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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 computationMon, 26 Oct 2009 13:26:04 -0600
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/Oct/26/t1256585456zfbpvyhualoujgs.htm/, Retrieved Thu, 02 May 2024 23:33:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50716, Retrieved Thu, 02 May 2024 23:33:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Harrell-Davis Quantiles] [Harrell-Davis ] [2009-10-19 18:47:17] [f15cf5036ae52d4243ad71d4fb151dbe]
- RMP         [Central Tendency] [Central Tendency] [2009-10-19 19:12:24] [f15cf5036ae52d4243ad71d4fb151dbe]
-    D            [Central Tendency] [central tendency ...] [2009-10-26 19:26:04] [1aecede37375310a889a187dca5e5c0a] [Current]
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Dataseries X:
203.5327635
233.3949787
265.3749378
238.2887181
233.8883315
200.1135257
193.075291
200.3316602
189.6318264
182.4144612
165.0136023
165.1644974
174.5445478
190.5782252
188.5721003
171.1662469
177.7862583
176.8870021
164.7797008
157.3494377
157.6769892
148.3253595
151.4509619
179.5390722
199.2856905
204.9991588
198.04192
227.3417515
216.5149126
198.1351744
188.54102
198.1050532
191.7526316
181.680574
185.3262878
177.5496333
170.1294823
142.5548596
147.9798013
135.9440529
131.9967053
118.6290495
115.4275422
103.2848045
90.8634411
83.36926589
99.34306884
109.5846973
121.2429684
155.2730714
196.2456621
185.3875028
174.7443763
152.3898484
156.4934404
145.2000346
124.4642236
132.2930956
128.6486894
140.8415436




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=50716&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=50716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50716&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 Mean168.97475884554.9341459948326234.24599900823
Geometric Mean164.387405105761
Harmonic Mean159.39585929651
Quadratic Mean173.172951502525
Winsorized Mean ( 1 / 20 )168.6482247706674.7675406380286135.3742605622347
Winsorized Mean ( 2 / 20 )168.7841994753334.6571593643504736.2418775632501
Winsorized Mean ( 3 / 20 )168.9566186183334.6025681559308636.7092051424847
Winsorized Mean ( 4 / 20 )168.9730629916674.4106024121020338.31065401135
Winsorized Mean ( 5 / 20 )168.5577301583334.110826157639941.0033710243552
Winsorized Mean ( 6 / 20 )167.7263055083333.8315319956835543.77525900796
Winsorized Mean ( 7 / 20 )167.8601832616673.7382342571498544.9036019988883
Winsorized Mean ( 8 / 20 )167.8628701816673.5813636642905346.8712160832514
Winsorized Mean ( 9 / 20 )168.4578198766673.4504202562095548.8224063644135
Winsorized Mean ( 10 / 20 )168.8778499933333.3218897910124250.8378846433264
Winsorized Mean ( 11 / 20 )168.7212602633333.2792635013354151.4509615328641
Winsorized Mean ( 12 / 20 )169.4454274833333.1435939064159353.9018182779598
Winsorized Mean ( 13 / 20 )170.4928716083332.9552226718996357.6920559081727
Winsorized Mean ( 14 / 20 )170.4735184983332.8221394994695360.4057731839184
Winsorized Mean ( 15 / 20 )170.3422194733332.5919370496679265.720044973761
Winsorized Mean ( 16 / 20 )170.730781422.4196775950585070.5593099546272
Winsorized Mean ( 17 / 20 )170.4959410966672.3555200752552472.3814425899945
Winsorized Mean ( 18 / 20 )171.1497021766672.1673648995562478.9667223141379
Winsorized Mean ( 19 / 20 )171.1114363033332.0735059303696482.5227619545943
Winsorized Mean ( 20 / 20 )172.0621505366671.9274386980122689.2698432972793
Trimmed Mean ( 1 / 20 )168.7886435696554.5870229222248136.7969915196737
Trimmed Mean ( 2 / 20 )168.9390922828574.3639964125061638.7120144734121
Trimmed Mean ( 3 / 20 )169.0251438425934.1627671993318540.6040347079035
Trimmed Mean ( 4 / 20 )169.0514996980773.9381165751025942.9269922497592
Trimmed Mean ( 5 / 20 )169.075030713.7359344659460945.2564230585836
Trimmed Mean ( 6 / 20 )169.2043558479173.5893951675675547.1400745665412
Trimmed Mean ( 7 / 20 )169.5256711391303.4906277945966848.5659546404655
Trimmed Mean ( 8 / 20 )169.8501168295453.3889468071833550.1188500420024
Trimmed Mean ( 9 / 20 )170.2049823023813.2984750254908251.6011129346216
Trimmed Mean ( 10 / 20 )170.496176043.2135943376648653.0546665587823
Trimmed Mean ( 11 / 20 )170.7517012052633.1325492184833254.5088646006767
Trimmed Mean ( 12 / 20 )171.0593437722223.0295582873690556.4634601966265
Trimmed Mean ( 13 / 20 )171.2966844029412.9247990338554358.5669929523809
Trimmed Mean ( 14 / 20 )171.4126189406252.8317822666410660.5317085850486
Trimmed Mean ( 15 / 20 )171.5467761466672.7343806434445962.7369772229529
Trimmed Mean ( 16 / 20 )171.7188556714292.6593132163648764.5726327439377
Trimmed Mean ( 17 / 20 )171.8613663807692.596141766154366.1987602608273
Trimmed Mean ( 18 / 20 )172.0621642166672.5093075821267468.5695788918938
Trimmed Mean ( 19 / 20 )172.2004160409092.4361107133611170.6866133367656
Trimmed Mean ( 20 / 20 )172.372360212.3399952916628873.663550018302
Median174.64446205
Midrange174.372101845
Midmean - Weighted Average at Xnp170.611553032258
Midmean - Weighted Average at X(n+1)p171.546776146667
Midmean - Empirical Distribution Function170.611553032258
Midmean - Empirical Distribution Function - Averaging171.546776146667
Midmean - Empirical Distribution Function - Interpolation171.546776146667
Midmean - Closest Observation170.611553032258
Midmean - True Basic - Statistics Graphics Toolkit171.546776146667
Midmean - MS Excel (old versions)171.412618940625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 168.9747588455 & 4.93414599483262 & 34.24599900823 \tabularnewline
Geometric Mean & 164.387405105761 &  &  \tabularnewline
Harmonic Mean & 159.39585929651 &  &  \tabularnewline
Quadratic Mean & 173.172951502525 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 168.648224770667 & 4.76754063802861 & 35.3742605622347 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 168.784199475333 & 4.65715936435047 & 36.2418775632501 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 168.956618618333 & 4.60256815593086 & 36.7092051424847 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 168.973062991667 & 4.41060241210203 & 38.31065401135 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 168.557730158333 & 4.1108261576399 & 41.0033710243552 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 167.726305508333 & 3.83153199568355 & 43.77525900796 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 167.860183261667 & 3.73823425714985 & 44.9036019988883 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 167.862870181667 & 3.58136366429053 & 46.8712160832514 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 168.457819876667 & 3.45042025620955 & 48.8224063644135 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 168.877849993333 & 3.32188979101242 & 50.8378846433264 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 168.721260263333 & 3.27926350133541 & 51.4509615328641 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 169.445427483333 & 3.14359390641593 & 53.9018182779598 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 170.492871608333 & 2.95522267189963 & 57.6920559081727 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 170.473518498333 & 2.82213949946953 & 60.4057731839184 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 170.342219473333 & 2.59193704966792 & 65.720044973761 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 170.73078142 & 2.41967759505850 & 70.5593099546272 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 170.495941096667 & 2.35552007525524 & 72.3814425899945 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 171.149702176667 & 2.16736489955624 & 78.9667223141379 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 171.111436303333 & 2.07350593036964 & 82.5227619545943 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 172.062150536667 & 1.92743869801226 & 89.2698432972793 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 168.788643569655 & 4.58702292222481 & 36.7969915196737 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 168.939092282857 & 4.36399641250616 & 38.7120144734121 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 169.025143842593 & 4.16276719933185 & 40.6040347079035 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 169.051499698077 & 3.93811657510259 & 42.9269922497592 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 169.07503071 & 3.73593446594609 & 45.2564230585836 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 169.204355847917 & 3.58939516756755 & 47.1400745665412 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 169.525671139130 & 3.49062779459668 & 48.5659546404655 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 169.850116829545 & 3.38894680718335 & 50.1188500420024 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 170.204982302381 & 3.29847502549082 & 51.6011129346216 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 170.49617604 & 3.21359433766486 & 53.0546665587823 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 170.751701205263 & 3.13254921848332 & 54.5088646006767 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 171.059343772222 & 3.02955828736905 & 56.4634601966265 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 171.296684402941 & 2.92479903385543 & 58.5669929523809 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 171.412618940625 & 2.83178226664106 & 60.5317085850486 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 171.546776146667 & 2.73438064344459 & 62.7369772229529 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 171.718855671429 & 2.65931321636487 & 64.5726327439377 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 171.861366380769 & 2.5961417661543 & 66.1987602608273 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 172.062164216667 & 2.50930758212674 & 68.5695788918938 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 172.200416040909 & 2.43611071336111 & 70.6866133367656 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 172.37236021 & 2.33999529166288 & 73.663550018302 \tabularnewline
Median & 174.64446205 &  &  \tabularnewline
Midrange & 174.372101845 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 170.611553032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 171.546776146667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 170.611553032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 171.546776146667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 171.546776146667 &  &  \tabularnewline
Midmean - Closest Observation & 170.611553032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 171.546776146667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 171.412618940625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50716&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]168.9747588455[/C][C]4.93414599483262[/C][C]34.24599900823[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]164.387405105761[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]159.39585929651[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]173.172951502525[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]168.648224770667[/C][C]4.76754063802861[/C][C]35.3742605622347[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]168.784199475333[/C][C]4.65715936435047[/C][C]36.2418775632501[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]168.956618618333[/C][C]4.60256815593086[/C][C]36.7092051424847[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]168.973062991667[/C][C]4.41060241210203[/C][C]38.31065401135[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]168.557730158333[/C][C]4.1108261576399[/C][C]41.0033710243552[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]167.726305508333[/C][C]3.83153199568355[/C][C]43.77525900796[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]167.860183261667[/C][C]3.73823425714985[/C][C]44.9036019988883[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]167.862870181667[/C][C]3.58136366429053[/C][C]46.8712160832514[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]168.457819876667[/C][C]3.45042025620955[/C][C]48.8224063644135[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]168.877849993333[/C][C]3.32188979101242[/C][C]50.8378846433264[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]168.721260263333[/C][C]3.27926350133541[/C][C]51.4509615328641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]169.445427483333[/C][C]3.14359390641593[/C][C]53.9018182779598[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]170.492871608333[/C][C]2.95522267189963[/C][C]57.6920559081727[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]170.473518498333[/C][C]2.82213949946953[/C][C]60.4057731839184[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]170.342219473333[/C][C]2.59193704966792[/C][C]65.720044973761[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]170.73078142[/C][C]2.41967759505850[/C][C]70.5593099546272[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]170.495941096667[/C][C]2.35552007525524[/C][C]72.3814425899945[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]171.149702176667[/C][C]2.16736489955624[/C][C]78.9667223141379[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]171.111436303333[/C][C]2.07350593036964[/C][C]82.5227619545943[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]172.062150536667[/C][C]1.92743869801226[/C][C]89.2698432972793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]168.788643569655[/C][C]4.58702292222481[/C][C]36.7969915196737[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]168.939092282857[/C][C]4.36399641250616[/C][C]38.7120144734121[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]169.025143842593[/C][C]4.16276719933185[/C][C]40.6040347079035[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]169.051499698077[/C][C]3.93811657510259[/C][C]42.9269922497592[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]169.07503071[/C][C]3.73593446594609[/C][C]45.2564230585836[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]169.204355847917[/C][C]3.58939516756755[/C][C]47.1400745665412[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]169.525671139130[/C][C]3.49062779459668[/C][C]48.5659546404655[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]169.850116829545[/C][C]3.38894680718335[/C][C]50.1188500420024[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]170.204982302381[/C][C]3.29847502549082[/C][C]51.6011129346216[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]170.49617604[/C][C]3.21359433766486[/C][C]53.0546665587823[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]170.751701205263[/C][C]3.13254921848332[/C][C]54.5088646006767[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]171.059343772222[/C][C]3.02955828736905[/C][C]56.4634601966265[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]171.296684402941[/C][C]2.92479903385543[/C][C]58.5669929523809[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]171.412618940625[/C][C]2.83178226664106[/C][C]60.5317085850486[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]171.546776146667[/C][C]2.73438064344459[/C][C]62.7369772229529[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]171.718855671429[/C][C]2.65931321636487[/C][C]64.5726327439377[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]171.861366380769[/C][C]2.5961417661543[/C][C]66.1987602608273[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]172.062164216667[/C][C]2.50930758212674[/C][C]68.5695788918938[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]172.200416040909[/C][C]2.43611071336111[/C][C]70.6866133367656[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]172.37236021[/C][C]2.33999529166288[/C][C]73.663550018302[/C][/ROW]
[ROW][C]Median[/C][C]174.64446205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]174.372101845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]170.611553032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]171.546776146667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]170.611553032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]171.546776146667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]171.546776146667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]170.611553032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]171.546776146667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]171.412618940625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50716&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 Mean168.97475884554.9341459948326234.24599900823
Geometric Mean164.387405105761
Harmonic Mean159.39585929651
Quadratic Mean173.172951502525
Winsorized Mean ( 1 / 20 )168.6482247706674.7675406380286135.3742605622347
Winsorized Mean ( 2 / 20 )168.7841994753334.6571593643504736.2418775632501
Winsorized Mean ( 3 / 20 )168.9566186183334.6025681559308636.7092051424847
Winsorized Mean ( 4 / 20 )168.9730629916674.4106024121020338.31065401135
Winsorized Mean ( 5 / 20 )168.5577301583334.110826157639941.0033710243552
Winsorized Mean ( 6 / 20 )167.7263055083333.8315319956835543.77525900796
Winsorized Mean ( 7 / 20 )167.8601832616673.7382342571498544.9036019988883
Winsorized Mean ( 8 / 20 )167.8628701816673.5813636642905346.8712160832514
Winsorized Mean ( 9 / 20 )168.4578198766673.4504202562095548.8224063644135
Winsorized Mean ( 10 / 20 )168.8778499933333.3218897910124250.8378846433264
Winsorized Mean ( 11 / 20 )168.7212602633333.2792635013354151.4509615328641
Winsorized Mean ( 12 / 20 )169.4454274833333.1435939064159353.9018182779598
Winsorized Mean ( 13 / 20 )170.4928716083332.9552226718996357.6920559081727
Winsorized Mean ( 14 / 20 )170.4735184983332.8221394994695360.4057731839184
Winsorized Mean ( 15 / 20 )170.3422194733332.5919370496679265.720044973761
Winsorized Mean ( 16 / 20 )170.730781422.4196775950585070.5593099546272
Winsorized Mean ( 17 / 20 )170.4959410966672.3555200752552472.3814425899945
Winsorized Mean ( 18 / 20 )171.1497021766672.1673648995562478.9667223141379
Winsorized Mean ( 19 / 20 )171.1114363033332.0735059303696482.5227619545943
Winsorized Mean ( 20 / 20 )172.0621505366671.9274386980122689.2698432972793
Trimmed Mean ( 1 / 20 )168.7886435696554.5870229222248136.7969915196737
Trimmed Mean ( 2 / 20 )168.9390922828574.3639964125061638.7120144734121
Trimmed Mean ( 3 / 20 )169.0251438425934.1627671993318540.6040347079035
Trimmed Mean ( 4 / 20 )169.0514996980773.9381165751025942.9269922497592
Trimmed Mean ( 5 / 20 )169.075030713.7359344659460945.2564230585836
Trimmed Mean ( 6 / 20 )169.2043558479173.5893951675675547.1400745665412
Trimmed Mean ( 7 / 20 )169.5256711391303.4906277945966848.5659546404655
Trimmed Mean ( 8 / 20 )169.8501168295453.3889468071833550.1188500420024
Trimmed Mean ( 9 / 20 )170.2049823023813.2984750254908251.6011129346216
Trimmed Mean ( 10 / 20 )170.496176043.2135943376648653.0546665587823
Trimmed Mean ( 11 / 20 )170.7517012052633.1325492184833254.5088646006767
Trimmed Mean ( 12 / 20 )171.0593437722223.0295582873690556.4634601966265
Trimmed Mean ( 13 / 20 )171.2966844029412.9247990338554358.5669929523809
Trimmed Mean ( 14 / 20 )171.4126189406252.8317822666410660.5317085850486
Trimmed Mean ( 15 / 20 )171.5467761466672.7343806434445962.7369772229529
Trimmed Mean ( 16 / 20 )171.7188556714292.6593132163648764.5726327439377
Trimmed Mean ( 17 / 20 )171.8613663807692.596141766154366.1987602608273
Trimmed Mean ( 18 / 20 )172.0621642166672.5093075821267468.5695788918938
Trimmed Mean ( 19 / 20 )172.2004160409092.4361107133611170.6866133367656
Trimmed Mean ( 20 / 20 )172.372360212.3399952916628873.663550018302
Median174.64446205
Midrange174.372101845
Midmean - Weighted Average at Xnp170.611553032258
Midmean - Weighted Average at X(n+1)p171.546776146667
Midmean - Empirical Distribution Function170.611553032258
Midmean - Empirical Distribution Function - Averaging171.546776146667
Midmean - Empirical Distribution Function - Interpolation171.546776146667
Midmean - Closest Observation170.611553032258
Midmean - True Basic - Statistics Graphics Toolkit171.546776146667
Midmean - MS Excel (old versions)171.412618940625
Number of observations60



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')