320996615511
Winsorized Mean ( 20 / 20 )168.4918032786893.3638087434845350.0895907370018
Trimmed Mean ( 1 / 20 )178.444067796617.806725536066922.8577355476637
Trimmed Mean ( 2 / 20 )177.1649122807027.5776661566163123.3798782658184
Trimmed Mean ( 3 / 20 )175.8872727272737.3304287427472223.9941317076845
Trimmed Mean ( 4 / 20 )174.5320754716987.0243753362781124.8466329198426
Trimmed Mean ( 5 / 20 )173.1196078431376.6612593872611825.9890206608988
Trimmed Mean ( 6 / 20 )172.0265306122456.3814081941255526.957456000167
Trimmed Mean ( 7 / 20 )170.9234042553196.0573364457859228.2175847065966
Trimmed Mean ( 8 / 20 )169.9422222222225.7392389324831429.6105849959265
Trimmed Mean ( 9 / 20 )169.1651162790705.4720996592985130.914114656449
Trimmed Mean ( 10 / 20 )168.6658536585375.2574414274321032.0813566801672
Trimmed Mean ( 11 / 20 )168.8256410256415.2095051168091732.4072320191993
Trimmed Mean ( 12 / 20 )168.9972972972975.1369042313809732.8986661392100
Trimmed Mean ( 13 / 20 )169.1885714285715.0372224096064633.5876714726578
Trimmed Mean ( 14 / 20 )169.4303030303034.8966177350639234.6014968285229
Trimmed Mean ( 15 / 20 )169.6096774193554.7270790609153435.8804401690104
Trimmed Mean ( 16 / 20 )169.9068965517244.5065604368845137.7021231449821
Trimmed Mean ( 17 / 20 )170.1629629629634.3483144985821539.1330854790857
Trimmed Mean ( 18 / 20 )170.6844.2054000206084240.5868643086433
Trimmed Mean ( 19 / 20 )171.1695652173914.0399606442659542.3691170012604
Trimmed Mean ( 20 / 20 )171.7142857142863.8640916243837544.4384611976355
Median175.8
Midrange220.7
Midmean - Weighted Average at Xnp168.216666666667
Midmean - Weighted Average at X(n+1)p169.609677419355
Midmean - Empirical Distribution Function169.609677419355
Midmean - Empirical Distribution Function - Averaging169.609677419355
Midmean - Empirical Distribution Function - Interpolation169.609677419355
Midmean - Closest Observation168.03125
Midmean - True Basic - Statistics Graphics Toolkit169.609677419355
Midmean - MS Excel (old versions)169.609677419355
Number of observations61



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')