Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Aug 2015 11:36:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/13/t1439462345628mfj1w1feunba.htm/, Retrieved Thu, 16 May 2024 10:20:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280033, Retrieved Thu, 16 May 2024 10:20:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-08-13 10:36:14] [70e23d918d09c907c02097a361cd6415] [Current]
Feedback Forum

Post a new message
Dataseries X:
209704,00
208923,00
208131,00
206492,00
222706,00
221848,00
209704,00
201630,00
202411,00
202411,00
203280,00
204842,00
207273,00
207273,00
205711,00
201630,00
222706,00
225918,00
221067,00
209704,00
214566,00
207273,00
210562,00
212135,00
213774,00
209704,00
210562,00
204842,00
222706,00
228349,00
223498,00
214566,00
224279,00
213774,00
223498,00
222706,00
225137,00
216205,00
225918,00
225137,00
239712,00
236423,00
223498,00
216986,00
225918,00
213774,00
222706,00
224279,00
227568,00
220286,00
224279,00
226710,00
235642,00
228349,00
218636,00
208131,00
217855,00
191125,00
204061,00
211343,00
218636,00
208131,00
208131,00
208131,00
213774,00
205711,00
195129,00
186274,00
192698,00
167618,00
182985,00
191917,00
193556,00
184624,00
185405,00
182985,00
191125,00
185405,00
174130,00
165979,00
179762,00
149831,00
169268,00
178123,00
178123,00
167618,00
157905,00
157124,00
165979,00
157905,00
142549,00
131967,00
143330,00
116611,00
140899,00
153824,00
157905,00
148973,00
137687,00
145761,00
148973,00
146542,00
122243,00
110968,00
119031,00
94743,00
119823,00
128755,00
136037,00
123893,00
112530,00
119031,00
122243,00
115819,00
91531,00
80949,00
90662,00
63943,00
93093,00
110968,00
















































































































Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=280033&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=280033&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280033&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean184542.5083333333808.5153101867148.4552360442753
Geometric Mean178771.045595015
Harmonic Mean171632.613376675
Quadratic Mean189161.326008362
Winsorized Mean ( 1 / 40 )184656.8166666673770.0175648229148.9803597706422
Winsorized Mean ( 2 / 40 )184805.6833333333732.6477607376749.5106142286543
Winsorized Mean ( 3 / 40 )184645.0833333333708.5878468965749.7885154555119
Winsorized Mean ( 4 / 40 )184697.153697.6753674897349.949530892807
Winsorized Mean ( 5 / 40 )184733.3583333333680.2499625631750.195872620748
Winsorized Mean ( 6 / 40 )185501.7083333333520.2761347515652.6952151571556
Winsorized Mean ( 7 / 40 )185455.5083333333515.7697001244552.7496179077853
Winsorized Mean ( 8 / 40 )185559.6416666673497.3631135085953.0570134253264
Winsorized Mean ( 9 / 40 )185806.3166666673454.7198171463453.7833244086769
Winsorized Mean ( 10 / 40 )185807.2333333333437.2149710551454.0574956463358
Winsorized Mean ( 11 / 40 )186029.0666666673400.0824613853654.7131043965531
Winsorized Mean ( 12 / 40 )185943.2666666673391.8613193594154.8204213436957
Winsorized Mean ( 13 / 40 )186029.0666666673377.6831960371655.0759369276917
Winsorized Mean ( 14 / 40 )186311.43331.6154061688855.9222411011254
Winsorized Mean ( 15 / 40 )186213.7753322.3374695460156.049024732411
Winsorized Mean ( 16 / 40 )186433.7753286.9498569935256.7193851781255
Winsorized Mean ( 17 / 40 )187122.5583333333178.7120684291358.8674136899119
Winsorized Mean ( 18 / 40 )187485.5583333333093.8066586792360.6002827640731
Winsorized Mean ( 19 / 40 )188129.9752998.1485206983362.7487176506454
Winsorized Mean ( 20 / 40 )188404.9752958.2606751829263.687752935549
Winsorized Mean ( 21 / 40 )188967.0752878.313292483465.6520176220844
Winsorized Mean ( 22 / 40 )189269.5752836.1475751977566.7347413989215
Winsorized Mean ( 23 / 40 )189254.8166666672799.2757510952667.608493587178
Winsorized Mean ( 24 / 40 )189584.8166666672717.5635793815169.7627897669331
Winsorized Mean ( 25 / 40 )189584.8166666672679.8052545359670.7457440594859
Winsorized Mean ( 26 / 40 )189754.0333333332575.1380693704973.686935698838
Winsorized Mean ( 27 / 40 )189754.0333333332575.1380693704973.686935698838
Winsorized Mean ( 28 / 40 )1897722531.4617397693374.965383445729
Winsorized Mean ( 29 / 40 )190526.9666666672385.4843473431679.8693007056896
Winsorized Mean ( 30 / 40 )191156.7166666672261.7758893610984.5162058565692
Winsorized Mean ( 31 / 40 )190935.0666666672197.436109679986.8899285970505
Winsorized Mean ( 32 / 40 )190935.0666666672197.436109679986.8899285970505
Winsorized Mean ( 33 / 40 )190717.2666666672177.9061632965587.5690926821156
Winsorized Mean ( 34 / 40 )193004.91895.50988862394101.822154111849
Winsorized Mean ( 35 / 40 )193004.91895.50988862394101.822154111849
Winsorized Mean ( 36 / 40 )193496.61836.94308580211105.336197672944
Winsorized Mean ( 37 / 40 )192991.2416666671790.79583567459107.768422185306
Winsorized Mean ( 38 / 40 )193262.9416666671706.38053296758113.258993485211
Winsorized Mean ( 39 / 40 )194589.2666666671499.60398449951129.760435873749
Winsorized Mean ( 40 / 40 )195920.2666666671349.41380133952145.189167675759
Trimmed Mean ( 1 / 40 )1850973704.8913330233949.9601697761405
Trimmed Mean ( 2 / 40 )185552.3620689663632.2618737158651.0845221297721
Trimmed Mean ( 3 / 40 )185945.3508771933573.1343098604952.0398436644418
Trimmed Mean ( 4 / 40 )186409.7321428573516.507339861153.0099084480285
Trimmed Mean ( 5 / 40 )186876.83456.4008012259854.0668778729929
Trimmed Mean ( 6 / 40 )187353.120370373393.4365529798355.2104385761545
Trimmed Mean ( 7 / 40 )187702.4433962263360.2976526076455.8588740644944
Trimmed Mean ( 8 / 40 )188072.8173076923323.3822303187556.5907874188922
Trimmed Mean ( 9 / 40 )188442.4019607843284.8305913742857.3674643848057
Trimmed Mean ( 10 / 40 )188793.883248.4464247390658.11820646393
Trimmed Mean ( 11 / 40 )189159.5918367353209.5695029790758.9361257518055
Trimmed Mean ( 12 / 40 )189515.3333333333170.9336697360159.7664136409107
Trimmed Mean ( 13 / 40 )189895.3404255323127.5382482175860.7171920387403
Trimmed Mean ( 14 / 40 )190283.2608695653079.6796418357761.7867060861366
Trimmed Mean ( 15 / 40 )190661.5333333333031.3706211047362.896147375028
Trimmed Mean ( 16 / 40 )191065.8752976.5681539980164.1899883069594
Trimmed Mean ( 17 / 40 )191469.8372093022918.2609751786265.6109370744619
Trimmed Mean ( 18 / 40 )191835.1547619052866.3978556884366.9255157239262
Trimmed Mean ( 19 / 40 )192188.7804878052817.7648369425168.2061107329114
Trimmed Mean ( 20 / 40 )192509.21252774.3058641309269.3900463495959
Trimmed Mean ( 21 / 40 )192824.9230769232728.6698906642370.6662699422335
Trimmed Mean ( 22 / 40 )193114.9868421052685.9914505548771.8970966203977
Trimmed Mean ( 23 / 40 )193398.4324324322641.2150343147473.2232816789979
Trimmed Mean ( 24 / 40 )193698.6944444442592.639074524474.7110140966987
Trimmed Mean ( 25 / 40 )193992.5428571432546.0005960459976.1950107782451
Trimmed Mean ( 26 / 40 )194303.6764705882494.9093188755977.8800555998392
Trimmed Mean ( 27 / 40 )194621.8333333332447.8495098043979.5072705874333
Trimmed Mean ( 28 / 40 )194959.8752390.3394453379481.5615854811939
Trimmed Mean ( 29 / 40 )195318.4838709682326.4143474211183.9568772809036
Trimmed Mean ( 30 / 40 )195648.9333333332271.8573747042686.1184929616466
Trimmed Mean ( 31 / 40 )195958.741379312224.4611582089188.0926783801846
Trimmed Mean ( 32 / 40 )1963062174.0626929454390.2945442360006
Trimmed Mean ( 33 / 40 )196678.9814814812110.0234187649193.2117528802624
Trimmed Mean ( 34 / 40 )197095.8846153852030.823351230297.0522052033681
Trimmed Mean ( 35 / 40 )197384.661988.4261150950199.2667811499592
Trimmed Mean ( 36 / 40 )197697.51932.74329916339102.288545036258
Trimmed Mean ( 37 / 40 )198001.9130434781872.73697218315105.728629265356
Trimmed Mean ( 38 / 40 )198371.251800.11440326041110.199246026089
Trimmed Mean ( 39 / 40 )198755.3333333331722.5359363095115.385304389737
Trimmed Mean ( 40 / 40 )199075.81671.6883785179119.086668638864
Median203670.5
Midrange151827.5
Midmean - Weighted Average at Xnp194963.278688525
Midmean - Weighted Average at X(n+1)p195648.933333333
Midmean - Empirical Distribution Function194963.278688525
Midmean - Empirical Distribution Function - Averaging195648.933333333
Midmean - Empirical Distribution Function - Interpolation195648.933333333
Midmean - Closest Observation194963.278688525
Midmean - True Basic - Statistics Graphics Toolkit195648.933333333
Midmean - MS Excel (old versions)195318.483870968
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 184542.508333333 & 3808.51531018671 & 48.4552360442753 \tabularnewline
Geometric Mean & 178771.045595015 &  &  \tabularnewline
Harmonic Mean & 171632.613376675 &  &  \tabularnewline
Quadratic Mean & 189161.326008362 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 184656.816666667 & 3770.01756482291 & 48.9803597706422 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 184805.683333333 & 3732.64776073767 & 49.5106142286543 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 184645.083333333 & 3708.58784689657 & 49.7885154555119 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 184697.15 & 3697.67536748973 & 49.949530892807 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 184733.358333333 & 3680.24996256317 & 50.195872620748 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 185501.708333333 & 3520.27613475156 & 52.6952151571556 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 185455.508333333 & 3515.76970012445 & 52.7496179077853 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 185559.641666667 & 3497.36311350859 & 53.0570134253264 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 185806.316666667 & 3454.71981714634 & 53.7833244086769 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 185807.233333333 & 3437.21497105514 & 54.0574956463358 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 186029.066666667 & 3400.08246138536 & 54.7131043965531 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 185943.266666667 & 3391.86131935941 & 54.8204213436957 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 186029.066666667 & 3377.68319603716 & 55.0759369276917 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 186311.4 & 3331.61540616888 & 55.9222411011254 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 186213.775 & 3322.33746954601 & 56.049024732411 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 186433.775 & 3286.94985699352 & 56.7193851781255 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 187122.558333333 & 3178.71206842913 & 58.8674136899119 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 187485.558333333 & 3093.80665867923 & 60.6002827640731 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 188129.975 & 2998.14852069833 & 62.7487176506454 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 188404.975 & 2958.26067518292 & 63.687752935549 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 188967.075 & 2878.3132924834 & 65.6520176220844 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 189269.575 & 2836.14757519775 & 66.7347413989215 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 189254.816666667 & 2799.27575109526 & 67.608493587178 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 189584.816666667 & 2717.56357938151 & 69.7627897669331 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 189584.816666667 & 2679.80525453596 & 70.7457440594859 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 189754.033333333 & 2575.13806937049 & 73.686935698838 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 189754.033333333 & 2575.13806937049 & 73.686935698838 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 189772 & 2531.46173976933 & 74.965383445729 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 190526.966666667 & 2385.48434734316 & 79.8693007056896 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 191156.716666667 & 2261.77588936109 & 84.5162058565692 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 190935.066666667 & 2197.4361096799 & 86.8899285970505 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 190935.066666667 & 2197.4361096799 & 86.8899285970505 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 190717.266666667 & 2177.90616329655 & 87.5690926821156 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 193004.9 & 1895.50988862394 & 101.822154111849 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 193004.9 & 1895.50988862394 & 101.822154111849 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 193496.6 & 1836.94308580211 & 105.336197672944 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 192991.241666667 & 1790.79583567459 & 107.768422185306 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 193262.941666667 & 1706.38053296758 & 113.258993485211 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 194589.266666667 & 1499.60398449951 & 129.760435873749 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 195920.266666667 & 1349.41380133952 & 145.189167675759 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 185097 & 3704.89133302339 & 49.9601697761405 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 185552.362068966 & 3632.26187371586 & 51.0845221297721 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 185945.350877193 & 3573.13430986049 & 52.0398436644418 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 186409.732142857 & 3516.5073398611 & 53.0099084480285 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 186876.8 & 3456.40080122598 & 54.0668778729929 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 187353.12037037 & 3393.43655297983 & 55.2104385761545 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 187702.443396226 & 3360.29765260764 & 55.8588740644944 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 188072.817307692 & 3323.38223031875 & 56.5907874188922 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 188442.401960784 & 3284.83059137428 & 57.3674643848057 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 188793.88 & 3248.44642473906 & 58.11820646393 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 189159.591836735 & 3209.56950297907 & 58.9361257518055 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 189515.333333333 & 3170.93366973601 & 59.7664136409107 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 189895.340425532 & 3127.53824821758 & 60.7171920387403 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 190283.260869565 & 3079.67964183577 & 61.7867060861366 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 190661.533333333 & 3031.37062110473 & 62.896147375028 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 191065.875 & 2976.56815399801 & 64.1899883069594 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 191469.837209302 & 2918.26097517862 & 65.6109370744619 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 191835.154761905 & 2866.39785568843 & 66.9255157239262 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 192188.780487805 & 2817.76483694251 & 68.2061107329114 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 192509.2125 & 2774.30586413092 & 69.3900463495959 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 192824.923076923 & 2728.66989066423 & 70.6662699422335 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 193114.986842105 & 2685.99145055487 & 71.8970966203977 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 193398.432432432 & 2641.21503431474 & 73.2232816789979 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 193698.694444444 & 2592.6390745244 & 74.7110140966987 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 193992.542857143 & 2546.00059604599 & 76.1950107782451 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 194303.676470588 & 2494.90931887559 & 77.8800555998392 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 194621.833333333 & 2447.84950980439 & 79.5072705874333 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 194959.875 & 2390.33944533794 & 81.5615854811939 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 195318.483870968 & 2326.41434742111 & 83.9568772809036 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 195648.933333333 & 2271.85737470426 & 86.1184929616466 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 195958.74137931 & 2224.46115820891 & 88.0926783801846 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 196306 & 2174.06269294543 & 90.2945442360006 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 196678.981481481 & 2110.02341876491 & 93.2117528802624 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 197095.884615385 & 2030.8233512302 & 97.0522052033681 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 197384.66 & 1988.42611509501 & 99.2667811499592 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 197697.5 & 1932.74329916339 & 102.288545036258 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 198001.913043478 & 1872.73697218315 & 105.728629265356 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 198371.25 & 1800.11440326041 & 110.199246026089 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 198755.333333333 & 1722.5359363095 & 115.385304389737 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 199075.8 & 1671.6883785179 & 119.086668638864 \tabularnewline
Median & 203670.5 &  &  \tabularnewline
Midrange & 151827.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 194963.278688525 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 195648.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 194963.278688525 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 195648.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 195648.933333333 &  &  \tabularnewline
Midmean - Closest Observation & 194963.278688525 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 195648.933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 195318.483870968 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280033&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]184542.508333333[/C][C]3808.51531018671[/C][C]48.4552360442753[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]178771.045595015[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]171632.613376675[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]189161.326008362[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]184656.816666667[/C][C]3770.01756482291[/C][C]48.9803597706422[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]184805.683333333[/C][C]3732.64776073767[/C][C]49.5106142286543[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]184645.083333333[/C][C]3708.58784689657[/C][C]49.7885154555119[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]184697.15[/C][C]3697.67536748973[/C][C]49.949530892807[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]184733.358333333[/C][C]3680.24996256317[/C][C]50.195872620748[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]185501.708333333[/C][C]3520.27613475156[/C][C]52.6952151571556[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]185455.508333333[/C][C]3515.76970012445[/C][C]52.7496179077853[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]185559.641666667[/C][C]3497.36311350859[/C][C]53.0570134253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]185806.316666667[/C][C]3454.71981714634[/C][C]53.7833244086769[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]185807.233333333[/C][C]3437.21497105514[/C][C]54.0574956463358[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]186029.066666667[/C][C]3400.08246138536[/C][C]54.7131043965531[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]185943.266666667[/C][C]3391.86131935941[/C][C]54.8204213436957[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]186029.066666667[/C][C]3377.68319603716[/C][C]55.0759369276917[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]186311.4[/C][C]3331.61540616888[/C][C]55.9222411011254[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]186213.775[/C][C]3322.33746954601[/C][C]56.049024732411[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]186433.775[/C][C]3286.94985699352[/C][C]56.7193851781255[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]187122.558333333[/C][C]3178.71206842913[/C][C]58.8674136899119[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]187485.558333333[/C][C]3093.80665867923[/C][C]60.6002827640731[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]188129.975[/C][C]2998.14852069833[/C][C]62.7487176506454[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]188404.975[/C][C]2958.26067518292[/C][C]63.687752935549[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]188967.075[/C][C]2878.3132924834[/C][C]65.6520176220844[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]189269.575[/C][C]2836.14757519775[/C][C]66.7347413989215[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]189254.816666667[/C][C]2799.27575109526[/C][C]67.608493587178[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]189584.816666667[/C][C]2717.56357938151[/C][C]69.7627897669331[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]189584.816666667[/C][C]2679.80525453596[/C][C]70.7457440594859[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]189754.033333333[/C][C]2575.13806937049[/C][C]73.686935698838[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]189754.033333333[/C][C]2575.13806937049[/C][C]73.686935698838[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]189772[/C][C]2531.46173976933[/C][C]74.965383445729[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]190526.966666667[/C][C]2385.48434734316[/C][C]79.8693007056896[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]191156.716666667[/C][C]2261.77588936109[/C][C]84.5162058565692[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]190935.066666667[/C][C]2197.4361096799[/C][C]86.8899285970505[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]190935.066666667[/C][C]2197.4361096799[/C][C]86.8899285970505[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]190717.266666667[/C][C]2177.90616329655[/C][C]87.5690926821156[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]193004.9[/C][C]1895.50988862394[/C][C]101.822154111849[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]193004.9[/C][C]1895.50988862394[/C][C]101.822154111849[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]193496.6[/C][C]1836.94308580211[/C][C]105.336197672944[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]192991.241666667[/C][C]1790.79583567459[/C][C]107.768422185306[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]193262.941666667[/C][C]1706.38053296758[/C][C]113.258993485211[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]194589.266666667[/C][C]1499.60398449951[/C][C]129.760435873749[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]195920.266666667[/C][C]1349.41380133952[/C][C]145.189167675759[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]185097[/C][C]3704.89133302339[/C][C]49.9601697761405[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]185552.362068966[/C][C]3632.26187371586[/C][C]51.0845221297721[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]185945.350877193[/C][C]3573.13430986049[/C][C]52.0398436644418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]186409.732142857[/C][C]3516.5073398611[/C][C]53.0099084480285[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]186876.8[/C][C]3456.40080122598[/C][C]54.0668778729929[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]187353.12037037[/C][C]3393.43655297983[/C][C]55.2104385761545[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]187702.443396226[/C][C]3360.29765260764[/C][C]55.8588740644944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]188072.817307692[/C][C]3323.38223031875[/C][C]56.5907874188922[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]188442.401960784[/C][C]3284.83059137428[/C][C]57.3674643848057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]188793.88[/C][C]3248.44642473906[/C][C]58.11820646393[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]189159.591836735[/C][C]3209.56950297907[/C][C]58.9361257518055[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]189515.333333333[/C][C]3170.93366973601[/C][C]59.7664136409107[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]189895.340425532[/C][C]3127.53824821758[/C][C]60.7171920387403[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]190283.260869565[/C][C]3079.67964183577[/C][C]61.7867060861366[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]190661.533333333[/C][C]3031.37062110473[/C][C]62.896147375028[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]191065.875[/C][C]2976.56815399801[/C][C]64.1899883069594[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]191469.837209302[/C][C]2918.26097517862[/C][C]65.6109370744619[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]191835.154761905[/C][C]2866.39785568843[/C][C]66.9255157239262[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]192188.780487805[/C][C]2817.76483694251[/C][C]68.2061107329114[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]192509.2125[/C][C]2774.30586413092[/C][C]69.3900463495959[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]192824.923076923[/C][C]2728.66989066423[/C][C]70.6662699422335[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]193114.986842105[/C][C]2685.99145055487[/C][C]71.8970966203977[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]193398.432432432[/C][C]2641.21503431474[/C][C]73.2232816789979[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]193698.694444444[/C][C]2592.6390745244[/C][C]74.7110140966987[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]193992.542857143[/C][C]2546.00059604599[/C][C]76.1950107782451[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]194303.676470588[/C][C]2494.90931887559[/C][C]77.8800555998392[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]194621.833333333[/C][C]2447.84950980439[/C][C]79.5072705874333[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]194959.875[/C][C]2390.33944533794[/C][C]81.5615854811939[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]195318.483870968[/C][C]2326.41434742111[/C][C]83.9568772809036[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]195648.933333333[/C][C]2271.85737470426[/C][C]86.1184929616466[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]195958.74137931[/C][C]2224.46115820891[/C][C]88.0926783801846[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]196306[/C][C]2174.06269294543[/C][C]90.2945442360006[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]196678.981481481[/C][C]2110.02341876491[/C][C]93.2117528802624[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]197095.884615385[/C][C]2030.8233512302[/C][C]97.0522052033681[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]197384.66[/C][C]1988.42611509501[/C][C]99.2667811499592[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]197697.5[/C][C]1932.74329916339[/C][C]102.288545036258[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]198001.913043478[/C][C]1872.73697218315[/C][C]105.728629265356[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]198371.25[/C][C]1800.11440326041[/C][C]110.199246026089[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]198755.333333333[/C][C]1722.5359363095[/C][C]115.385304389737[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]199075.8[/C][C]1671.6883785179[/C][C]119.086668638864[/C][/ROW]
[ROW][C]Median[/C][C]203670.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]151827.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]194963.278688525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]195648.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]194963.278688525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]195648.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]195648.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]194963.278688525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]195648.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]195318.483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280033&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280033&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 Mean184542.5083333333808.5153101867148.4552360442753
Geometric Mean178771.045595015
Harmonic Mean171632.613376675
Quadratic Mean189161.326008362
Winsorized Mean ( 1 / 40 )184656.8166666673770.0175648229148.9803597706422
Winsorized Mean ( 2 / 40 )184805.6833333333732.6477607376749.5106142286543
Winsorized Mean ( 3 / 40 )184645.0833333333708.5878468965749.7885154555119
Winsorized Mean ( 4 / 40 )184697.153697.6753674897349.949530892807
Winsorized Mean ( 5 / 40 )184733.3583333333680.2499625631750.195872620748
Winsorized Mean ( 6 / 40 )185501.7083333333520.2761347515652.6952151571556
Winsorized Mean ( 7 / 40 )185455.5083333333515.7697001244552.7496179077853
Winsorized Mean ( 8 / 40 )185559.6416666673497.3631135085953.0570134253264
Winsorized Mean ( 9 / 40 )185806.3166666673454.7198171463453.7833244086769
Winsorized Mean ( 10 / 40 )185807.2333333333437.2149710551454.0574956463358
Winsorized Mean ( 11 / 40 )186029.0666666673400.0824613853654.7131043965531
Winsorized Mean ( 12 / 40 )185943.2666666673391.8613193594154.8204213436957
Winsorized Mean ( 13 / 40 )186029.0666666673377.6831960371655.0759369276917
Winsorized Mean ( 14 / 40 )186311.43331.6154061688855.9222411011254
Winsorized Mean ( 15 / 40 )186213.7753322.3374695460156.049024732411
Winsorized Mean ( 16 / 40 )186433.7753286.9498569935256.7193851781255
Winsorized Mean ( 17 / 40 )187122.5583333333178.7120684291358.8674136899119
Winsorized Mean ( 18 / 40 )187485.5583333333093.8066586792360.6002827640731
Winsorized Mean ( 19 / 40 )188129.9752998.1485206983362.7487176506454
Winsorized Mean ( 20 / 40 )188404.9752958.2606751829263.687752935549
Winsorized Mean ( 21 / 40 )188967.0752878.313292483465.6520176220844
Winsorized Mean ( 22 / 40 )189269.5752836.1475751977566.7347413989215
Winsorized Mean ( 23 / 40 )189254.8166666672799.2757510952667.608493587178
Winsorized Mean ( 24 / 40 )189584.8166666672717.5635793815169.7627897669331
Winsorized Mean ( 25 / 40 )189584.8166666672679.8052545359670.7457440594859
Winsorized Mean ( 26 / 40 )189754.0333333332575.1380693704973.686935698838
Winsorized Mean ( 27 / 40 )189754.0333333332575.1380693704973.686935698838
Winsorized Mean ( 28 / 40 )1897722531.4617397693374.965383445729
Winsorized Mean ( 29 / 40 )190526.9666666672385.4843473431679.8693007056896
Winsorized Mean ( 30 / 40 )191156.7166666672261.7758893610984.5162058565692
Winsorized Mean ( 31 / 40 )190935.0666666672197.436109679986.8899285970505
Winsorized Mean ( 32 / 40 )190935.0666666672197.436109679986.8899285970505
Winsorized Mean ( 33 / 40 )190717.2666666672177.9061632965587.5690926821156
Winsorized Mean ( 34 / 40 )193004.91895.50988862394101.822154111849
Winsorized Mean ( 35 / 40 )193004.91895.50988862394101.822154111849
Winsorized Mean ( 36 / 40 )193496.61836.94308580211105.336197672944
Winsorized Mean ( 37 / 40 )192991.2416666671790.79583567459107.768422185306
Winsorized Mean ( 38 / 40 )193262.9416666671706.38053296758113.258993485211
Winsorized Mean ( 39 / 40 )194589.2666666671499.60398449951129.760435873749
Winsorized Mean ( 40 / 40 )195920.2666666671349.41380133952145.189167675759
Trimmed Mean ( 1 / 40 )1850973704.8913330233949.9601697761405
Trimmed Mean ( 2 / 40 )185552.3620689663632.2618737158651.0845221297721
Trimmed Mean ( 3 / 40 )185945.3508771933573.1343098604952.0398436644418
Trimmed Mean ( 4 / 40 )186409.7321428573516.507339861153.0099084480285
Trimmed Mean ( 5 / 40 )186876.83456.4008012259854.0668778729929
Trimmed Mean ( 6 / 40 )187353.120370373393.4365529798355.2104385761545
Trimmed Mean ( 7 / 40 )187702.4433962263360.2976526076455.8588740644944
Trimmed Mean ( 8 / 40 )188072.8173076923323.3822303187556.5907874188922
Trimmed Mean ( 9 / 40 )188442.4019607843284.8305913742857.3674643848057
Trimmed Mean ( 10 / 40 )188793.883248.4464247390658.11820646393
Trimmed Mean ( 11 / 40 )189159.5918367353209.5695029790758.9361257518055
Trimmed Mean ( 12 / 40 )189515.3333333333170.9336697360159.7664136409107
Trimmed Mean ( 13 / 40 )189895.3404255323127.5382482175860.7171920387403
Trimmed Mean ( 14 / 40 )190283.2608695653079.6796418357761.7867060861366
Trimmed Mean ( 15 / 40 )190661.5333333333031.3706211047362.896147375028
Trimmed Mean ( 16 / 40 )191065.8752976.5681539980164.1899883069594
Trimmed Mean ( 17 / 40 )191469.8372093022918.2609751786265.6109370744619
Trimmed Mean ( 18 / 40 )191835.1547619052866.3978556884366.9255157239262
Trimmed Mean ( 19 / 40 )192188.7804878052817.7648369425168.2061107329114
Trimmed Mean ( 20 / 40 )192509.21252774.3058641309269.3900463495959
Trimmed Mean ( 21 / 40 )192824.9230769232728.6698906642370.6662699422335
Trimmed Mean ( 22 / 40 )193114.9868421052685.9914505548771.8970966203977
Trimmed Mean ( 23 / 40 )193398.4324324322641.2150343147473.2232816789979
Trimmed Mean ( 24 / 40 )193698.6944444442592.639074524474.7110140966987
Trimmed Mean ( 25 / 40 )193992.5428571432546.0005960459976.1950107782451
Trimmed Mean ( 26 / 40 )194303.6764705882494.9093188755977.8800555998392
Trimmed Mean ( 27 / 40 )194621.8333333332447.8495098043979.5072705874333
Trimmed Mean ( 28 / 40 )194959.8752390.3394453379481.5615854811939
Trimmed Mean ( 29 / 40 )195318.4838709682326.4143474211183.9568772809036
Trimmed Mean ( 30 / 40 )195648.9333333332271.8573747042686.1184929616466
Trimmed Mean ( 31 / 40 )195958.741379312224.4611582089188.0926783801846
Trimmed Mean ( 32 / 40 )1963062174.0626929454390.2945442360006
Trimmed Mean ( 33 / 40 )196678.9814814812110.0234187649193.2117528802624
Trimmed Mean ( 34 / 40 )197095.8846153852030.823351230297.0522052033681
Trimmed Mean ( 35 / 40 )197384.661988.4261150950199.2667811499592
Trimmed Mean ( 36 / 40 )197697.51932.74329916339102.288545036258
Trimmed Mean ( 37 / 40 )198001.9130434781872.73697218315105.728629265356
Trimmed Mean ( 38 / 40 )198371.251800.11440326041110.199246026089
Trimmed Mean ( 39 / 40 )198755.3333333331722.5359363095115.385304389737
Trimmed Mean ( 40 / 40 )199075.81671.6883785179119.086668638864
Median203670.5
Midrange151827.5
Midmean - Weighted Average at Xnp194963.278688525
Midmean - Weighted Average at X(n+1)p195648.933333333
Midmean - Empirical Distribution Function194963.278688525
Midmean - Empirical Distribution Function - Averaging195648.933333333
Midmean - Empirical Distribution Function - Interpolation195648.933333333
Midmean - Closest Observation194963.278688525
Midmean - True Basic - Statistics Graphics Toolkit195648.933333333
Midmean - MS Excel (old versions)195318.483870968
Number of observations120



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')