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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 computationTue, 15 Nov 2011 05:41:32 -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/2011/Nov/15/t1321353715cs9ni7u6j0suyxu.htm/, Retrieved Fri, 26 Apr 2024 16:01:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142691, Retrieved Fri, 26 Apr 2024 16:01:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R  D      [Central Tendency] [] [2011-11-15 10:41:32] [ce4468323d272130d499477f5e05a6d2] [Current]
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Dataseries X:
138900
136400
133900
130400
133200
132500
130400
132000
131400
133300
129700
129500
134257
133802
134542
132423
135853
135676
137311
139515
138554
139560
136171
137454
142388
143616
140197
148011
152637
152341
159219
161478
163350
166044
160925
163439
165411
160522
159302
151933
156735
156254
158051
157038
154626
153093
147274
150847
157165
157384
152655
154088
156583
156608
159543
162916
167167
172470
167473
164832
174144
177945
180962
179105
185076
183863
189329
191268
190450




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142691&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142691&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean152644.5652173912044.7798820871974.6508543802673
Geometric Mean151736.5869925
Harmonic Mean150853.499489888
Quadratic Mean153573.043775616
Winsorized Mean ( 1 / 23 )152635.6086956522041.0375908436274.783340287507
Winsorized Mean ( 2 / 23 )152623.4057971012028.9779846301375.2218146048163
Winsorized Mean ( 3 / 23 )152438.4927536231981.9652646186376.9127973506413
Winsorized Mean ( 4 / 23 )152426.1449275361955.8153613618277.9348336958572
Winsorized Mean ( 5 / 23 )152259.4057971011900.7628166875980.1043688672529
Winsorized Mean ( 6 / 23 )152134.7101449281859.8582685898181.7990879811933
Winsorized Mean ( 7 / 23 )152024.840579711833.8573922331782.8989436275536
Winsorized Mean ( 8 / 23 )151665.3043478261733.2128295180487.5052975404064
Winsorized Mean ( 9 / 23 )1514601690.3725351998389.6015504547318
Winsorized Mean ( 10 / 23 )150808.5507246381555.1526952680396.9734683825667
Winsorized Mean ( 11 / 23 )150775.3913043481544.992332342897.5897343617977
Winsorized Mean ( 12 / 23 )150642.1739130431505.09744439256100.087987308915
Winsorized Mean ( 13 / 23 )150576.6086956521478.74572554201101.827248657277
Winsorized Mean ( 14 / 23 )150689.2173913041425.33256598042105.722145826124
Winsorized Mean ( 15 / 23 )150424.8695652171376.1880129935109.305464184368
Winsorized Mean ( 16 / 23 )150477.9710144931361.88139495249110.492713662295
Winsorized Mean ( 17 / 23 )150427.4637681161338.40688730465112.392924151081
Winsorized Mean ( 18 / 23 )150289.9855072461251.53263440977120.0847515879
Winsorized Mean ( 19 / 23 )150177.0869565221225.69512451179122.524014294614
Winsorized Mean ( 20 / 23 )150379.1159420291162.47131555078129.361571275227
Winsorized Mean ( 21 / 23 )150186.4637681161109.10245091421135.412615529178
Winsorized Mean ( 22 / 23 )150305.7101449281070.37701668326140.423147920977
Winsorized Mean ( 23 / 23 )150293.0434782611064.73807889824141.154943602449
Trimmed Mean ( 1 / 23 )152413.5373134331994.2715757244276.4256679825909
Trimmed Mean ( 2 / 23 )152177.81937.7655700375878.5326163045866
Trimmed Mean ( 3 / 23 )151933.7777777781877.0650411443880.9422020268137
Trimmed Mean ( 4 / 23 )151743.4754098361825.590405525583.1202196015905
Trimmed Mean ( 5 / 23 )151543.8813559321772.4187875103285.5011707299734
Trimmed Mean ( 6 / 23 )151370.6491228071725.2551646466387.7381225830506
Trimmed Mean ( 7 / 23 )151210.8909090911678.8838894508890.0663183792583
Trimmed Mean ( 8 / 23 )151059.5094339621628.1015076830392.7826113550723
Trimmed Mean ( 9 / 23 )150957.0588235291590.7795759144394.8950194666379
Trimmed Mean ( 10 / 23 )150878.3673469391553.7556460823897.1055955467394
Trimmed Mean ( 11 / 23 )150878.3673469391537.5514324868298.1289888318791
Trimmed Mean ( 12 / 23 )150904.41517.1572930712299.4652305922218
Trimmed Mean ( 13 / 23 )150939.4651162791497.70974894359100.780184693826
Trimmed Mean ( 14 / 23 )150986.439024391475.96769416062102.296574390983
Trimmed Mean ( 15 / 23 )1510241457.11158369613103.646146039764
Trimmed Mean ( 16 / 23 )151098.4864864861440.00317119981104.929273426941
Trimmed Mean ( 17 / 23 )151174.9428571431416.85927196127106.697218170356
Trimmed Mean ( 18 / 23 )151266.8787878791387.33552516662109.034098849095
Trimmed Mean ( 19 / 23 )151387.6774193551365.07794128346110.90039098941
Trimmed Mean ( 20 / 23 )151539.2758620691335.02586264551113.510367178787
Trimmed Mean ( 21 / 23 )151687.5185185191305.98158210332116.1482830977
Trimmed Mean ( 22 / 23 )151687.5185185191272.21623031097119.23092545474
Trimmed Mean ( 23 / 23 )152100.1304347831227.18485373418123.942313965137
Median153093
Midrange160384
Midmean - Weighted Average at Xnp150829.617647059
Midmean - Weighted Average at X(n+1)p151174.942857143
Midmean - Empirical Distribution Function151174.942857143
Midmean - Empirical Distribution Function - Averaging151174.942857143
Midmean - Empirical Distribution Function - Interpolation151174.942857143
Midmean - Closest Observation150758.166666667
Midmean - True Basic - Statistics Graphics Toolkit151174.942857143
Midmean - MS Excel (old versions)151174.942857143
Number of observations69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 152644.565217391 & 2044.77988208719 & 74.6508543802673 \tabularnewline
Geometric Mean & 151736.5869925 &  &  \tabularnewline
Harmonic Mean & 150853.499489888 &  &  \tabularnewline
Quadratic Mean & 153573.043775616 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 152635.608695652 & 2041.03759084362 & 74.783340287507 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 152623.405797101 & 2028.97798463013 & 75.2218146048163 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 152438.492753623 & 1981.96526461863 & 76.9127973506413 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 152426.144927536 & 1955.81536136182 & 77.9348336958572 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 152259.405797101 & 1900.76281668759 & 80.1043688672529 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 152134.710144928 & 1859.85826858981 & 81.7990879811933 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 152024.84057971 & 1833.85739223317 & 82.8989436275536 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 151665.304347826 & 1733.21282951804 & 87.5052975404064 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 151460 & 1690.37253519983 & 89.6015504547318 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 150808.550724638 & 1555.15269526803 & 96.9734683825667 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 150775.391304348 & 1544.9923323428 & 97.5897343617977 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 150642.173913043 & 1505.09744439256 & 100.087987308915 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 150576.608695652 & 1478.74572554201 & 101.827248657277 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 150689.217391304 & 1425.33256598042 & 105.722145826124 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 150424.869565217 & 1376.1880129935 & 109.305464184368 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 150477.971014493 & 1361.88139495249 & 110.492713662295 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 150427.463768116 & 1338.40688730465 & 112.392924151081 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 150289.985507246 & 1251.53263440977 & 120.0847515879 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 150177.086956522 & 1225.69512451179 & 122.524014294614 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 150379.115942029 & 1162.47131555078 & 129.361571275227 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 150186.463768116 & 1109.10245091421 & 135.412615529178 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 150305.710144928 & 1070.37701668326 & 140.423147920977 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 150293.043478261 & 1064.73807889824 & 141.154943602449 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 152413.537313433 & 1994.27157572442 & 76.4256679825909 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 152177.8 & 1937.76557003758 & 78.5326163045866 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 151933.777777778 & 1877.06504114438 & 80.9422020268137 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 151743.475409836 & 1825.5904055255 & 83.1202196015905 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 151543.881355932 & 1772.41878751032 & 85.5011707299734 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 151370.649122807 & 1725.25516464663 & 87.7381225830506 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 151210.890909091 & 1678.88388945088 & 90.0663183792583 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 151059.509433962 & 1628.10150768303 & 92.7826113550723 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 150957.058823529 & 1590.77957591443 & 94.8950194666379 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 150878.367346939 & 1553.75564608238 & 97.1055955467394 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 150878.367346939 & 1537.55143248682 & 98.1289888318791 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 150904.4 & 1517.15729307122 & 99.4652305922218 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 150939.465116279 & 1497.70974894359 & 100.780184693826 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 150986.43902439 & 1475.96769416062 & 102.296574390983 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 151024 & 1457.11158369613 & 103.646146039764 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 151098.486486486 & 1440.00317119981 & 104.929273426941 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 151174.942857143 & 1416.85927196127 & 106.697218170356 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 151266.878787879 & 1387.33552516662 & 109.034098849095 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 151387.677419355 & 1365.07794128346 & 110.90039098941 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 151539.275862069 & 1335.02586264551 & 113.510367178787 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 151687.518518519 & 1305.98158210332 & 116.1482830977 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 151687.518518519 & 1272.21623031097 & 119.23092545474 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 152100.130434783 & 1227.18485373418 & 123.942313965137 \tabularnewline
Median & 153093 &  &  \tabularnewline
Midrange & 160384 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 150829.617647059 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 151174.942857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 151174.942857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 151174.942857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 151174.942857143 &  &  \tabularnewline
Midmean - Closest Observation & 150758.166666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 151174.942857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 151174.942857143 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142691&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]152644.565217391[/C][C]2044.77988208719[/C][C]74.6508543802673[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]151736.5869925[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]150853.499489888[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]153573.043775616[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]152635.608695652[/C][C]2041.03759084362[/C][C]74.783340287507[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]152623.405797101[/C][C]2028.97798463013[/C][C]75.2218146048163[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]152438.492753623[/C][C]1981.96526461863[/C][C]76.9127973506413[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]152426.144927536[/C][C]1955.81536136182[/C][C]77.9348336958572[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]152259.405797101[/C][C]1900.76281668759[/C][C]80.1043688672529[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]152134.710144928[/C][C]1859.85826858981[/C][C]81.7990879811933[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]152024.84057971[/C][C]1833.85739223317[/C][C]82.8989436275536[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]151665.304347826[/C][C]1733.21282951804[/C][C]87.5052975404064[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]151460[/C][C]1690.37253519983[/C][C]89.6015504547318[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]150808.550724638[/C][C]1555.15269526803[/C][C]96.9734683825667[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]150775.391304348[/C][C]1544.9923323428[/C][C]97.5897343617977[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]150642.173913043[/C][C]1505.09744439256[/C][C]100.087987308915[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]150576.608695652[/C][C]1478.74572554201[/C][C]101.827248657277[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]150689.217391304[/C][C]1425.33256598042[/C][C]105.722145826124[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]150424.869565217[/C][C]1376.1880129935[/C][C]109.305464184368[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]150477.971014493[/C][C]1361.88139495249[/C][C]110.492713662295[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]150427.463768116[/C][C]1338.40688730465[/C][C]112.392924151081[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]150289.985507246[/C][C]1251.53263440977[/C][C]120.0847515879[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]150177.086956522[/C][C]1225.69512451179[/C][C]122.524014294614[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]150379.115942029[/C][C]1162.47131555078[/C][C]129.361571275227[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]150186.463768116[/C][C]1109.10245091421[/C][C]135.412615529178[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]150305.710144928[/C][C]1070.37701668326[/C][C]140.423147920977[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]150293.043478261[/C][C]1064.73807889824[/C][C]141.154943602449[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]152413.537313433[/C][C]1994.27157572442[/C][C]76.4256679825909[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]152177.8[/C][C]1937.76557003758[/C][C]78.5326163045866[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]151933.777777778[/C][C]1877.06504114438[/C][C]80.9422020268137[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]151743.475409836[/C][C]1825.5904055255[/C][C]83.1202196015905[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]151543.881355932[/C][C]1772.41878751032[/C][C]85.5011707299734[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]151370.649122807[/C][C]1725.25516464663[/C][C]87.7381225830506[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]151210.890909091[/C][C]1678.88388945088[/C][C]90.0663183792583[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]151059.509433962[/C][C]1628.10150768303[/C][C]92.7826113550723[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]150957.058823529[/C][C]1590.77957591443[/C][C]94.8950194666379[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]150878.367346939[/C][C]1553.75564608238[/C][C]97.1055955467394[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]150878.367346939[/C][C]1537.55143248682[/C][C]98.1289888318791[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]150904.4[/C][C]1517.15729307122[/C][C]99.4652305922218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]150939.465116279[/C][C]1497.70974894359[/C][C]100.780184693826[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]150986.43902439[/C][C]1475.96769416062[/C][C]102.296574390983[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]151024[/C][C]1457.11158369613[/C][C]103.646146039764[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]151098.486486486[/C][C]1440.00317119981[/C][C]104.929273426941[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]151174.942857143[/C][C]1416.85927196127[/C][C]106.697218170356[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]151266.878787879[/C][C]1387.33552516662[/C][C]109.034098849095[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]151387.677419355[/C][C]1365.07794128346[/C][C]110.90039098941[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]151539.275862069[/C][C]1335.02586264551[/C][C]113.510367178787[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]151687.518518519[/C][C]1305.98158210332[/C][C]116.1482830977[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]151687.518518519[/C][C]1272.21623031097[/C][C]119.23092545474[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]152100.130434783[/C][C]1227.18485373418[/C][C]123.942313965137[/C][/ROW]
[ROW][C]Median[/C][C]153093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]160384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]150829.617647059[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]150758.166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]151174.942857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142691&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 Mean152644.5652173912044.7798820871974.6508543802673
Geometric Mean151736.5869925
Harmonic Mean150853.499489888
Quadratic Mean153573.043775616
Winsorized Mean ( 1 / 23 )152635.6086956522041.0375908436274.783340287507
Winsorized Mean ( 2 / 23 )152623.4057971012028.9779846301375.2218146048163
Winsorized Mean ( 3 / 23 )152438.4927536231981.9652646186376.9127973506413
Winsorized Mean ( 4 / 23 )152426.1449275361955.8153613618277.9348336958572
Winsorized Mean ( 5 / 23 )152259.4057971011900.7628166875980.1043688672529
Winsorized Mean ( 6 / 23 )152134.7101449281859.8582685898181.7990879811933
Winsorized Mean ( 7 / 23 )152024.840579711833.8573922331782.8989436275536
Winsorized Mean ( 8 / 23 )151665.3043478261733.2128295180487.5052975404064
Winsorized Mean ( 9 / 23 )1514601690.3725351998389.6015504547318
Winsorized Mean ( 10 / 23 )150808.5507246381555.1526952680396.9734683825667
Winsorized Mean ( 11 / 23 )150775.3913043481544.992332342897.5897343617977
Winsorized Mean ( 12 / 23 )150642.1739130431505.09744439256100.087987308915
Winsorized Mean ( 13 / 23 )150576.6086956521478.74572554201101.827248657277
Winsorized Mean ( 14 / 23 )150689.2173913041425.33256598042105.722145826124
Winsorized Mean ( 15 / 23 )150424.8695652171376.1880129935109.305464184368
Winsorized Mean ( 16 / 23 )150477.9710144931361.88139495249110.492713662295
Winsorized Mean ( 17 / 23 )150427.4637681161338.40688730465112.392924151081
Winsorized Mean ( 18 / 23 )150289.9855072461251.53263440977120.0847515879
Winsorized Mean ( 19 / 23 )150177.0869565221225.69512451179122.524014294614
Winsorized Mean ( 20 / 23 )150379.1159420291162.47131555078129.361571275227
Winsorized Mean ( 21 / 23 )150186.4637681161109.10245091421135.412615529178
Winsorized Mean ( 22 / 23 )150305.7101449281070.37701668326140.423147920977
Winsorized Mean ( 23 / 23 )150293.0434782611064.73807889824141.154943602449
Trimmed Mean ( 1 / 23 )152413.5373134331994.2715757244276.4256679825909
Trimmed Mean ( 2 / 23 )152177.81937.7655700375878.5326163045866
Trimmed Mean ( 3 / 23 )151933.7777777781877.0650411443880.9422020268137
Trimmed Mean ( 4 / 23 )151743.4754098361825.590405525583.1202196015905
Trimmed Mean ( 5 / 23 )151543.8813559321772.4187875103285.5011707299734
Trimmed Mean ( 6 / 23 )151370.6491228071725.2551646466387.7381225830506
Trimmed Mean ( 7 / 23 )151210.8909090911678.8838894508890.0663183792583
Trimmed Mean ( 8 / 23 )151059.5094339621628.1015076830392.7826113550723
Trimmed Mean ( 9 / 23 )150957.0588235291590.7795759144394.8950194666379
Trimmed Mean ( 10 / 23 )150878.3673469391553.7556460823897.1055955467394
Trimmed Mean ( 11 / 23 )150878.3673469391537.5514324868298.1289888318791
Trimmed Mean ( 12 / 23 )150904.41517.1572930712299.4652305922218
Trimmed Mean ( 13 / 23 )150939.4651162791497.70974894359100.780184693826
Trimmed Mean ( 14 / 23 )150986.439024391475.96769416062102.296574390983
Trimmed Mean ( 15 / 23 )1510241457.11158369613103.646146039764
Trimmed Mean ( 16 / 23 )151098.4864864861440.00317119981104.929273426941
Trimmed Mean ( 17 / 23 )151174.9428571431416.85927196127106.697218170356
Trimmed Mean ( 18 / 23 )151266.8787878791387.33552516662109.034098849095
Trimmed Mean ( 19 / 23 )151387.6774193551365.07794128346110.90039098941
Trimmed Mean ( 20 / 23 )151539.2758620691335.02586264551113.510367178787
Trimmed Mean ( 21 / 23 )151687.5185185191305.98158210332116.1482830977
Trimmed Mean ( 22 / 23 )151687.5185185191272.21623031097119.23092545474
Trimmed Mean ( 23 / 23 )152100.1304347831227.18485373418123.942313965137
Median153093
Midrange160384
Midmean - Weighted Average at Xnp150829.617647059
Midmean - Weighted Average at X(n+1)p151174.942857143
Midmean - Empirical Distribution Function151174.942857143
Midmean - Empirical Distribution Function - Averaging151174.942857143
Midmean - Empirical Distribution Function - Interpolation151174.942857143
Midmean - Closest Observation150758.166666667
Midmean - True Basic - Statistics Graphics Toolkit151174.942857143
Midmean - MS Excel (old versions)151174.942857143
Number of observations69



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')