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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 02 Mar 2014 14:13:47 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Mar/02/t13937876732i7j5eurpitsmas.htm/, Retrieved Tue, 14 May 2024 22:50:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234114, Retrieved Tue, 14 May 2024 22:50:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-03-02 19:13:47] [3faf596b3f292f8d9ff7bbf57fa10dd3] [Current]
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Dataseries X:
812
100
113
213
149
134
228
138
162
291
182
2081
2752
125
144
274
257
186
327
209
213
375
400
1054
3377
101
120
221
222
167
297
185
189
298
237
1011
3013
110
109
215
176
134
202
139
169
262
214
1238
3748
127
160
138
134
163
172
163
193
226
344
1294
3524
141
186
135
161
131
170
146
160
151
151
1365




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234114&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234114&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean508.44444444444499.40686160891045.11478218118164
Geometric Mean263.533115155309
Harmonic Mean199.774875853158
Quadratic Mean979.856196932319
Winsorized Mean ( 1 / 24 )505.34722222222298.01703957394185.1557078689466
Winsorized Mean ( 2 / 24 )501.48611111111196.25934906336695.20973927198475
Winsorized Mean ( 3 / 24 )486.36111111111190.063478104315.40020351587817
Winsorized Mean ( 4 / 24 )472.02777777777884.42790993867355.59089734805289
Winsorized Mean ( 5 / 24 )425.91666666666767.38654683283016.32049996156152
Winsorized Mean ( 6 / 24 )366.66666666666748.04026007859877.63248712781244
Winsorized Mean ( 7 / 24 )359.95833333333346.02930548061937.82019910087269
Winsorized Mean ( 8 / 24 )354.18055555555644.2326786624388.0072147169401
Winsorized Mean ( 9 / 24 )331.55555555555637.86777862015098.75561143634451
Winsorized Mean ( 10 / 24 )325.58333333333336.27044644889978.97654606463246
Winsorized Mean ( 11 / 24 )295.18055555555628.297314349062810.4313982561858
Winsorized Mean ( 12 / 24 )226.68055555555611.518947892886519.6789288104639
Winsorized Mean ( 13 / 24 )222.70833333333310.518528950907521.1729543525303
Winsorized Mean ( 14 / 24 )216.6805555555569.3220678656308723.2438294462998
Winsorized Mean ( 15 / 24 )213.3472222222228.6273748113464224.729100901196
Winsorized Mean ( 16 / 24 )207.3472222222227.4166510977898127.9569875255441
Winsorized Mean ( 17 / 24 )207.8194444444447.2876652706730728.5166012331479
Winsorized Mean ( 18 / 24 )206.8194444444446.9692013715906729.6762044052172
Winsorized Mean ( 19 / 24 )203.1256.1229875969722533.1741648636432
Winsorized Mean ( 20 / 24 )200.3472222222225.5190011698886736.3013552733608
Winsorized Mean ( 21 / 24 )198.8888888888895.2914492231231237.5868463444313
Winsorized Mean ( 22 / 24 )195.5277777777784.0245710617302348.5835073548726
Winsorized Mean ( 23 / 24 )192.6527777777783.6175303333793253.2553316830963
Winsorized Mean ( 24 / 24 )192.3194444444443.4839687847777255.2012536061556
Trimmed Mean ( 1 / 24 )46890.70613712770165.15951858186973
Trimmed Mean ( 2 / 24 )428.45588235294181.36128479064665.2660904194841
Trimmed Mean ( 3 / 24 )388.62121212121270.39428008771955.52063621699014
Trimmed Mean ( 4 / 24 )351.9687559.36063931909785.92932882861931
Trimmed Mean ( 5 / 24 )317.11290322580646.88870394690586.76309807123029
Trimmed Mean ( 6 / 24 )29138.04492586641217.64885180803859
Trimmed Mean ( 7 / 24 )275.34482758620734.47211057618337.98746647605737
Trimmed Mean ( 8 / 24 )259.80357142857130.44804409774928.53268507476239
Trimmed Mean ( 9 / 24 )244.07407407407425.5518936194859.55209338723733
Trimmed Mean ( 10 / 24 )230.61538461538521.192594430779510.881885432604
Trimmed Mean ( 11 / 24 )216.9415.164362357655714.3059097958364
Trimmed Mean ( 12 / 24 )206.2708333333339.3436527733186422.0760379626212
Trimmed Mean ( 13 / 24 )203.6086956521748.6259062821970223.6043250403035
Trimmed Mean ( 14 / 24 )201.2045454545457.9668697942581125.2551567492113
Trimmed Mean ( 15 / 24 )199.3095238095247.4490517363938926.7563618649278
Trimmed Mean ( 16 / 24 )197.6256.9566134831429428.4082190966738
Trimmed Mean ( 17 / 24 )196.4736842105266.6492854451022429.5480899162249
Trimmed Mean ( 18 / 24 )195.1388888888896.25136845688831.2153875162929
Trimmed Mean ( 19 / 24 )193.7647058823535.7867724917106333.4840718483256
Trimmed Mean ( 20 / 24 )192.656255.4153324323463835.5760707965485
Trimmed Mean ( 21 / 24 )191.7333333333335.0879468418148937.6838318666359
Trimmed Mean ( 22 / 24 )190.8571428571434.6832794680612140.7528835634816
Trimmed Mean ( 23 / 24 )190.2692307692314.5558272717671741.7639255000611
Trimmed Mean ( 24 / 24 )189.9583333333334.4941504519791242.2679069966783
Median186
Midrange1924
Midmean - Weighted Average at Xnp193.756756756757
Midmean - Weighted Average at X(n+1)p195.138888888889
Midmean - Empirical Distribution Function193.756756756757
Midmean - Empirical Distribution Function - Averaging195.138888888889
Midmean - Empirical Distribution Function - Interpolation195.138888888889
Midmean - Closest Observation193.756756756757
Midmean - True Basic - Statistics Graphics Toolkit195.138888888889
Midmean - MS Excel (old versions)196.473684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 508.444444444444 & 99.4068616089104 & 5.11478218118164 \tabularnewline
Geometric Mean & 263.533115155309 &  &  \tabularnewline
Harmonic Mean & 199.774875853158 &  &  \tabularnewline
Quadratic Mean & 979.856196932319 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 505.347222222222 & 98.0170395739418 & 5.1557078689466 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 501.486111111111 & 96.2593490633669 & 5.20973927198475 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 486.361111111111 & 90.06347810431 & 5.40020351587817 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 472.027777777778 & 84.4279099386735 & 5.59089734805289 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 425.916666666667 & 67.3865468328301 & 6.32049996156152 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 366.666666666667 & 48.0402600785987 & 7.63248712781244 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 359.958333333333 & 46.0293054806193 & 7.82019910087269 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 354.180555555556 & 44.232678662438 & 8.0072147169401 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 331.555555555556 & 37.8677786201509 & 8.75561143634451 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 325.583333333333 & 36.2704464488997 & 8.97654606463246 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 295.180555555556 & 28.2973143490628 & 10.4313982561858 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 226.680555555556 & 11.5189478928865 & 19.6789288104639 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 222.708333333333 & 10.5185289509075 & 21.1729543525303 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 216.680555555556 & 9.32206786563087 & 23.2438294462998 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 213.347222222222 & 8.62737481134642 & 24.729100901196 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 207.347222222222 & 7.41665109778981 & 27.9569875255441 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 207.819444444444 & 7.28766527067307 & 28.5166012331479 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 206.819444444444 & 6.96920137159067 & 29.6762044052172 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 203.125 & 6.12298759697225 & 33.1741648636432 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 200.347222222222 & 5.51900116988867 & 36.3013552733608 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 198.888888888889 & 5.29144922312312 & 37.5868463444313 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 195.527777777778 & 4.02457106173023 & 48.5835073548726 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 192.652777777778 & 3.61753033337932 & 53.2553316830963 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 192.319444444444 & 3.48396878477772 & 55.2012536061556 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 468 & 90.7061371277016 & 5.15951858186973 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 428.455882352941 & 81.3612847906466 & 5.2660904194841 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 388.621212121212 & 70.3942800877195 & 5.52063621699014 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 351.96875 & 59.3606393190978 & 5.92932882861931 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 317.112903225806 & 46.8887039469058 & 6.76309807123029 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 291 & 38.0449258664121 & 7.64885180803859 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 275.344827586207 & 34.4721105761833 & 7.98746647605737 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 259.803571428571 & 30.4480440977492 & 8.53268507476239 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 244.074074074074 & 25.551893619485 & 9.55209338723733 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 230.615384615385 & 21.1925944307795 & 10.881885432604 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 216.94 & 15.1643623576557 & 14.3059097958364 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 206.270833333333 & 9.34365277331864 & 22.0760379626212 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 203.608695652174 & 8.62590628219702 & 23.6043250403035 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 201.204545454545 & 7.96686979425811 & 25.2551567492113 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 199.309523809524 & 7.44905173639389 & 26.7563618649278 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 197.625 & 6.95661348314294 & 28.4082190966738 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 196.473684210526 & 6.64928544510224 & 29.5480899162249 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 195.138888888889 & 6.251368456888 & 31.2153875162929 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 193.764705882353 & 5.78677249171063 & 33.4840718483256 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 192.65625 & 5.41533243234638 & 35.5760707965485 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 191.733333333333 & 5.08794684181489 & 37.6838318666359 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 190.857142857143 & 4.68327946806121 & 40.7528835634816 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 190.269230769231 & 4.55582727176717 & 41.7639255000611 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 189.958333333333 & 4.49415045197912 & 42.2679069966783 \tabularnewline
Median & 186 &  &  \tabularnewline
Midrange & 1924 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 193.756756756757 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 195.138888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 193.756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 195.138888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 195.138888888889 &  &  \tabularnewline
Midmean - Closest Observation & 193.756756756757 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 195.138888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 196.473684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234114&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]508.444444444444[/C][C]99.4068616089104[/C][C]5.11478218118164[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]263.533115155309[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]199.774875853158[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]979.856196932319[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]505.347222222222[/C][C]98.0170395739418[/C][C]5.1557078689466[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]501.486111111111[/C][C]96.2593490633669[/C][C]5.20973927198475[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]486.361111111111[/C][C]90.06347810431[/C][C]5.40020351587817[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]472.027777777778[/C][C]84.4279099386735[/C][C]5.59089734805289[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]425.916666666667[/C][C]67.3865468328301[/C][C]6.32049996156152[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]366.666666666667[/C][C]48.0402600785987[/C][C]7.63248712781244[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]359.958333333333[/C][C]46.0293054806193[/C][C]7.82019910087269[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]354.180555555556[/C][C]44.232678662438[/C][C]8.0072147169401[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]331.555555555556[/C][C]37.8677786201509[/C][C]8.75561143634451[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]325.583333333333[/C][C]36.2704464488997[/C][C]8.97654606463246[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]295.180555555556[/C][C]28.2973143490628[/C][C]10.4313982561858[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]226.680555555556[/C][C]11.5189478928865[/C][C]19.6789288104639[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]222.708333333333[/C][C]10.5185289509075[/C][C]21.1729543525303[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]216.680555555556[/C][C]9.32206786563087[/C][C]23.2438294462998[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]213.347222222222[/C][C]8.62737481134642[/C][C]24.729100901196[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]207.347222222222[/C][C]7.41665109778981[/C][C]27.9569875255441[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]207.819444444444[/C][C]7.28766527067307[/C][C]28.5166012331479[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]206.819444444444[/C][C]6.96920137159067[/C][C]29.6762044052172[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]203.125[/C][C]6.12298759697225[/C][C]33.1741648636432[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]200.347222222222[/C][C]5.51900116988867[/C][C]36.3013552733608[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]198.888888888889[/C][C]5.29144922312312[/C][C]37.5868463444313[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]195.527777777778[/C][C]4.02457106173023[/C][C]48.5835073548726[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]192.652777777778[/C][C]3.61753033337932[/C][C]53.2553316830963[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]192.319444444444[/C][C]3.48396878477772[/C][C]55.2012536061556[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]468[/C][C]90.7061371277016[/C][C]5.15951858186973[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]428.455882352941[/C][C]81.3612847906466[/C][C]5.2660904194841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]388.621212121212[/C][C]70.3942800877195[/C][C]5.52063621699014[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]351.96875[/C][C]59.3606393190978[/C][C]5.92932882861931[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]317.112903225806[/C][C]46.8887039469058[/C][C]6.76309807123029[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]291[/C][C]38.0449258664121[/C][C]7.64885180803859[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]275.344827586207[/C][C]34.4721105761833[/C][C]7.98746647605737[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]259.803571428571[/C][C]30.4480440977492[/C][C]8.53268507476239[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]244.074074074074[/C][C]25.551893619485[/C][C]9.55209338723733[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]230.615384615385[/C][C]21.1925944307795[/C][C]10.881885432604[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]216.94[/C][C]15.1643623576557[/C][C]14.3059097958364[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]206.270833333333[/C][C]9.34365277331864[/C][C]22.0760379626212[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]203.608695652174[/C][C]8.62590628219702[/C][C]23.6043250403035[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]201.204545454545[/C][C]7.96686979425811[/C][C]25.2551567492113[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]199.309523809524[/C][C]7.44905173639389[/C][C]26.7563618649278[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]197.625[/C][C]6.95661348314294[/C][C]28.4082190966738[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]196.473684210526[/C][C]6.64928544510224[/C][C]29.5480899162249[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]195.138888888889[/C][C]6.251368456888[/C][C]31.2153875162929[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]193.764705882353[/C][C]5.78677249171063[/C][C]33.4840718483256[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]192.65625[/C][C]5.41533243234638[/C][C]35.5760707965485[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]191.733333333333[/C][C]5.08794684181489[/C][C]37.6838318666359[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]190.857142857143[/C][C]4.68327946806121[/C][C]40.7528835634816[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]190.269230769231[/C][C]4.55582727176717[/C][C]41.7639255000611[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]189.958333333333[/C][C]4.49415045197912[/C][C]42.2679069966783[/C][/ROW]
[ROW][C]Median[/C][C]186[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1924[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]193.756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]195.138888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]193.756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]195.138888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]195.138888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]193.756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]195.138888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]196.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234114&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 Mean508.44444444444499.40686160891045.11478218118164
Geometric Mean263.533115155309
Harmonic Mean199.774875853158
Quadratic Mean979.856196932319
Winsorized Mean ( 1 / 24 )505.34722222222298.01703957394185.1557078689466
Winsorized Mean ( 2 / 24 )501.48611111111196.25934906336695.20973927198475
Winsorized Mean ( 3 / 24 )486.36111111111190.063478104315.40020351587817
Winsorized Mean ( 4 / 24 )472.02777777777884.42790993867355.59089734805289
Winsorized Mean ( 5 / 24 )425.91666666666767.38654683283016.32049996156152
Winsorized Mean ( 6 / 24 )366.66666666666748.04026007859877.63248712781244
Winsorized Mean ( 7 / 24 )359.95833333333346.02930548061937.82019910087269
Winsorized Mean ( 8 / 24 )354.18055555555644.2326786624388.0072147169401
Winsorized Mean ( 9 / 24 )331.55555555555637.86777862015098.75561143634451
Winsorized Mean ( 10 / 24 )325.58333333333336.27044644889978.97654606463246
Winsorized Mean ( 11 / 24 )295.18055555555628.297314349062810.4313982561858
Winsorized Mean ( 12 / 24 )226.68055555555611.518947892886519.6789288104639
Winsorized Mean ( 13 / 24 )222.70833333333310.518528950907521.1729543525303
Winsorized Mean ( 14 / 24 )216.6805555555569.3220678656308723.2438294462998
Winsorized Mean ( 15 / 24 )213.3472222222228.6273748113464224.729100901196
Winsorized Mean ( 16 / 24 )207.3472222222227.4166510977898127.9569875255441
Winsorized Mean ( 17 / 24 )207.8194444444447.2876652706730728.5166012331479
Winsorized Mean ( 18 / 24 )206.8194444444446.9692013715906729.6762044052172
Winsorized Mean ( 19 / 24 )203.1256.1229875969722533.1741648636432
Winsorized Mean ( 20 / 24 )200.3472222222225.5190011698886736.3013552733608
Winsorized Mean ( 21 / 24 )198.8888888888895.2914492231231237.5868463444313
Winsorized Mean ( 22 / 24 )195.5277777777784.0245710617302348.5835073548726
Winsorized Mean ( 23 / 24 )192.6527777777783.6175303333793253.2553316830963
Winsorized Mean ( 24 / 24 )192.3194444444443.4839687847777255.2012536061556
Trimmed Mean ( 1 / 24 )46890.70613712770165.15951858186973
Trimmed Mean ( 2 / 24 )428.45588235294181.36128479064665.2660904194841
Trimmed Mean ( 3 / 24 )388.62121212121270.39428008771955.52063621699014
Trimmed Mean ( 4 / 24 )351.9687559.36063931909785.92932882861931
Trimmed Mean ( 5 / 24 )317.11290322580646.88870394690586.76309807123029
Trimmed Mean ( 6 / 24 )29138.04492586641217.64885180803859
Trimmed Mean ( 7 / 24 )275.34482758620734.47211057618337.98746647605737
Trimmed Mean ( 8 / 24 )259.80357142857130.44804409774928.53268507476239
Trimmed Mean ( 9 / 24 )244.07407407407425.5518936194859.55209338723733
Trimmed Mean ( 10 / 24 )230.61538461538521.192594430779510.881885432604
Trimmed Mean ( 11 / 24 )216.9415.164362357655714.3059097958364
Trimmed Mean ( 12 / 24 )206.2708333333339.3436527733186422.0760379626212
Trimmed Mean ( 13 / 24 )203.6086956521748.6259062821970223.6043250403035
Trimmed Mean ( 14 / 24 )201.2045454545457.9668697942581125.2551567492113
Trimmed Mean ( 15 / 24 )199.3095238095247.4490517363938926.7563618649278
Trimmed Mean ( 16 / 24 )197.6256.9566134831429428.4082190966738
Trimmed Mean ( 17 / 24 )196.4736842105266.6492854451022429.5480899162249
Trimmed Mean ( 18 / 24 )195.1388888888896.25136845688831.2153875162929
Trimmed Mean ( 19 / 24 )193.7647058823535.7867724917106333.4840718483256
Trimmed Mean ( 20 / 24 )192.656255.4153324323463835.5760707965485
Trimmed Mean ( 21 / 24 )191.7333333333335.0879468418148937.6838318666359
Trimmed Mean ( 22 / 24 )190.8571428571434.6832794680612140.7528835634816
Trimmed Mean ( 23 / 24 )190.2692307692314.5558272717671741.7639255000611
Trimmed Mean ( 24 / 24 )189.9583333333334.4941504519791242.2679069966783
Median186
Midrange1924
Midmean - Weighted Average at Xnp193.756756756757
Midmean - Weighted Average at X(n+1)p195.138888888889
Midmean - Empirical Distribution Function193.756756756757
Midmean - Empirical Distribution Function - Averaging195.138888888889
Midmean - Empirical Distribution Function - Interpolation195.138888888889
Midmean - Closest Observation193.756756756757
Midmean - True Basic - Statistics Graphics Toolkit195.138888888889
Midmean - MS Excel (old versions)196.473684210526
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')