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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Dec 2012 14:29:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/18/t1355858986wafaul7n778tcyz.htm/, Retrieved Fri, 04 Apr 2025 19:21:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201599, Retrieved Fri, 04 Apr 2025 19:21:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [ARIMA Backward Selection] [] [2011-12-06 19:59:13] [b98453cac15ba1066b407e146608df68]
- R PD    [ARIMA Backward Selection] [Maandelijks geboo...] [2012-12-15 10:01:40] [dc1c1ef052cd9b8b4f9db3f2b24d140d]
-   P       [ARIMA Backward Selection] [paper - ARIMA] [2012-12-18 19:20:35] [00d51cc5abcfaf80a667f39a85fc0ddc]
- RMP           [Central Tendency] [Paper - Central t...] [2012-12-18 19:29:21] [0ab7a1f5c5e2896cc7067de738ff1e9d] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9769
9321
9939
9336
10195
9464
10010
10213
9563
9890
9305
9391
9928
8686
9843
9627
10074
9503
10119
10000
9313
9866
9172
9241
9659
8904
9755
9080
9435
8971
10063
9793
9454
9759
8820
9403
9676
8642
9402
9610
9294
9448
10319
9548
9801
9596
8923
9746
9829
9125
9782
9441
9162
9915
10444
10209
9985
9842
9429
10132
9849
9172
10313
9819
9955
10048
10082
10541
10208
10233
9439
9963
10158
9225
10474
9757
10490
10281
10444
10640
10695
10786
9832
9747
10411
9511
10402
9701
10540
10112
10915
11183
10384
10834
9886
10216
10943
9867
10203
10837
10573
10647
11502
10656
10866
10835
9945
10331
10718
9462
10579
10633
10346
10757
11207
11013
11015
10765
10042
10661

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201599&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201599&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9973.4416666666753.9339475627044184.919556557053
Geometric Mean9956.09789902532
Harmonic Mean9938.76355085124
Quadratic Mean9990.78046459168
Winsorized Mean ( 1 / 40 )9971.3553.3263913330449186.987151216082
Winsorized Mean ( 2 / 40 )9973.1833333333352.8177883404136188.822433628905
Winsorized Mean ( 3 / 40 )9971.0833333333351.6816607636634192.932718995436
Winsorized Mean ( 4 / 40 )9971.6551.5612804074424193.394150052191
Winsorized Mean ( 5 / 40 )9970.7333333333350.7423459936318196.497287188587
Winsorized Mean ( 6 / 40 )9974.7833333333349.6540048107317200.885776914765
Winsorized Mean ( 7 / 40 )9974.5548.8164556019281204.327616108328
Winsorized Mean ( 8 / 40 )9975.0833333333348.1673823282396207.092078729907
Winsorized Mean ( 9 / 40 )9975.6833333333348.0389153980782207.658379683826
Winsorized Mean ( 10 / 40 )9975.648.0263938871525207.710785520138
Winsorized Mean ( 11 / 40 )9976.0583333333346.7052131157705213.596249065499
Winsorized Mean ( 12 / 40 )9975.5583333333346.1863382674324215.985044659136
Winsorized Mean ( 13 / 40 )9980.4333333333345.3123701324647220.258470350522
Winsorized Mean ( 14 / 40 )9977.1666666666744.5032704764482224.189515958085
Winsorized Mean ( 15 / 40 )9975.2916666666743.9777324540202226.82596646146
Winsorized Mean ( 16 / 40 )9971.82543.2272942981507230.683533677161
Winsorized Mean ( 17 / 40 )9973.2416666666742.8652716312573232.664842356771
Winsorized Mean ( 18 / 40 )9980.1416666666741.678511978728239.455325846575
Winsorized Mean ( 19 / 40 )9980.77541.3237719285227241.526233792589
Winsorized Mean ( 20 / 40 )9979.77541.1481293884773242.532896350682
Winsorized Mean ( 21 / 40 )9974.87539.3750595793422253.32977541025
Winsorized Mean ( 22 / 40 )9974.87539.1055716879937255.075544722506
Winsorized Mean ( 23 / 40 )9969.5083333333338.236984010185260.729463669985
Winsorized Mean ( 24 / 40 )9969.7083333333338.1652668070439261.224646580835
Winsorized Mean ( 25 / 40 )9960.7536.7093479306048271.340967941729
Winsorized Mean ( 26 / 40 )9958.5833333333336.1390319947847275.563090200381
Winsorized Mean ( 27 / 40 )9953.6333333333335.1270561632561283.360873939249
Winsorized Mean ( 28 / 40 )9954.135.0722132186724283.817275457838
Winsorized Mean ( 29 / 40 )9955.5533.0461243950787301.262256383765
Winsorized Mean ( 30 / 40 )9955.332.5563476192911305.786758281848
Winsorized Mean ( 31 / 40 )9960.2083333333330.9371004958691321.950285375428
Winsorized Mean ( 32 / 40 )9954.07529.3366916904708339.30461911059
Winsorized Mean ( 33 / 40 )9959.02527.8685074274259357.357674282877
Winsorized Mean ( 34 / 40 )9959.5916666666727.05555674306368.116308278203
Winsorized Mean ( 35 / 40 )9962.826.3250783075599378.452815357398
Winsorized Mean ( 36 / 40 )9962.824.2382016694322411.037094908097
Winsorized Mean ( 37 / 40 )9953.2416666666722.0800586732253450.779674726868
Winsorized Mean ( 38 / 40 )9955.77520.6811002587668481.394842413169
Winsorized Mean ( 39 / 40 )9969.42519.0999936296497521.959598170966
Winsorized Mean ( 40 / 40 )9968.42518.9245615104114526.745361815429
Trimmed Mean ( 1 / 40 )9971.7711864406852.0679950970978191.514406649326
Trimmed Mean ( 2 / 40 )9972.2068965517250.6702431493653196.805980724342
Trimmed Mean ( 3 / 40 )9971.6929824561449.4155142519043201.792759488926
Trimmed Mean ( 4 / 40 )9971.9107142857148.4874195122885205.659752871742
Trimmed Mean ( 5 / 40 )9971.9818181818247.4925234128468209.9695089161
Trimmed Mean ( 6 / 40 )9972.2592592592646.6042015748094213.977687038618
Trimmed Mean ( 7 / 40 )9971.7830188679345.8660908923976217.410789209437
Trimmed Mean ( 8 / 40 )9971.3269230769245.212834667309220.541954435046
Trimmed Mean ( 9 / 40 )9970.7745098039244.6007807786085223.556052960089
Trimmed Mean ( 10 / 40 )9970.1243.9330005965236226.939199795721
Trimmed Mean ( 11 / 40 )9969.4489795918443.180842163015230.876668453002
Trimmed Mean ( 12 / 40 )9968.6979166666742.5396257989208234.339106878546
Trimmed Mean ( 13 / 40 )9967.9680851063841.889758610998237.957162218866
Trimmed Mean ( 14 / 40 )9966.7173913043541.2754903971106241.468176281245
Trimmed Mean ( 15 / 40 )9965.7222222222240.6880708323628244.929828776635
Trimmed Mean ( 16 / 40 )9964.8522727272740.0866829168497248.58261017498
Trimmed Mean ( 17 / 40 )9964.2441860465139.4967485061389252.280113247747
Trimmed Mean ( 18 / 40 )9963.488095238138.8634519627967256.3716703492
Trimmed Mean ( 19 / 40 )9962.1341463414638.2845090356047260.213187978371
Trimmed Mean ( 20 / 40 )9960.662537.6563783481714264.514617096301
Trimmed Mean ( 21 / 40 )9959.1923076923136.946794451984269.554976430641
Trimmed Mean ( 22 / 40 )9958.0131578947436.3540412262663273.917639470022
Trimmed Mean ( 23 / 40 )9956.7702702702735.6910596521822278.970990699109
Trimmed Mean ( 24 / 40 )9955.8472222222235.0270276803918284.23328730789
Trimmed Mean ( 25 / 40 )9954.8571428571434.2488293657633290.66269788504
Trimmed Mean ( 26 / 40 )9954.4411764705933.5302556383802296.879370197115
Trimmed Mean ( 27 / 40 )9954.1515151515232.7518838222182303.926075494895
Trimmed Mean ( 28 / 40 )9954.187531.9646760251509311.412119183304
Trimmed Mean ( 29 / 40 )9954.193548387131.0211271954246320.884327822081
Trimmed Mean ( 30 / 40 )9954.130.1933945333467329.678068791051
Trimmed Mean ( 31 / 40 )9954.0172413793129.2591368801879340.202012183054
Trimmed Mean ( 32 / 40 )9953.5892857142928.3788811269348350.739313547749
Trimmed Mean ( 33 / 40 )9953.5555555555527.5607792438343361.149279107639
Trimmed Mean ( 34 / 40 )9953.1730769230826.7920842347589371.496782023783
Trimmed Mean ( 35 / 40 )9952.7225.9673270374405383.27857101541
Trimmed Mean ( 36 / 40 )995225.0541965737768397.218883898132
Trimmed Mean ( 37 / 40 )9951.2173913043524.2968937607016409.567473493246
Trimmed Mean ( 38 / 40 )9951.0681818181823.7460889786842419.061353250669
Trimmed Mean ( 39 / 40 )9950.7142857142923.2909009992008427.236124787777
Trimmed Mean ( 40 / 40 )9949.27522.9735351504224433.075490335108
Median9933.5
Midrange10072
Midmean - Weighted Average at Xnp9946.70491803279
Midmean - Weighted Average at X(n+1)p9954.1
Midmean - Empirical Distribution Function9946.70491803279
Midmean - Empirical Distribution Function - Averaging9954.1
Midmean - Empirical Distribution Function - Interpolation9954.1
Midmean - Closest Observation9946.70491803279
Midmean - True Basic - Statistics Graphics Toolkit9954.1
Midmean - MS Excel (old versions)9954.1935483871
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9973.44166666667 & 53.9339475627044 & 184.919556557053 \tabularnewline
Geometric Mean & 9956.09789902532 &  &  \tabularnewline
Harmonic Mean & 9938.76355085124 &  &  \tabularnewline
Quadratic Mean & 9990.78046459168 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 9971.35 & 53.3263913330449 & 186.987151216082 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 9973.18333333333 & 52.8177883404136 & 188.822433628905 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 9971.08333333333 & 51.6816607636634 & 192.932718995436 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 9971.65 & 51.5612804074424 & 193.394150052191 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 9970.73333333333 & 50.7423459936318 & 196.497287188587 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 9974.78333333333 & 49.6540048107317 & 200.885776914765 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 9974.55 & 48.8164556019281 & 204.327616108328 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 9975.08333333333 & 48.1673823282396 & 207.092078729907 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 9975.68333333333 & 48.0389153980782 & 207.658379683826 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 9975.6 & 48.0263938871525 & 207.710785520138 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 9976.05833333333 & 46.7052131157705 & 213.596249065499 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 9975.55833333333 & 46.1863382674324 & 215.985044659136 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 9980.43333333333 & 45.3123701324647 & 220.258470350522 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 9977.16666666667 & 44.5032704764482 & 224.189515958085 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 9975.29166666667 & 43.9777324540202 & 226.82596646146 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 9971.825 & 43.2272942981507 & 230.683533677161 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 9973.24166666667 & 42.8652716312573 & 232.664842356771 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 9980.14166666667 & 41.678511978728 & 239.455325846575 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 9980.775 & 41.3237719285227 & 241.526233792589 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 9979.775 & 41.1481293884773 & 242.532896350682 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 9974.875 & 39.3750595793422 & 253.32977541025 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 9974.875 & 39.1055716879937 & 255.075544722506 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 9969.50833333333 & 38.236984010185 & 260.729463669985 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 9969.70833333333 & 38.1652668070439 & 261.224646580835 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 9960.75 & 36.7093479306048 & 271.340967941729 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 9958.58333333333 & 36.1390319947847 & 275.563090200381 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 9953.63333333333 & 35.1270561632561 & 283.360873939249 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 9954.1 & 35.0722132186724 & 283.817275457838 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 9955.55 & 33.0461243950787 & 301.262256383765 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 9955.3 & 32.5563476192911 & 305.786758281848 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 9960.20833333333 & 30.9371004958691 & 321.950285375428 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 9954.075 & 29.3366916904708 & 339.30461911059 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 9959.025 & 27.8685074274259 & 357.357674282877 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 9959.59166666667 & 27.05555674306 & 368.116308278203 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 9962.8 & 26.3250783075599 & 378.452815357398 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 9962.8 & 24.2382016694322 & 411.037094908097 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 9953.24166666667 & 22.0800586732253 & 450.779674726868 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 9955.775 & 20.6811002587668 & 481.394842413169 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 9969.425 & 19.0999936296497 & 521.959598170966 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 9968.425 & 18.9245615104114 & 526.745361815429 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 9971.77118644068 & 52.0679950970978 & 191.514406649326 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 9972.20689655172 & 50.6702431493653 & 196.805980724342 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 9971.69298245614 & 49.4155142519043 & 201.792759488926 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 9971.91071428571 & 48.4874195122885 & 205.659752871742 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 9971.98181818182 & 47.4925234128468 & 209.9695089161 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 9972.25925925926 & 46.6042015748094 & 213.977687038618 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 9971.78301886793 & 45.8660908923976 & 217.410789209437 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 9971.32692307692 & 45.212834667309 & 220.541954435046 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 9970.77450980392 & 44.6007807786085 & 223.556052960089 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 9970.12 & 43.9330005965236 & 226.939199795721 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 9969.44897959184 & 43.180842163015 & 230.876668453002 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 9968.69791666667 & 42.5396257989208 & 234.339106878546 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 9967.96808510638 & 41.889758610998 & 237.957162218866 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 9966.71739130435 & 41.2754903971106 & 241.468176281245 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 9965.72222222222 & 40.6880708323628 & 244.929828776635 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 9964.85227272727 & 40.0866829168497 & 248.58261017498 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 9964.24418604651 & 39.4967485061389 & 252.280113247747 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 9963.4880952381 & 38.8634519627967 & 256.3716703492 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 9962.13414634146 & 38.2845090356047 & 260.213187978371 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 9960.6625 & 37.6563783481714 & 264.514617096301 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 9959.19230769231 & 36.946794451984 & 269.554976430641 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 9958.01315789474 & 36.3540412262663 & 273.917639470022 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 9956.77027027027 & 35.6910596521822 & 278.970990699109 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 9955.84722222222 & 35.0270276803918 & 284.23328730789 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 9954.85714285714 & 34.2488293657633 & 290.66269788504 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 9954.44117647059 & 33.5302556383802 & 296.879370197115 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 9954.15151515152 & 32.7518838222182 & 303.926075494895 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 9954.1875 & 31.9646760251509 & 311.412119183304 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 9954.1935483871 & 31.0211271954246 & 320.884327822081 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 9954.1 & 30.1933945333467 & 329.678068791051 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 9954.01724137931 & 29.2591368801879 & 340.202012183054 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 9953.58928571429 & 28.3788811269348 & 350.739313547749 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 9953.55555555555 & 27.5607792438343 & 361.149279107639 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 9953.17307692308 & 26.7920842347589 & 371.496782023783 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 9952.72 & 25.9673270374405 & 383.27857101541 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 9952 & 25.0541965737768 & 397.218883898132 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 9951.21739130435 & 24.2968937607016 & 409.567473493246 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 9951.06818181818 & 23.7460889786842 & 419.061353250669 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 9950.71428571429 & 23.2909009992008 & 427.236124787777 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 9949.275 & 22.9735351504224 & 433.075490335108 \tabularnewline
Median & 9933.5 &  &  \tabularnewline
Midrange & 10072 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9946.70491803279 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9954.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9946.70491803279 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9954.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9954.1 &  &  \tabularnewline
Midmean - Closest Observation & 9946.70491803279 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9954.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9954.1935483871 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201599&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]9973.44166666667[/C][C]53.9339475627044[/C][C]184.919556557053[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9956.09789902532[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9938.76355085124[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9990.78046459168[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]9971.35[/C][C]53.3263913330449[/C][C]186.987151216082[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]9973.18333333333[/C][C]52.8177883404136[/C][C]188.822433628905[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]9971.08333333333[/C][C]51.6816607636634[/C][C]192.932718995436[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]9971.65[/C][C]51.5612804074424[/C][C]193.394150052191[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]9970.73333333333[/C][C]50.7423459936318[/C][C]196.497287188587[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]9974.78333333333[/C][C]49.6540048107317[/C][C]200.885776914765[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]9974.55[/C][C]48.8164556019281[/C][C]204.327616108328[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]9975.08333333333[/C][C]48.1673823282396[/C][C]207.092078729907[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]9975.68333333333[/C][C]48.0389153980782[/C][C]207.658379683826[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]9975.6[/C][C]48.0263938871525[/C][C]207.710785520138[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]9976.05833333333[/C][C]46.7052131157705[/C][C]213.596249065499[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]9975.55833333333[/C][C]46.1863382674324[/C][C]215.985044659136[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]9980.43333333333[/C][C]45.3123701324647[/C][C]220.258470350522[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]9977.16666666667[/C][C]44.5032704764482[/C][C]224.189515958085[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]9975.29166666667[/C][C]43.9777324540202[/C][C]226.82596646146[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]9971.825[/C][C]43.2272942981507[/C][C]230.683533677161[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]9973.24166666667[/C][C]42.8652716312573[/C][C]232.664842356771[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]9980.14166666667[/C][C]41.678511978728[/C][C]239.455325846575[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]9980.775[/C][C]41.3237719285227[/C][C]241.526233792589[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]9979.775[/C][C]41.1481293884773[/C][C]242.532896350682[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]9974.875[/C][C]39.3750595793422[/C][C]253.32977541025[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]9974.875[/C][C]39.1055716879937[/C][C]255.075544722506[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]9969.50833333333[/C][C]38.236984010185[/C][C]260.729463669985[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]9969.70833333333[/C][C]38.1652668070439[/C][C]261.224646580835[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]9960.75[/C][C]36.7093479306048[/C][C]271.340967941729[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]9958.58333333333[/C][C]36.1390319947847[/C][C]275.563090200381[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]9953.63333333333[/C][C]35.1270561632561[/C][C]283.360873939249[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]9954.1[/C][C]35.0722132186724[/C][C]283.817275457838[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]9955.55[/C][C]33.0461243950787[/C][C]301.262256383765[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]9955.3[/C][C]32.5563476192911[/C][C]305.786758281848[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]9960.20833333333[/C][C]30.9371004958691[/C][C]321.950285375428[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]9954.075[/C][C]29.3366916904708[/C][C]339.30461911059[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]9959.025[/C][C]27.8685074274259[/C][C]357.357674282877[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]9959.59166666667[/C][C]27.05555674306[/C][C]368.116308278203[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]9962.8[/C][C]26.3250783075599[/C][C]378.452815357398[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]9962.8[/C][C]24.2382016694322[/C][C]411.037094908097[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]9953.24166666667[/C][C]22.0800586732253[/C][C]450.779674726868[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]9955.775[/C][C]20.6811002587668[/C][C]481.394842413169[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]9969.425[/C][C]19.0999936296497[/C][C]521.959598170966[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]9968.425[/C][C]18.9245615104114[/C][C]526.745361815429[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]9971.77118644068[/C][C]52.0679950970978[/C][C]191.514406649326[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]9972.20689655172[/C][C]50.6702431493653[/C][C]196.805980724342[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]9971.69298245614[/C][C]49.4155142519043[/C][C]201.792759488926[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]9971.91071428571[/C][C]48.4874195122885[/C][C]205.659752871742[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]9971.98181818182[/C][C]47.4925234128468[/C][C]209.9695089161[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]9972.25925925926[/C][C]46.6042015748094[/C][C]213.977687038618[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]9971.78301886793[/C][C]45.8660908923976[/C][C]217.410789209437[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]9971.32692307692[/C][C]45.212834667309[/C][C]220.541954435046[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]9970.77450980392[/C][C]44.6007807786085[/C][C]223.556052960089[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]9970.12[/C][C]43.9330005965236[/C][C]226.939199795721[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]9969.44897959184[/C][C]43.180842163015[/C][C]230.876668453002[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]9968.69791666667[/C][C]42.5396257989208[/C][C]234.339106878546[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]9967.96808510638[/C][C]41.889758610998[/C][C]237.957162218866[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]9966.71739130435[/C][C]41.2754903971106[/C][C]241.468176281245[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]9965.72222222222[/C][C]40.6880708323628[/C][C]244.929828776635[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]9964.85227272727[/C][C]40.0866829168497[/C][C]248.58261017498[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]9964.24418604651[/C][C]39.4967485061389[/C][C]252.280113247747[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]9963.4880952381[/C][C]38.8634519627967[/C][C]256.3716703492[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]9962.13414634146[/C][C]38.2845090356047[/C][C]260.213187978371[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]9960.6625[/C][C]37.6563783481714[/C][C]264.514617096301[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]9959.19230769231[/C][C]36.946794451984[/C][C]269.554976430641[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]9958.01315789474[/C][C]36.3540412262663[/C][C]273.917639470022[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]9956.77027027027[/C][C]35.6910596521822[/C][C]278.970990699109[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]9955.84722222222[/C][C]35.0270276803918[/C][C]284.23328730789[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]9954.85714285714[/C][C]34.2488293657633[/C][C]290.66269788504[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]9954.44117647059[/C][C]33.5302556383802[/C][C]296.879370197115[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]9954.15151515152[/C][C]32.7518838222182[/C][C]303.926075494895[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]9954.1875[/C][C]31.9646760251509[/C][C]311.412119183304[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]9954.1935483871[/C][C]31.0211271954246[/C][C]320.884327822081[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]9954.1[/C][C]30.1933945333467[/C][C]329.678068791051[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]9954.01724137931[/C][C]29.2591368801879[/C][C]340.202012183054[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]9953.58928571429[/C][C]28.3788811269348[/C][C]350.739313547749[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]9953.55555555555[/C][C]27.5607792438343[/C][C]361.149279107639[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]9953.17307692308[/C][C]26.7920842347589[/C][C]371.496782023783[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]9952.72[/C][C]25.9673270374405[/C][C]383.27857101541[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]9952[/C][C]25.0541965737768[/C][C]397.218883898132[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]9951.21739130435[/C][C]24.2968937607016[/C][C]409.567473493246[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]9951.06818181818[/C][C]23.7460889786842[/C][C]419.061353250669[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]9950.71428571429[/C][C]23.2909009992008[/C][C]427.236124787777[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]9949.275[/C][C]22.9735351504224[/C][C]433.075490335108[/C][/ROW]
[ROW][C]Median[/C][C]9933.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10072[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9946.70491803279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9954.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9946.70491803279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9954.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9954.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9946.70491803279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9954.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9954.1935483871[/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=201599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201599&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 Mean9973.4416666666753.9339475627044184.919556557053
Geometric Mean9956.09789902532
Harmonic Mean9938.76355085124
Quadratic Mean9990.78046459168
Winsorized Mean ( 1 / 40 )9971.3553.3263913330449186.987151216082
Winsorized Mean ( 2 / 40 )9973.1833333333352.8177883404136188.822433628905
Winsorized Mean ( 3 / 40 )9971.0833333333351.6816607636634192.932718995436
Winsorized Mean ( 4 / 40 )9971.6551.5612804074424193.394150052191
Winsorized Mean ( 5 / 40 )9970.7333333333350.7423459936318196.497287188587
Winsorized Mean ( 6 / 40 )9974.7833333333349.6540048107317200.885776914765
Winsorized Mean ( 7 / 40 )9974.5548.8164556019281204.327616108328
Winsorized Mean ( 8 / 40 )9975.0833333333348.1673823282396207.092078729907
Winsorized Mean ( 9 / 40 )9975.6833333333348.0389153980782207.658379683826
Winsorized Mean ( 10 / 40 )9975.648.0263938871525207.710785520138
Winsorized Mean ( 11 / 40 )9976.0583333333346.7052131157705213.596249065499
Winsorized Mean ( 12 / 40 )9975.5583333333346.1863382674324215.985044659136
Winsorized Mean ( 13 / 40 )9980.4333333333345.3123701324647220.258470350522
Winsorized Mean ( 14 / 40 )9977.1666666666744.5032704764482224.189515958085
Winsorized Mean ( 15 / 40 )9975.2916666666743.9777324540202226.82596646146
Winsorized Mean ( 16 / 40 )9971.82543.2272942981507230.683533677161
Winsorized Mean ( 17 / 40 )9973.2416666666742.8652716312573232.664842356771
Winsorized Mean ( 18 / 40 )9980.1416666666741.678511978728239.455325846575
Winsorized Mean ( 19 / 40 )9980.77541.3237719285227241.526233792589
Winsorized Mean ( 20 / 40 )9979.77541.1481293884773242.532896350682
Winsorized Mean ( 21 / 40 )9974.87539.3750595793422253.32977541025
Winsorized Mean ( 22 / 40 )9974.87539.1055716879937255.075544722506
Winsorized Mean ( 23 / 40 )9969.5083333333338.236984010185260.729463669985
Winsorized Mean ( 24 / 40 )9969.7083333333338.1652668070439261.224646580835
Winsorized Mean ( 25 / 40 )9960.7536.7093479306048271.340967941729
Winsorized Mean ( 26 / 40 )9958.5833333333336.1390319947847275.563090200381
Winsorized Mean ( 27 / 40 )9953.6333333333335.1270561632561283.360873939249
Winsorized Mean ( 28 / 40 )9954.135.0722132186724283.817275457838
Winsorized Mean ( 29 / 40 )9955.5533.0461243950787301.262256383765
Winsorized Mean ( 30 / 40 )9955.332.5563476192911305.786758281848
Winsorized Mean ( 31 / 40 )9960.2083333333330.9371004958691321.950285375428
Winsorized Mean ( 32 / 40 )9954.07529.3366916904708339.30461911059
Winsorized Mean ( 33 / 40 )9959.02527.8685074274259357.357674282877
Winsorized Mean ( 34 / 40 )9959.5916666666727.05555674306368.116308278203
Winsorized Mean ( 35 / 40 )9962.826.3250783075599378.452815357398
Winsorized Mean ( 36 / 40 )9962.824.2382016694322411.037094908097
Winsorized Mean ( 37 / 40 )9953.2416666666722.0800586732253450.779674726868
Winsorized Mean ( 38 / 40 )9955.77520.6811002587668481.394842413169
Winsorized Mean ( 39 / 40 )9969.42519.0999936296497521.959598170966
Winsorized Mean ( 40 / 40 )9968.42518.9245615104114526.745361815429
Trimmed Mean ( 1 / 40 )9971.7711864406852.0679950970978191.514406649326
Trimmed Mean ( 2 / 40 )9972.2068965517250.6702431493653196.805980724342
Trimmed Mean ( 3 / 40 )9971.6929824561449.4155142519043201.792759488926
Trimmed Mean ( 4 / 40 )9971.9107142857148.4874195122885205.659752871742
Trimmed Mean ( 5 / 40 )9971.9818181818247.4925234128468209.9695089161
Trimmed Mean ( 6 / 40 )9972.2592592592646.6042015748094213.977687038618
Trimmed Mean ( 7 / 40 )9971.7830188679345.8660908923976217.410789209437
Trimmed Mean ( 8 / 40 )9971.3269230769245.212834667309220.541954435046
Trimmed Mean ( 9 / 40 )9970.7745098039244.6007807786085223.556052960089
Trimmed Mean ( 10 / 40 )9970.1243.9330005965236226.939199795721
Trimmed Mean ( 11 / 40 )9969.4489795918443.180842163015230.876668453002
Trimmed Mean ( 12 / 40 )9968.6979166666742.5396257989208234.339106878546
Trimmed Mean ( 13 / 40 )9967.9680851063841.889758610998237.957162218866
Trimmed Mean ( 14 / 40 )9966.7173913043541.2754903971106241.468176281245
Trimmed Mean ( 15 / 40 )9965.7222222222240.6880708323628244.929828776635
Trimmed Mean ( 16 / 40 )9964.8522727272740.0866829168497248.58261017498
Trimmed Mean ( 17 / 40 )9964.2441860465139.4967485061389252.280113247747
Trimmed Mean ( 18 / 40 )9963.488095238138.8634519627967256.3716703492
Trimmed Mean ( 19 / 40 )9962.1341463414638.2845090356047260.213187978371
Trimmed Mean ( 20 / 40 )9960.662537.6563783481714264.514617096301
Trimmed Mean ( 21 / 40 )9959.1923076923136.946794451984269.554976430641
Trimmed Mean ( 22 / 40 )9958.0131578947436.3540412262663273.917639470022
Trimmed Mean ( 23 / 40 )9956.7702702702735.6910596521822278.970990699109
Trimmed Mean ( 24 / 40 )9955.8472222222235.0270276803918284.23328730789
Trimmed Mean ( 25 / 40 )9954.8571428571434.2488293657633290.66269788504
Trimmed Mean ( 26 / 40 )9954.4411764705933.5302556383802296.879370197115
Trimmed Mean ( 27 / 40 )9954.1515151515232.7518838222182303.926075494895
Trimmed Mean ( 28 / 40 )9954.187531.9646760251509311.412119183304
Trimmed Mean ( 29 / 40 )9954.193548387131.0211271954246320.884327822081
Trimmed Mean ( 30 / 40 )9954.130.1933945333467329.678068791051
Trimmed Mean ( 31 / 40 )9954.0172413793129.2591368801879340.202012183054
Trimmed Mean ( 32 / 40 )9953.5892857142928.3788811269348350.739313547749
Trimmed Mean ( 33 / 40 )9953.5555555555527.5607792438343361.149279107639
Trimmed Mean ( 34 / 40 )9953.1730769230826.7920842347589371.496782023783
Trimmed Mean ( 35 / 40 )9952.7225.9673270374405383.27857101541
Trimmed Mean ( 36 / 40 )995225.0541965737768397.218883898132
Trimmed Mean ( 37 / 40 )9951.2173913043524.2968937607016409.567473493246
Trimmed Mean ( 38 / 40 )9951.0681818181823.7460889786842419.061353250669
Trimmed Mean ( 39 / 40 )9950.7142857142923.2909009992008427.236124787777
Trimmed Mean ( 40 / 40 )9949.27522.9735351504224433.075490335108
Median9933.5
Midrange10072
Midmean - Weighted Average at Xnp9946.70491803279
Midmean - Weighted Average at X(n+1)p9954.1
Midmean - Empirical Distribution Function9946.70491803279
Midmean - Empirical Distribution Function - Averaging9954.1
Midmean - Empirical Distribution Function - Interpolation9954.1
Midmean - Closest Observation9946.70491803279
Midmean - True Basic - Statistics Graphics Toolkit9954.1
Midmean - MS Excel (old versions)9954.1935483871
Number of observations120


Figures (Output of Computation)

Input Parameters & R Code

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')