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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 13 Aug 2014 17:03:19 +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/2014/Aug/13/t1407947525lzrlq8xt62708d6.htm/, Retrieved Mon, 07 Apr 2025 06:17:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235545, Retrieved Mon, 07 Apr 2025 06:17:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTanguy Peers
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Omzet Het Laatste...] [2014-08-13 16:03:19] [edfef9daf94f6afee2f7e041aec7fc2a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84728
84412
84092
83430
89981
89635
84728
81466
81781
81781
82133
82764
83746
83746
83115
81466
89981
91279
89319
84728
86692
83746
85075
85710
86372
84728
85075
82764
89981
92261
90301
86692
90617
86372
90301
89981
90964
87355
91279
90964
96852
95523
90301
87670
91279
86372
89981
90617
91946
89004
90617
91599
95208
92261
88337
84092
88021
77221
82448
85390
88337
84092
84092
84092
86372
83115
78839
75261
77857
67724
73933
77541
78204
74595
74910
73933
77221
74910
70355
67062
72630
60537
68390
71968
71968
67724
63799
63484
67062
63799
57595
53319
57911
47115
56928
62150
63799
60191
55631
58893
60191
59208
49391
44835
48093
38280
48413
52022
54964
50057
45466
48093
49391
46795
36982
32706
36631
25835
37613
44835

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235545&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235545&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ yule.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean74561.8251538.7735115021448.4553603520334
Geometric Mean72229.9557466631
Harmonic Mean69345.7770484317
Quadratic Mean76427.9843628955
Winsorized Mean ( 1 / 40 )74608.00833333331523.2188752133248.9804909507077
Winsorized Mean ( 2 / 40 )74668.1751508.1189256588249.5108003285491
Winsorized Mean ( 3 / 40 )74603.2751498.3974441699549.7887094577416
Winsorized Mean ( 4 / 40 )74624.30833333331493.989136281549.9496994463234
Winsorized Mean ( 5 / 40 )74638.9751486.9479836992450.1960901243583
Winsorized Mean ( 6 / 40 )74949.3751422.3158831417652.695309029696
Winsorized Mean ( 7 / 40 )74930.70833333331420.4950994799252.7497126605838
Winsorized Mean ( 8 / 40 )74972.7751413.0593640435953.0570596733169
Winsorized Mean ( 9 / 40 )75072.451395.8282158282453.7834449459488
Winsorized Mean ( 10 / 40 )75072.86666666671388.7599811143554.0574812693176
Winsorized Mean ( 11 / 40 )75162.51666666671373.7535374477954.7132470401541
Winsorized Mean ( 12 / 40 )75127.81666666671370.4285929697554.8206721985151
Winsorized Mean ( 13 / 40 )75162.48333333331364.7000670355655.076192306932
Winsorized Mean ( 14 / 40 )75276.58333333331346.0826618654255.9227047980946
Winsorized Mean ( 15 / 40 )75237.08333333331342.3286996473156.0496720014269
Winsorized Mean ( 16 / 40 )75325.88333333331328.044955860956.7193776090988
Winsorized Mean ( 17 / 40 )75604.25833333331284.3000533209558.8680644665826
Winsorized Mean ( 18 / 40 )75750.80833333331250.0125684687960.6000373469241
Winsorized Mean ( 19 / 40 )76011.26666666671211.3495208185462.7492440128296
Winsorized Mean ( 20 / 40 )76122.43333333331195.2252096502163.6887782475834
Winsorized Mean ( 21 / 40 )76349.40833333331162.9425720365.6519162421408
Winsorized Mean ( 22 / 40 )76471.69166666671145.8973084740466.7352048924018
Winsorized Mean ( 23 / 40 )76465.94166666671131.0004002490767.6091198993626
Winsorized Mean ( 24 / 40 )76599.14166666671097.9829116480569.7635098452425
Winsorized Mean ( 25 / 40 )76599.14166666671082.7538097399770.7447445371376
Winsorized Mean ( 26 / 40 )76667.60833333331040.4343995742173.6880752546332
Winsorized Mean ( 27 / 40 )76667.60833333331040.4343995742173.6880752546332
Winsorized Mean ( 28 / 40 )76674.60833333331022.7983536212274.9655179458067
Winsorized Mean ( 29 / 40 )76979.5916666667963.83040110086379.8683996466001
Winsorized Mean ( 30 / 40 )77234.3416666667913.8386887679184.5163841452133
Winsorized Mean ( 31 / 40 )77144.4416666667887.84245878650586.8897864741759
Winsorized Mean ( 32 / 40 )77144.4416666667887.84245878650586.8897864741759
Winsorized Mean ( 33 / 40 )77056.4416666667879.95172373594487.568942236415
Winsorized Mean ( 34 / 40 )77980.9583333333765.824675267594101.826123983385
Winsorized Mean ( 35 / 40 )77980.9583333333765.824675267594101.826123983385
Winsorized Mean ( 36 / 40 )78179.5583333333742.169347741947105.339244434164
Winsorized Mean ( 37 / 40 )77975.4416666667723.530439892059107.770782495757
Winsorized Mean ( 38 / 40 )78085.0083333333689.448356749123113.257225967611
Winsorized Mean ( 39 / 40 )78621.2583333333605.897355953793129.760028758616
Winsorized Mean ( 40 / 40 )79158.925545.227335743364145.185172882197
Trimmed Mean ( 1 / 40 )74785.86440677971496.9050921262349.9603246726567
Trimmed Mean ( 2 / 40 )74969.85344827591467.5596715443651.0847053799066
Trimmed Mean ( 3 / 40 )75128.63157894741443.6701663396652.040025021388
Trimmed Mean ( 4 / 40 )75316.25892857141420.7911630769253.0100840192894
Trimmed Mean ( 5 / 40 )75504.97272727271396.5060857784354.0670559879338
Trimmed Mean ( 6 / 40 )75697.41666666671371.066637573455.2106036221846
Trimmed Mean ( 7 / 40 )75838.55660377361357.6769929792155.8590570481403
Trimmed Mean ( 8 / 40 )75988.20192307691342.7614667146356.5909908846278
Trimmed Mean ( 9 / 40 )76137.52941176471327.1845846398657.3677017446864
Trimmed Mean ( 10 / 40 )76279.541312.4836840482758.1184672442712
Trimmed Mean ( 11 / 40 )76427.29591836741296.7749404597358.9364380308526
Trimmed Mean ( 12 / 40 )76571.02083333331281.1640832108459.7667557471889
Trimmed Mean ( 13 / 40 )76724.55319148941263.6305768068860.7175503661585
Trimmed Mean ( 14 / 40 )76881.28260869561244.2937809122661.7870825910016
Trimmed Mean ( 15 / 40 )77034.11111111111224.7756437972962.8965080267884
Trimmed Mean ( 16 / 40 )77197.47727272731202.6346498796964.1902985918875
Trimmed Mean ( 17 / 40 )77360.69767441861179.0756843871165.6113078225603
Trimmed Mean ( 18 / 40 )77508.29761904761158.1221381673466.9258406040832
Trimmed Mean ( 19 / 40 )77651.18292682931138.4713189322568.2065341792334
Trimmed Mean ( 20 / 40 )77780.651120.9127684727869.3904576588724
Trimmed Mean ( 21 / 40 )77908.20512820511102.4758356315670.6665875207822
Trimmed Mean ( 22 / 40 )78025.40789473681085.2314144316671.8974836676645
Trimmed Mean ( 23 / 40 )78139.93243243241067.1404563351773.2236623291227
Trimmed Mean ( 24 / 40 )78261.23611111111047.5146746188774.7113505971509
Trimmed Mean ( 25 / 40 )78379.95714285711028.6719584542176.1952889827373
Trimmed Mean ( 26 / 40 )78505.66176470591008.0267225635677.8805363066708
Trimmed Mean ( 27 / 40 )78634.196969697989.01431687490879.507642738849
Trimmed Mean ( 28 / 40 )78770.765625965.77994704907681.5618152620405
Trimmed Mean ( 29 / 40 )78915.6612903226939.95177114018283.9571387738289
Trimmed Mean ( 30 / 40 )79049.1833333333917.90672583870186.1189716864807
Trimmed Mean ( 31 / 40 )79174.3448275862898.7567276555988.0931873902215
Trimmed Mean ( 32 / 40 )79314.6607142857878.39281337868290.2952067756645
Trimmed Mean ( 33 / 40 )79465.3703703704852.51720271197193.2126297482097
Trimmed Mean ( 34 / 40 )79633.8269230769820.51560221913797.0533975316278
Trimmed Mean ( 35 / 40 )79750.5803.3891385618799.2675854975581
Trimmed Mean ( 36 / 40 )79876.8958333333780.895678937084102.288817812461
Trimmed Mean ( 37 / 40 )79999.8913043478756.654628154417105.728410727465
Trimmed Mean ( 38 / 40 )80149.1136363636727.316114679311110.198457065265
Trimmed Mean ( 39 / 40 )80304.3095238095695.96957868697115.384798392069
Trimmed Mean ( 40 / 40 )80433.775675.426139452545119.085967068426
Median82290.5
Midrange61343.5
Midmean - Weighted Average at Xnp78772.1475409836
Midmean - Weighted Average at X(n+1)p79049.1833333333
Midmean - Empirical Distribution Function78772.1475409836
Midmean - Empirical Distribution Function - Averaging79049.1833333333
Midmean - Empirical Distribution Function - Interpolation79049.1833333333
Midmean - Closest Observation78772.1475409836
Midmean - True Basic - Statistics Graphics Toolkit79049.1833333333
Midmean - MS Excel (old versions)78915.6612903226
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 74561.825 & 1538.77351150214 & 48.4553603520334 \tabularnewline
Geometric Mean & 72229.9557466631 &  &  \tabularnewline
Harmonic Mean & 69345.7770484317 &  &  \tabularnewline
Quadratic Mean & 76427.9843628955 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 74608.0083333333 & 1523.21887521332 & 48.9804909507077 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 74668.175 & 1508.11892565882 & 49.5108003285491 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 74603.275 & 1498.39744416995 & 49.7887094577416 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 74624.3083333333 & 1493.9891362815 & 49.9496994463234 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 74638.975 & 1486.94798369924 & 50.1960901243583 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 74949.375 & 1422.31588314176 & 52.695309029696 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 74930.7083333333 & 1420.49509947992 & 52.7497126605838 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 74972.775 & 1413.05936404359 & 53.0570596733169 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 75072.45 & 1395.82821582824 & 53.7834449459488 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 75072.8666666667 & 1388.75998111435 & 54.0574812693176 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 75162.5166666667 & 1373.75353744779 & 54.7132470401541 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 75127.8166666667 & 1370.42859296975 & 54.8206721985151 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 75162.4833333333 & 1364.70006703556 & 55.076192306932 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 75276.5833333333 & 1346.08266186542 & 55.9227047980946 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 75237.0833333333 & 1342.32869964731 & 56.0496720014269 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 75325.8833333333 & 1328.0449558609 & 56.7193776090988 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 75604.2583333333 & 1284.30005332095 & 58.8680644665826 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 75750.8083333333 & 1250.01256846879 & 60.6000373469241 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 76011.2666666667 & 1211.34952081854 & 62.7492440128296 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 76122.4333333333 & 1195.22520965021 & 63.6887782475834 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 76349.4083333333 & 1162.94257203 & 65.6519162421408 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 76471.6916666667 & 1145.89730847404 & 66.7352048924018 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 76465.9416666667 & 1131.00040024907 & 67.6091198993626 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 76599.1416666667 & 1097.98291164805 & 69.7635098452425 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 76599.1416666667 & 1082.75380973997 & 70.7447445371376 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 76667.6083333333 & 1040.43439957421 & 73.6880752546332 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 76667.6083333333 & 1040.43439957421 & 73.6880752546332 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 76674.6083333333 & 1022.79835362122 & 74.9655179458067 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 76979.5916666667 & 963.830401100863 & 79.8683996466001 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 77234.3416666667 & 913.83868876791 & 84.5163841452133 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 77144.4416666667 & 887.842458786505 & 86.8897864741759 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 77144.4416666667 & 887.842458786505 & 86.8897864741759 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 77056.4416666667 & 879.951723735944 & 87.568942236415 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 77980.9583333333 & 765.824675267594 & 101.826123983385 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 77980.9583333333 & 765.824675267594 & 101.826123983385 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 78179.5583333333 & 742.169347741947 & 105.339244434164 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 77975.4416666667 & 723.530439892059 & 107.770782495757 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 78085.0083333333 & 689.448356749123 & 113.257225967611 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 78621.2583333333 & 605.897355953793 & 129.760028758616 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 79158.925 & 545.227335743364 & 145.185172882197 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 74785.8644067797 & 1496.90509212623 & 49.9603246726567 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 74969.8534482759 & 1467.55967154436 & 51.0847053799066 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 75128.6315789474 & 1443.67016633966 & 52.040025021388 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 75316.2589285714 & 1420.79116307692 & 53.0100840192894 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 75504.9727272727 & 1396.50608577843 & 54.0670559879338 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 75697.4166666667 & 1371.0666375734 & 55.2106036221846 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 75838.5566037736 & 1357.67699297921 & 55.8590570481403 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 75988.2019230769 & 1342.76146671463 & 56.5909908846278 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 76137.5294117647 & 1327.18458463986 & 57.3677017446864 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 76279.54 & 1312.48368404827 & 58.1184672442712 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 76427.2959183674 & 1296.77494045973 & 58.9364380308526 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 76571.0208333333 & 1281.16408321084 & 59.7667557471889 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 76724.5531914894 & 1263.63057680688 & 60.7175503661585 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 76881.2826086956 & 1244.29378091226 & 61.7870825910016 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 77034.1111111111 & 1224.77564379729 & 62.8965080267884 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 77197.4772727273 & 1202.63464987969 & 64.1902985918875 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 77360.6976744186 & 1179.07568438711 & 65.6113078225603 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 77508.2976190476 & 1158.12213816734 & 66.9258406040832 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 77651.1829268293 & 1138.47131893225 & 68.2065341792334 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 77780.65 & 1120.91276847278 & 69.3904576588724 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 77908.2051282051 & 1102.47583563156 & 70.6665875207822 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 78025.4078947368 & 1085.23141443166 & 71.8974836676645 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 78139.9324324324 & 1067.14045633517 & 73.2236623291227 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 78261.2361111111 & 1047.51467461887 & 74.7113505971509 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 78379.9571428571 & 1028.67195845421 & 76.1952889827373 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 78505.6617647059 & 1008.02672256356 & 77.8805363066708 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 78634.196969697 & 989.014316874908 & 79.507642738849 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 78770.765625 & 965.779947049076 & 81.5618152620405 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 78915.6612903226 & 939.951771140182 & 83.9571387738289 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 79049.1833333333 & 917.906725838701 & 86.1189716864807 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 79174.3448275862 & 898.75672765559 & 88.0931873902215 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 79314.6607142857 & 878.392813378682 & 90.2952067756645 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 79465.3703703704 & 852.517202711971 & 93.2126297482097 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 79633.8269230769 & 820.515602219137 & 97.0533975316278 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 79750.5 & 803.38913856187 & 99.2675854975581 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 79876.8958333333 & 780.895678937084 & 102.288817812461 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 79999.8913043478 & 756.654628154417 & 105.728410727465 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 80149.1136363636 & 727.316114679311 & 110.198457065265 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 80304.3095238095 & 695.96957868697 & 115.384798392069 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 80433.775 & 675.426139452545 & 119.085967068426 \tabularnewline
Median & 82290.5 &  &  \tabularnewline
Midrange & 61343.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 78772.1475409836 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 79049.1833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 78772.1475409836 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 79049.1833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 79049.1833333333 &  &  \tabularnewline
Midmean - Closest Observation & 78772.1475409836 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 79049.1833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78915.6612903226 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235545&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]74561.825[/C][C]1538.77351150214[/C][C]48.4553603520334[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]72229.9557466631[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]69345.7770484317[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]76427.9843628955[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]74608.0083333333[/C][C]1523.21887521332[/C][C]48.9804909507077[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]74668.175[/C][C]1508.11892565882[/C][C]49.5108003285491[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]74603.275[/C][C]1498.39744416995[/C][C]49.7887094577416[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]74624.3083333333[/C][C]1493.9891362815[/C][C]49.9496994463234[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]74638.975[/C][C]1486.94798369924[/C][C]50.1960901243583[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]74949.375[/C][C]1422.31588314176[/C][C]52.695309029696[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]74930.7083333333[/C][C]1420.49509947992[/C][C]52.7497126605838[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]74972.775[/C][C]1413.05936404359[/C][C]53.0570596733169[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]75072.45[/C][C]1395.82821582824[/C][C]53.7834449459488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]75072.8666666667[/C][C]1388.75998111435[/C][C]54.0574812693176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]75162.5166666667[/C][C]1373.75353744779[/C][C]54.7132470401541[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]75127.8166666667[/C][C]1370.42859296975[/C][C]54.8206721985151[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]75162.4833333333[/C][C]1364.70006703556[/C][C]55.076192306932[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]75276.5833333333[/C][C]1346.08266186542[/C][C]55.9227047980946[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]75237.0833333333[/C][C]1342.32869964731[/C][C]56.0496720014269[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]75325.8833333333[/C][C]1328.0449558609[/C][C]56.7193776090988[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]75604.2583333333[/C][C]1284.30005332095[/C][C]58.8680644665826[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]75750.8083333333[/C][C]1250.01256846879[/C][C]60.6000373469241[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]76011.2666666667[/C][C]1211.34952081854[/C][C]62.7492440128296[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]76122.4333333333[/C][C]1195.22520965021[/C][C]63.6887782475834[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]76349.4083333333[/C][C]1162.94257203[/C][C]65.6519162421408[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]76471.6916666667[/C][C]1145.89730847404[/C][C]66.7352048924018[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]76465.9416666667[/C][C]1131.00040024907[/C][C]67.6091198993626[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]76599.1416666667[/C][C]1097.98291164805[/C][C]69.7635098452425[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]76599.1416666667[/C][C]1082.75380973997[/C][C]70.7447445371376[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]76667.6083333333[/C][C]1040.43439957421[/C][C]73.6880752546332[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]76667.6083333333[/C][C]1040.43439957421[/C][C]73.6880752546332[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]76674.6083333333[/C][C]1022.79835362122[/C][C]74.9655179458067[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]76979.5916666667[/C][C]963.830401100863[/C][C]79.8683996466001[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]77234.3416666667[/C][C]913.83868876791[/C][C]84.5163841452133[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]77144.4416666667[/C][C]887.842458786505[/C][C]86.8897864741759[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]77144.4416666667[/C][C]887.842458786505[/C][C]86.8897864741759[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]77056.4416666667[/C][C]879.951723735944[/C][C]87.568942236415[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]77980.9583333333[/C][C]765.824675267594[/C][C]101.826123983385[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]77980.9583333333[/C][C]765.824675267594[/C][C]101.826123983385[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]78179.5583333333[/C][C]742.169347741947[/C][C]105.339244434164[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]77975.4416666667[/C][C]723.530439892059[/C][C]107.770782495757[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]78085.0083333333[/C][C]689.448356749123[/C][C]113.257225967611[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]78621.2583333333[/C][C]605.897355953793[/C][C]129.760028758616[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]79158.925[/C][C]545.227335743364[/C][C]145.185172882197[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]74785.8644067797[/C][C]1496.90509212623[/C][C]49.9603246726567[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]74969.8534482759[/C][C]1467.55967154436[/C][C]51.0847053799066[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]75128.6315789474[/C][C]1443.67016633966[/C][C]52.040025021388[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]75316.2589285714[/C][C]1420.79116307692[/C][C]53.0100840192894[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]75504.9727272727[/C][C]1396.50608577843[/C][C]54.0670559879338[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]75697.4166666667[/C][C]1371.0666375734[/C][C]55.2106036221846[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]75838.5566037736[/C][C]1357.67699297921[/C][C]55.8590570481403[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]75988.2019230769[/C][C]1342.76146671463[/C][C]56.5909908846278[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]76137.5294117647[/C][C]1327.18458463986[/C][C]57.3677017446864[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]76279.54[/C][C]1312.48368404827[/C][C]58.1184672442712[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]76427.2959183674[/C][C]1296.77494045973[/C][C]58.9364380308526[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]76571.0208333333[/C][C]1281.16408321084[/C][C]59.7667557471889[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]76724.5531914894[/C][C]1263.63057680688[/C][C]60.7175503661585[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]76881.2826086956[/C][C]1244.29378091226[/C][C]61.7870825910016[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]77034.1111111111[/C][C]1224.77564379729[/C][C]62.8965080267884[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]77197.4772727273[/C][C]1202.63464987969[/C][C]64.1902985918875[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]77360.6976744186[/C][C]1179.07568438711[/C][C]65.6113078225603[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]77508.2976190476[/C][C]1158.12213816734[/C][C]66.9258406040832[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]77651.1829268293[/C][C]1138.47131893225[/C][C]68.2065341792334[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]77780.65[/C][C]1120.91276847278[/C][C]69.3904576588724[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]77908.2051282051[/C][C]1102.47583563156[/C][C]70.6665875207822[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]78025.4078947368[/C][C]1085.23141443166[/C][C]71.8974836676645[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]78139.9324324324[/C][C]1067.14045633517[/C][C]73.2236623291227[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]78261.2361111111[/C][C]1047.51467461887[/C][C]74.7113505971509[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]78379.9571428571[/C][C]1028.67195845421[/C][C]76.1952889827373[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]78505.6617647059[/C][C]1008.02672256356[/C][C]77.8805363066708[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]78634.196969697[/C][C]989.014316874908[/C][C]79.507642738849[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]78770.765625[/C][C]965.779947049076[/C][C]81.5618152620405[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]78915.6612903226[/C][C]939.951771140182[/C][C]83.9571387738289[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]79049.1833333333[/C][C]917.906725838701[/C][C]86.1189716864807[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]79174.3448275862[/C][C]898.75672765559[/C][C]88.0931873902215[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]79314.6607142857[/C][C]878.392813378682[/C][C]90.2952067756645[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]79465.3703703704[/C][C]852.517202711971[/C][C]93.2126297482097[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]79633.8269230769[/C][C]820.515602219137[/C][C]97.0533975316278[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]79750.5[/C][C]803.38913856187[/C][C]99.2675854975581[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]79876.8958333333[/C][C]780.895678937084[/C][C]102.288817812461[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]79999.8913043478[/C][C]756.654628154417[/C][C]105.728410727465[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]80149.1136363636[/C][C]727.316114679311[/C][C]110.198457065265[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]80304.3095238095[/C][C]695.96957868697[/C][C]115.384798392069[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]80433.775[/C][C]675.426139452545[/C][C]119.085967068426[/C][/ROW]
[ROW][C]Median[/C][C]82290.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]61343.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]78772.1475409836[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]79049.1833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]78772.1475409836[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]79049.1833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]79049.1833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]78772.1475409836[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]79049.1833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78915.6612903226[/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=235545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235545&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean74561.8251538.7735115021448.4553603520334
Geometric Mean72229.9557466631
Harmonic Mean69345.7770484317
Quadratic Mean76427.9843628955
Winsorized Mean ( 1 / 40 )74608.00833333331523.2188752133248.9804909507077
Winsorized Mean ( 2 / 40 )74668.1751508.1189256588249.5108003285491
Winsorized Mean ( 3 / 40 )74603.2751498.3974441699549.7887094577416
Winsorized Mean ( 4 / 40 )74624.30833333331493.989136281549.9496994463234
Winsorized Mean ( 5 / 40 )74638.9751486.9479836992450.1960901243583
Winsorized Mean ( 6 / 40 )74949.3751422.3158831417652.695309029696
Winsorized Mean ( 7 / 40 )74930.70833333331420.4950994799252.7497126605838
Winsorized Mean ( 8 / 40 )74972.7751413.0593640435953.0570596733169
Winsorized Mean ( 9 / 40 )75072.451395.8282158282453.7834449459488
Winsorized Mean ( 10 / 40 )75072.86666666671388.7599811143554.0574812693176
Winsorized Mean ( 11 / 40 )75162.51666666671373.7535374477954.7132470401541
Winsorized Mean ( 12 / 40 )75127.81666666671370.4285929697554.8206721985151
Winsorized Mean ( 13 / 40 )75162.48333333331364.7000670355655.076192306932
Winsorized Mean ( 14 / 40 )75276.58333333331346.0826618654255.9227047980946
Winsorized Mean ( 15 / 40 )75237.08333333331342.3286996473156.0496720014269
Winsorized Mean ( 16 / 40 )75325.88333333331328.044955860956.7193776090988
Winsorized Mean ( 17 / 40 )75604.25833333331284.3000533209558.8680644665826
Winsorized Mean ( 18 / 40 )75750.80833333331250.0125684687960.6000373469241
Winsorized Mean ( 19 / 40 )76011.26666666671211.3495208185462.7492440128296
Winsorized Mean ( 20 / 40 )76122.43333333331195.2252096502163.6887782475834
Winsorized Mean ( 21 / 40 )76349.40833333331162.9425720365.6519162421408
Winsorized Mean ( 22 / 40 )76471.69166666671145.8973084740466.7352048924018
Winsorized Mean ( 23 / 40 )76465.94166666671131.0004002490767.6091198993626
Winsorized Mean ( 24 / 40 )76599.14166666671097.9829116480569.7635098452425
Winsorized Mean ( 25 / 40 )76599.14166666671082.7538097399770.7447445371376
Winsorized Mean ( 26 / 40 )76667.60833333331040.4343995742173.6880752546332
Winsorized Mean ( 27 / 40 )76667.60833333331040.4343995742173.6880752546332
Winsorized Mean ( 28 / 40 )76674.60833333331022.7983536212274.9655179458067
Winsorized Mean ( 29 / 40 )76979.5916666667963.83040110086379.8683996466001
Winsorized Mean ( 30 / 40 )77234.3416666667913.8386887679184.5163841452133
Winsorized Mean ( 31 / 40 )77144.4416666667887.84245878650586.8897864741759
Winsorized Mean ( 32 / 40 )77144.4416666667887.84245878650586.8897864741759
Winsorized Mean ( 33 / 40 )77056.4416666667879.95172373594487.568942236415
Winsorized Mean ( 34 / 40 )77980.9583333333765.824675267594101.826123983385
Winsorized Mean ( 35 / 40 )77980.9583333333765.824675267594101.826123983385
Winsorized Mean ( 36 / 40 )78179.5583333333742.169347741947105.339244434164
Winsorized Mean ( 37 / 40 )77975.4416666667723.530439892059107.770782495757
Winsorized Mean ( 38 / 40 )78085.0083333333689.448356749123113.257225967611
Winsorized Mean ( 39 / 40 )78621.2583333333605.897355953793129.760028758616
Winsorized Mean ( 40 / 40 )79158.925545.227335743364145.185172882197
Trimmed Mean ( 1 / 40 )74785.86440677971496.9050921262349.9603246726567
Trimmed Mean ( 2 / 40 )74969.85344827591467.5596715443651.0847053799066
Trimmed Mean ( 3 / 40 )75128.63157894741443.6701663396652.040025021388
Trimmed Mean ( 4 / 40 )75316.25892857141420.7911630769253.0100840192894
Trimmed Mean ( 5 / 40 )75504.97272727271396.5060857784354.0670559879338
Trimmed Mean ( 6 / 40 )75697.41666666671371.066637573455.2106036221846
Trimmed Mean ( 7 / 40 )75838.55660377361357.6769929792155.8590570481403
Trimmed Mean ( 8 / 40 )75988.20192307691342.7614667146356.5909908846278
Trimmed Mean ( 9 / 40 )76137.52941176471327.1845846398657.3677017446864
Trimmed Mean ( 10 / 40 )76279.541312.4836840482758.1184672442712
Trimmed Mean ( 11 / 40 )76427.29591836741296.7749404597358.9364380308526
Trimmed Mean ( 12 / 40 )76571.02083333331281.1640832108459.7667557471889
Trimmed Mean ( 13 / 40 )76724.55319148941263.6305768068860.7175503661585
Trimmed Mean ( 14 / 40 )76881.28260869561244.2937809122661.7870825910016
Trimmed Mean ( 15 / 40 )77034.11111111111224.7756437972962.8965080267884
Trimmed Mean ( 16 / 40 )77197.47727272731202.6346498796964.1902985918875
Trimmed Mean ( 17 / 40 )77360.69767441861179.0756843871165.6113078225603
Trimmed Mean ( 18 / 40 )77508.29761904761158.1221381673466.9258406040832
Trimmed Mean ( 19 / 40 )77651.18292682931138.4713189322568.2065341792334
Trimmed Mean ( 20 / 40 )77780.651120.9127684727869.3904576588724
Trimmed Mean ( 21 / 40 )77908.20512820511102.4758356315670.6665875207822
Trimmed Mean ( 22 / 40 )78025.40789473681085.2314144316671.8974836676645
Trimmed Mean ( 23 / 40 )78139.93243243241067.1404563351773.2236623291227
Trimmed Mean ( 24 / 40 )78261.23611111111047.5146746188774.7113505971509
Trimmed Mean ( 25 / 40 )78379.95714285711028.6719584542176.1952889827373
Trimmed Mean ( 26 / 40 )78505.66176470591008.0267225635677.8805363066708
Trimmed Mean ( 27 / 40 )78634.196969697989.01431687490879.507642738849
Trimmed Mean ( 28 / 40 )78770.765625965.77994704907681.5618152620405
Trimmed Mean ( 29 / 40 )78915.6612903226939.95177114018283.9571387738289
Trimmed Mean ( 30 / 40 )79049.1833333333917.90672583870186.1189716864807
Trimmed Mean ( 31 / 40 )79174.3448275862898.7567276555988.0931873902215
Trimmed Mean ( 32 / 40 )79314.6607142857878.39281337868290.2952067756645
Trimmed Mean ( 33 / 40 )79465.3703703704852.51720271197193.2126297482097
Trimmed Mean ( 34 / 40 )79633.8269230769820.51560221913797.0533975316278
Trimmed Mean ( 35 / 40 )79750.5803.3891385618799.2675854975581
Trimmed Mean ( 36 / 40 )79876.8958333333780.895678937084102.288817812461
Trimmed Mean ( 37 / 40 )79999.8913043478756.654628154417105.728410727465
Trimmed Mean ( 38 / 40 )80149.1136363636727.316114679311110.198457065265
Trimmed Mean ( 39 / 40 )80304.3095238095695.96957868697115.384798392069
Trimmed Mean ( 40 / 40 )80433.775675.426139452545119.085967068426
Median82290.5
Midrange61343.5
Midmean - Weighted Average at Xnp78772.1475409836
Midmean - Weighted Average at X(n+1)p79049.1833333333
Midmean - Empirical Distribution Function78772.1475409836
Midmean - Empirical Distribution Function - Averaging79049.1833333333
Midmean - Empirical Distribution Function - Interpolation79049.1833333333
Midmean - Closest Observation78772.1475409836
Midmean - True Basic - Statistics Graphics Toolkit79049.1833333333
Midmean - MS Excel (old versions)78915.6612903226
Number of observations120


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')