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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 computationFri, 12 Dec 2008 05:54:43 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/12/t1229086536i8z3svtial3qkly.htm/, Retrieved Tue, 14 May 2024 12:08:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32653, Retrieved Tue, 14 May 2024 12:08:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency:...] [2008-12-12 12:54:43] [e81ac192d6ae6d77191d83851a692999] [Current]
- RM      [Tukey lambda PPCC Plot] [PPCC plot- Goudprijs] [2008-12-12 14:43:10] [73d6180dc45497329efd1b6934a84aba]
- RM D    [Tukey lambda PPCC Plot] [PPCC Plot- Prijs ...] [2008-12-12 14:44:50] [73d6180dc45497329efd1b6934a84aba]
- RM D    [Mean Plot] [Mean plot Bel 20] [2008-12-12 14:53:40] [73d6180dc45497329efd1b6934a84aba]
- RM D    [Mean Plot] [Mean Plot: Dow Jones] [2008-12-12 14:55:28] [73d6180dc45497329efd1b6934a84aba]
- RM D    [Partial Correlation] [Partial Correlati...] [2008-12-12 14:58:36] [73d6180dc45497329efd1b6934a84aba]
- RMPD    [Multiple Regression] [Multiple regression] [2008-12-13 15:07:42] [73d6180dc45497329efd1b6934a84aba]
- RMPD    [Multiple Regression] [multiple regressi...] [2008-12-13 15:26:12] [73d6180dc45497329efd1b6934a84aba]
- RMPD    [Multiple Regression] [Met lineaire trend] [2008-12-13 15:36:57] [73d6180dc45497329efd1b6934a84aba]
-    D      [Multiple Regression] [Met dummy variabe...] [2008-12-13 15:45:07] [73d6180dc45497329efd1b6934a84aba]
-    D        [Multiple Regression] [Met dummy variabe...] [2008-12-17 22:49:07] [73d6180dc45497329efd1b6934a84aba]
-  M D          [Multiple Regression] [multiple regressi...] [2009-12-31 12:41:12] [e7f1ba0a0206726eaff83376fb7dde21]
- RMP     [ARIMA Backward Selection] [ARIMA goudprijs] [2008-12-14 20:12:57] [73d6180dc45497329efd1b6934a84aba]
- RMPD      [Central Tendency] [Central tendency ...] [2008-12-14 21:08:06] [73d6180dc45497329efd1b6934a84aba]
- RMP       [ARIMA Forecasting] [ARIMA forecast: P...] [2008-12-14 22:37:34] [73d6180dc45497329efd1b6934a84aba]
-   P         [ARIMA Forecasting] [Arima forecasting...] [2008-12-19 23:12:59] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD      [ARIMA Forecasting] [ARIMA forecast: O...] [2008-12-14 22:42:36] [73d6180dc45497329efd1b6934a84aba]
-   PD        [ARIMA Forecasting] [arima forecast ol...] [2008-12-16 16:27:50] [73d6180dc45497329efd1b6934a84aba]
-   P           [ARIMA Forecasting] [Lambda -0,2 ARIMA...] [2008-12-19 21:26:09] [73d6180dc45497329efd1b6934a84aba]
- R  D            [ARIMA Forecasting] [ARIMA Forecast olie] [2008-12-22 13:09:43] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 22:22:39] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:35:36] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:39:14] [74be16979710d4c4e7c6647856088456]
- R PD            [ARIMA Forecasting] [Forecast BEL20] [2008-12-22 14:06:40] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
-   P       [ARIMA Backward Selection] [Backward selectio...] [2008-12-17 20:53:03] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD    [ARIMA Backward Selection] [Arima Olieprijs] [2008-12-14 20:17:24] [73d6180dc45497329efd1b6934a84aba]
- RMPD      [Central Tendency] [Central tendency:...] [2008-12-14 21:10:49] [73d6180dc45497329efd1b6934a84aba]
-    D        [Central Tendency] [Central tendency ...] [2008-12-16 16:14:21] [73d6180dc45497329efd1b6934a84aba]
- RMPD      [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-14 22:19:56] [73d6180dc45497329efd1b6934a84aba]
- RMP       [ARIMA Forecasting] [ARIMA forecast Ol...] [2008-12-14 22:26:28] [73d6180dc45497329efd1b6934a84aba]
-   PD      [ARIMA Backward Selection] [Arima backward se...] [2008-12-16 16:06:23] [73d6180dc45497329efd1b6934a84aba]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10070
10137
9984
9732
9103
9155
9308
9394
9948
10177
10002
9728
10002
10063
10018
9960
10236
10893
10756
10940
10997
10827
10166
10186
10457
10368
10244
10511
10812
10738
10171
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32653&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32653&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean12765.7777777778330.00478484426638.6836141900249
Geometric Mean12387.9539316305
Harmonic Mean12056.236229819
Quadratic Mean13177.1617489342
Winsorized Mean ( 1 / 33 )12765.898989899329.85370516325238.7016995415615
Winsorized Mean ( 2 / 33 )12759.6161616162327.44457113684238.9672551825078
Winsorized Mean ( 3 / 33 )12754.6464646465325.56621159919339.1768126120802
Winsorized Mean ( 4 / 33 )12759.8181818182322.58006517209239.5555074831143
Winsorized Mean ( 5 / 33 )12759.3131313131322.37150409350439.579531594121
Winsorized Mean ( 6 / 33 )12723.5555555556315.2741449621240.3571170007749
Winsorized Mean ( 7 / 33 )12723.2020202020313.27824749657440.6131039160042
Winsorized Mean ( 8 / 33 )12725.3838383838312.12208704051440.7705329636991
Winsorized Mean ( 9 / 33 )12723.2929292929311.04864703616940.9045114020812
Winsorized Mean ( 10 / 33 )12694.2020202020305.0570131599141.612555924252
Winsorized Mean ( 11 / 33 )12658.4242424242298.36279021488142.4262832282391
Winsorized Mean ( 12 / 33 )12655.3939393939297.06427768917342.6015340445465
Winsorized Mean ( 13 / 33 )12574.7676767677282.93196199835744.4444932553810
Winsorized Mean ( 14 / 33 )12570.2424242424282.20059141919444.5436430909885
Winsorized Mean ( 15 / 33 )12482.6666666667267.92292256272146.5905139704666
Winsorized Mean ( 16 / 33 )12475.3939393939265.06397745747147.0655954802293
Winsorized Mean ( 17 / 33 )12446.2020202020260.46861934903847.7838829541443
Winsorized Mean ( 18 / 33 )12436.3838383838256.15485023501348.5502571080496
Winsorized Mean ( 19 / 33 )12433.3131313131254.40664376742348.8718098992713
Winsorized Mean ( 20 / 33 )12420.5858585859252.35410296212449.2188782064307
Winsorized Mean ( 21 / 33 )12419.9494949495251.96707810039749.2919534908474
Winsorized Mean ( 22 / 33 )12402.1717171717248.98761373929749.8103963121532
Winsorized Mean ( 23 / 33 )12384.5151515152243.83737976845050.7900600116176
Winsorized Mean ( 24 / 33 )12379.1818181818242.65139887019551.016321668947
Winsorized Mean ( 25 / 33 )12383.4747474747240.25301647226651.5434724995608
Winsorized Mean ( 26 / 33 )12369.5555555556238.267347847251.914606291283
Winsorized Mean ( 27 / 33 )12384.8282828283235.99867973751252.4783795256958
Winsorized Mean ( 28 / 33 )12308.1818181818225.31206392925054.6272649743543
Winsorized Mean ( 29 / 33 )12271.5656565657219.57913171766255.8867573642863
Winsorized Mean ( 30 / 33 )12269.4444444444217.67891710218056.3648726655742
Winsorized Mean ( 31 / 33 )12214.0202020202209.84521097838458.2049032478438
Winsorized Mean ( 32 / 33 )12212.4040404040208.34643220128958.6158539475507
Winsorized Mean ( 33 / 33 )12206.0707070707205.59599234955259.369205438198
Trimmed Mean ( 1 / 33 )12727.4329896907325.81556930791439.0633050984209
Trimmed Mean ( 2 / 33 )12687.3473684211321.17069128121939.5034407336749
Trimmed Mean ( 3 / 33 )12648.8817204301317.25770346666839.8694234441467
Trimmed Mean ( 4 / 33 )12610.5274725275313.50506257318040.2243184496706
Trimmed Mean ( 5 / 33 )12569.0112359551310.09150042355140.5332336384170
Trimmed Mean ( 6 / 33 )12525.7011494253306.1313887683540.9160955360363
Trimmed Mean ( 7 / 33 )12487.2941176471303.23955217119841.1796351374282
Trimmed Mean ( 8 / 33 )12447.0963855422300.21021218470841.4612690719659
Trimmed Mean ( 9 / 33 )12404.5802469136296.7993964754841.7944928265324
Trimmed Mean ( 10 / 33 )12360.2025316456292.90993039194842.1979634323294
Trimmed Mean ( 11 / 33 )12317.2597402597289.36816667708142.566049616664
Trimmed Mean ( 12 / 33 )12276.32286.28350162190842.8816887122375
Trimmed Mean ( 13 / 33 )12233.4794520548282.71710122723043.2710982071874
Trimmed Mean ( 14 / 33 )12196.8732394366280.73561026176443.4461208111930
Trimmed Mean ( 15 / 33 )12158.6086956522278.30058070617543.688765092765
Trimmed Mean ( 16 / 33 )12126.6865671642277.46568334022643.7051761543229
Trimmed Mean ( 17 / 33 )12093.4923076923276.60697968962743.7208501436301
Trimmed Mean ( 18 / 33 )12060.8888888889275.97982323371143.7020675916415
Trimmed Mean ( 19 / 33 )12027.0327868852275.51029551162643.6536600730325
Trimmed Mean ( 20 / 33 )11991.1525423729274.82104885110043.6325841579543
Trimmed Mean ( 21 / 33 )11953.8596491228273.91281729378343.6411109462680
Trimmed Mean ( 22 / 33 )11913.9090909091272.44454570918743.7296663799842
Trimmed Mean ( 23 / 33 )11872.4528301887270.70850915229643.8569621153263
Trimmed Mean ( 24 / 33 )11829.2352941176268.94505538176843.9838363167749
Trimmed Mean ( 25 / 33 )11782.9387755102266.44523184243244.2227421148909
Trimmed Mean ( 26 / 33 )11732.3404255319263.14266869068944.5854732868226
Trimmed Mean ( 27 / 33 )11732.3404255319258.78721318092345.3358582957869
Trimmed Mean ( 28 / 33 )11618.1860465116252.90613479830845.9387276460379
Trimmed Mean ( 29 / 33 )11558.6829268293247.20542568199246.7573998221968
Trimmed Mean ( 30 / 33 )11496.2820512821240.41686117506647.8181188918805
Trimmed Mean ( 31 / 33 )11427.3243243243230.94448344898149.4808282651566
Trimmed Mean ( 32 / 33 )11355.5428571429219.61780530768351.7059299505968
Trimmed Mean ( 33 / 33 )11275.2121212121203.06466706583955.5252289043292
Median10812
Midrange14625.5
Midmean - Weighted Average at Xnp11752.16
Midmean - Weighted Average at X(n+1)p11829.2352941176
Midmean - Empirical Distribution Function11829.2352941176
Midmean - Empirical Distribution Function - Averaging11829.2352941176
Midmean - Empirical Distribution Function - Interpolation11782.9387755102
Midmean - Closest Observation11752.16
Midmean - True Basic - Statistics Graphics Toolkit11829.2352941176
Midmean - MS Excel (old versions)11829.2352941176
Number of observations99

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12765.7777777778 & 330.004784844266 & 38.6836141900249 \tabularnewline
Geometric Mean & 12387.9539316305 &  &  \tabularnewline
Harmonic Mean & 12056.236229819 &  &  \tabularnewline
Quadratic Mean & 13177.1617489342 &  &  \tabularnewline
Winsorized Mean ( 1 / 33 ) & 12765.898989899 & 329.853705163252 & 38.7016995415615 \tabularnewline
Winsorized Mean ( 2 / 33 ) & 12759.6161616162 & 327.444571136842 & 38.9672551825078 \tabularnewline
Winsorized Mean ( 3 / 33 ) & 12754.6464646465 & 325.566211599193 & 39.1768126120802 \tabularnewline
Winsorized Mean ( 4 / 33 ) & 12759.8181818182 & 322.580065172092 & 39.5555074831143 \tabularnewline
Winsorized Mean ( 5 / 33 ) & 12759.3131313131 & 322.371504093504 & 39.579531594121 \tabularnewline
Winsorized Mean ( 6 / 33 ) & 12723.5555555556 & 315.27414496212 & 40.3571170007749 \tabularnewline
Winsorized Mean ( 7 / 33 ) & 12723.2020202020 & 313.278247496574 & 40.6131039160042 \tabularnewline
Winsorized Mean ( 8 / 33 ) & 12725.3838383838 & 312.122087040514 & 40.7705329636991 \tabularnewline
Winsorized Mean ( 9 / 33 ) & 12723.2929292929 & 311.048647036169 & 40.9045114020812 \tabularnewline
Winsorized Mean ( 10 / 33 ) & 12694.2020202020 & 305.05701315991 & 41.612555924252 \tabularnewline
Winsorized Mean ( 11 / 33 ) & 12658.4242424242 & 298.362790214881 & 42.4262832282391 \tabularnewline
Winsorized Mean ( 12 / 33 ) & 12655.3939393939 & 297.064277689173 & 42.6015340445465 \tabularnewline
Winsorized Mean ( 13 / 33 ) & 12574.7676767677 & 282.931961998357 & 44.4444932553810 \tabularnewline
Winsorized Mean ( 14 / 33 ) & 12570.2424242424 & 282.200591419194 & 44.5436430909885 \tabularnewline
Winsorized Mean ( 15 / 33 ) & 12482.6666666667 & 267.922922562721 & 46.5905139704666 \tabularnewline
Winsorized Mean ( 16 / 33 ) & 12475.3939393939 & 265.063977457471 & 47.0655954802293 \tabularnewline
Winsorized Mean ( 17 / 33 ) & 12446.2020202020 & 260.468619349038 & 47.7838829541443 \tabularnewline
Winsorized Mean ( 18 / 33 ) & 12436.3838383838 & 256.154850235013 & 48.5502571080496 \tabularnewline
Winsorized Mean ( 19 / 33 ) & 12433.3131313131 & 254.406643767423 & 48.8718098992713 \tabularnewline
Winsorized Mean ( 20 / 33 ) & 12420.5858585859 & 252.354102962124 & 49.2188782064307 \tabularnewline
Winsorized Mean ( 21 / 33 ) & 12419.9494949495 & 251.967078100397 & 49.2919534908474 \tabularnewline
Winsorized Mean ( 22 / 33 ) & 12402.1717171717 & 248.987613739297 & 49.8103963121532 \tabularnewline
Winsorized Mean ( 23 / 33 ) & 12384.5151515152 & 243.837379768450 & 50.7900600116176 \tabularnewline
Winsorized Mean ( 24 / 33 ) & 12379.1818181818 & 242.651398870195 & 51.016321668947 \tabularnewline
Winsorized Mean ( 25 / 33 ) & 12383.4747474747 & 240.253016472266 & 51.5434724995608 \tabularnewline
Winsorized Mean ( 26 / 33 ) & 12369.5555555556 & 238.2673478472 & 51.914606291283 \tabularnewline
Winsorized Mean ( 27 / 33 ) & 12384.8282828283 & 235.998679737512 & 52.4783795256958 \tabularnewline
Winsorized Mean ( 28 / 33 ) & 12308.1818181818 & 225.312063929250 & 54.6272649743543 \tabularnewline
Winsorized Mean ( 29 / 33 ) & 12271.5656565657 & 219.579131717662 & 55.8867573642863 \tabularnewline
Winsorized Mean ( 30 / 33 ) & 12269.4444444444 & 217.678917102180 & 56.3648726655742 \tabularnewline
Winsorized Mean ( 31 / 33 ) & 12214.0202020202 & 209.845210978384 & 58.2049032478438 \tabularnewline
Winsorized Mean ( 32 / 33 ) & 12212.4040404040 & 208.346432201289 & 58.6158539475507 \tabularnewline
Winsorized Mean ( 33 / 33 ) & 12206.0707070707 & 205.595992349552 & 59.369205438198 \tabularnewline
Trimmed Mean ( 1 / 33 ) & 12727.4329896907 & 325.815569307914 & 39.0633050984209 \tabularnewline
Trimmed Mean ( 2 / 33 ) & 12687.3473684211 & 321.170691281219 & 39.5034407336749 \tabularnewline
Trimmed Mean ( 3 / 33 ) & 12648.8817204301 & 317.257703466668 & 39.8694234441467 \tabularnewline
Trimmed Mean ( 4 / 33 ) & 12610.5274725275 & 313.505062573180 & 40.2243184496706 \tabularnewline
Trimmed Mean ( 5 / 33 ) & 12569.0112359551 & 310.091500423551 & 40.5332336384170 \tabularnewline
Trimmed Mean ( 6 / 33 ) & 12525.7011494253 & 306.13138876835 & 40.9160955360363 \tabularnewline
Trimmed Mean ( 7 / 33 ) & 12487.2941176471 & 303.239552171198 & 41.1796351374282 \tabularnewline
Trimmed Mean ( 8 / 33 ) & 12447.0963855422 & 300.210212184708 & 41.4612690719659 \tabularnewline
Trimmed Mean ( 9 / 33 ) & 12404.5802469136 & 296.79939647548 & 41.7944928265324 \tabularnewline
Trimmed Mean ( 10 / 33 ) & 12360.2025316456 & 292.909930391948 & 42.1979634323294 \tabularnewline
Trimmed Mean ( 11 / 33 ) & 12317.2597402597 & 289.368166677081 & 42.566049616664 \tabularnewline
Trimmed Mean ( 12 / 33 ) & 12276.32 & 286.283501621908 & 42.8816887122375 \tabularnewline
Trimmed Mean ( 13 / 33 ) & 12233.4794520548 & 282.717101227230 & 43.2710982071874 \tabularnewline
Trimmed Mean ( 14 / 33 ) & 12196.8732394366 & 280.735610261764 & 43.4461208111930 \tabularnewline
Trimmed Mean ( 15 / 33 ) & 12158.6086956522 & 278.300580706175 & 43.688765092765 \tabularnewline
Trimmed Mean ( 16 / 33 ) & 12126.6865671642 & 277.465683340226 & 43.7051761543229 \tabularnewline
Trimmed Mean ( 17 / 33 ) & 12093.4923076923 & 276.606979689627 & 43.7208501436301 \tabularnewline
Trimmed Mean ( 18 / 33 ) & 12060.8888888889 & 275.979823233711 & 43.7020675916415 \tabularnewline
Trimmed Mean ( 19 / 33 ) & 12027.0327868852 & 275.510295511626 & 43.6536600730325 \tabularnewline
Trimmed Mean ( 20 / 33 ) & 11991.1525423729 & 274.821048851100 & 43.6325841579543 \tabularnewline
Trimmed Mean ( 21 / 33 ) & 11953.8596491228 & 273.912817293783 & 43.6411109462680 \tabularnewline
Trimmed Mean ( 22 / 33 ) & 11913.9090909091 & 272.444545709187 & 43.7296663799842 \tabularnewline
Trimmed Mean ( 23 / 33 ) & 11872.4528301887 & 270.708509152296 & 43.8569621153263 \tabularnewline
Trimmed Mean ( 24 / 33 ) & 11829.2352941176 & 268.945055381768 & 43.9838363167749 \tabularnewline
Trimmed Mean ( 25 / 33 ) & 11782.9387755102 & 266.445231842432 & 44.2227421148909 \tabularnewline
Trimmed Mean ( 26 / 33 ) & 11732.3404255319 & 263.142668690689 & 44.5854732868226 \tabularnewline
Trimmed Mean ( 27 / 33 ) & 11732.3404255319 & 258.787213180923 & 45.3358582957869 \tabularnewline
Trimmed Mean ( 28 / 33 ) & 11618.1860465116 & 252.906134798308 & 45.9387276460379 \tabularnewline
Trimmed Mean ( 29 / 33 ) & 11558.6829268293 & 247.205425681992 & 46.7573998221968 \tabularnewline
Trimmed Mean ( 30 / 33 ) & 11496.2820512821 & 240.416861175066 & 47.8181188918805 \tabularnewline
Trimmed Mean ( 31 / 33 ) & 11427.3243243243 & 230.944483448981 & 49.4808282651566 \tabularnewline
Trimmed Mean ( 32 / 33 ) & 11355.5428571429 & 219.617805307683 & 51.7059299505968 \tabularnewline
Trimmed Mean ( 33 / 33 ) & 11275.2121212121 & 203.064667065839 & 55.5252289043292 \tabularnewline
Median & 10812 &  &  \tabularnewline
Midrange & 14625.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11752.16 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11829.2352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11829.2352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11829.2352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11782.9387755102 &  &  \tabularnewline
Midmean - Closest Observation & 11752.16 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11829.2352941176 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11829.2352941176 &  &  \tabularnewline
Number of observations & 99 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32653&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]12765.7777777778[/C][C]330.004784844266[/C][C]38.6836141900249[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12387.9539316305[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12056.236229819[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13177.1617489342[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 33 )[/C][C]12765.898989899[/C][C]329.853705163252[/C][C]38.7016995415615[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 33 )[/C][C]12759.6161616162[/C][C]327.444571136842[/C][C]38.9672551825078[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 33 )[/C][C]12754.6464646465[/C][C]325.566211599193[/C][C]39.1768126120802[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 33 )[/C][C]12759.8181818182[/C][C]322.580065172092[/C][C]39.5555074831143[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 33 )[/C][C]12759.3131313131[/C][C]322.371504093504[/C][C]39.579531594121[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 33 )[/C][C]12723.5555555556[/C][C]315.27414496212[/C][C]40.3571170007749[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 33 )[/C][C]12723.2020202020[/C][C]313.278247496574[/C][C]40.6131039160042[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 33 )[/C][C]12725.3838383838[/C][C]312.122087040514[/C][C]40.7705329636991[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 33 )[/C][C]12723.2929292929[/C][C]311.048647036169[/C][C]40.9045114020812[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 33 )[/C][C]12694.2020202020[/C][C]305.05701315991[/C][C]41.612555924252[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 33 )[/C][C]12658.4242424242[/C][C]298.362790214881[/C][C]42.4262832282391[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 33 )[/C][C]12655.3939393939[/C][C]297.064277689173[/C][C]42.6015340445465[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 33 )[/C][C]12574.7676767677[/C][C]282.931961998357[/C][C]44.4444932553810[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 33 )[/C][C]12570.2424242424[/C][C]282.200591419194[/C][C]44.5436430909885[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 33 )[/C][C]12482.6666666667[/C][C]267.922922562721[/C][C]46.5905139704666[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 33 )[/C][C]12475.3939393939[/C][C]265.063977457471[/C][C]47.0655954802293[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 33 )[/C][C]12446.2020202020[/C][C]260.468619349038[/C][C]47.7838829541443[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 33 )[/C][C]12436.3838383838[/C][C]256.154850235013[/C][C]48.5502571080496[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 33 )[/C][C]12433.3131313131[/C][C]254.406643767423[/C][C]48.8718098992713[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 33 )[/C][C]12420.5858585859[/C][C]252.354102962124[/C][C]49.2188782064307[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 33 )[/C][C]12419.9494949495[/C][C]251.967078100397[/C][C]49.2919534908474[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 33 )[/C][C]12402.1717171717[/C][C]248.987613739297[/C][C]49.8103963121532[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 33 )[/C][C]12384.5151515152[/C][C]243.837379768450[/C][C]50.7900600116176[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 33 )[/C][C]12379.1818181818[/C][C]242.651398870195[/C][C]51.016321668947[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 33 )[/C][C]12383.4747474747[/C][C]240.253016472266[/C][C]51.5434724995608[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 33 )[/C][C]12369.5555555556[/C][C]238.2673478472[/C][C]51.914606291283[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 33 )[/C][C]12384.8282828283[/C][C]235.998679737512[/C][C]52.4783795256958[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 33 )[/C][C]12308.1818181818[/C][C]225.312063929250[/C][C]54.6272649743543[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 33 )[/C][C]12271.5656565657[/C][C]219.579131717662[/C][C]55.8867573642863[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 33 )[/C][C]12269.4444444444[/C][C]217.678917102180[/C][C]56.3648726655742[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 33 )[/C][C]12214.0202020202[/C][C]209.845210978384[/C][C]58.2049032478438[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 33 )[/C][C]12212.4040404040[/C][C]208.346432201289[/C][C]58.6158539475507[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 33 )[/C][C]12206.0707070707[/C][C]205.595992349552[/C][C]59.369205438198[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 33 )[/C][C]12727.4329896907[/C][C]325.815569307914[/C][C]39.0633050984209[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 33 )[/C][C]12687.3473684211[/C][C]321.170691281219[/C][C]39.5034407336749[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 33 )[/C][C]12648.8817204301[/C][C]317.257703466668[/C][C]39.8694234441467[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 33 )[/C][C]12610.5274725275[/C][C]313.505062573180[/C][C]40.2243184496706[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 33 )[/C][C]12569.0112359551[/C][C]310.091500423551[/C][C]40.5332336384170[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 33 )[/C][C]12525.7011494253[/C][C]306.13138876835[/C][C]40.9160955360363[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 33 )[/C][C]12487.2941176471[/C][C]303.239552171198[/C][C]41.1796351374282[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 33 )[/C][C]12447.0963855422[/C][C]300.210212184708[/C][C]41.4612690719659[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 33 )[/C][C]12404.5802469136[/C][C]296.79939647548[/C][C]41.7944928265324[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 33 )[/C][C]12360.2025316456[/C][C]292.909930391948[/C][C]42.1979634323294[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 33 )[/C][C]12317.2597402597[/C][C]289.368166677081[/C][C]42.566049616664[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 33 )[/C][C]12276.32[/C][C]286.283501621908[/C][C]42.8816887122375[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 33 )[/C][C]12233.4794520548[/C][C]282.717101227230[/C][C]43.2710982071874[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 33 )[/C][C]12196.8732394366[/C][C]280.735610261764[/C][C]43.4461208111930[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 33 )[/C][C]12158.6086956522[/C][C]278.300580706175[/C][C]43.688765092765[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 33 )[/C][C]12126.6865671642[/C][C]277.465683340226[/C][C]43.7051761543229[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 33 )[/C][C]12093.4923076923[/C][C]276.606979689627[/C][C]43.7208501436301[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 33 )[/C][C]12060.8888888889[/C][C]275.979823233711[/C][C]43.7020675916415[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 33 )[/C][C]12027.0327868852[/C][C]275.510295511626[/C][C]43.6536600730325[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 33 )[/C][C]11991.1525423729[/C][C]274.821048851100[/C][C]43.6325841579543[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 33 )[/C][C]11953.8596491228[/C][C]273.912817293783[/C][C]43.6411109462680[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 33 )[/C][C]11913.9090909091[/C][C]272.444545709187[/C][C]43.7296663799842[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 33 )[/C][C]11872.4528301887[/C][C]270.708509152296[/C][C]43.8569621153263[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 33 )[/C][C]11829.2352941176[/C][C]268.945055381768[/C][C]43.9838363167749[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 33 )[/C][C]11782.9387755102[/C][C]266.445231842432[/C][C]44.2227421148909[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 33 )[/C][C]11732.3404255319[/C][C]263.142668690689[/C][C]44.5854732868226[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 33 )[/C][C]11732.3404255319[/C][C]258.787213180923[/C][C]45.3358582957869[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 33 )[/C][C]11618.1860465116[/C][C]252.906134798308[/C][C]45.9387276460379[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 33 )[/C][C]11558.6829268293[/C][C]247.205425681992[/C][C]46.7573998221968[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 33 )[/C][C]11496.2820512821[/C][C]240.416861175066[/C][C]47.8181188918805[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 33 )[/C][C]11427.3243243243[/C][C]230.944483448981[/C][C]49.4808282651566[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 33 )[/C][C]11355.5428571429[/C][C]219.617805307683[/C][C]51.7059299505968[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 33 )[/C][C]11275.2121212121[/C][C]203.064667065839[/C][C]55.5252289043292[/C][/ROW]
[ROW][C]Median[/C][C]10812[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14625.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11752.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11829.2352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11829.2352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11829.2352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11782.9387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11752.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11829.2352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11829.2352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]99[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32653&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 Mean12765.7777777778330.00478484426638.6836141900249
Geometric Mean12387.9539316305
Harmonic Mean12056.236229819
Quadratic Mean13177.1617489342
Winsorized Mean ( 1 / 33 )12765.898989899329.85370516325238.7016995415615
Winsorized Mean ( 2 / 33 )12759.6161616162327.44457113684238.9672551825078
Winsorized Mean ( 3 / 33 )12754.6464646465325.56621159919339.1768126120802
Winsorized Mean ( 4 / 33 )12759.8181818182322.58006517209239.5555074831143
Winsorized Mean ( 5 / 33 )12759.3131313131322.37150409350439.579531594121
Winsorized Mean ( 6 / 33 )12723.5555555556315.2741449621240.3571170007749
Winsorized Mean ( 7 / 33 )12723.2020202020313.27824749657440.6131039160042
Winsorized Mean ( 8 / 33 )12725.3838383838312.12208704051440.7705329636991
Winsorized Mean ( 9 / 33 )12723.2929292929311.04864703616940.9045114020812
Winsorized Mean ( 10 / 33 )12694.2020202020305.0570131599141.612555924252
Winsorized Mean ( 11 / 33 )12658.4242424242298.36279021488142.4262832282391
Winsorized Mean ( 12 / 33 )12655.3939393939297.06427768917342.6015340445465
Winsorized Mean ( 13 / 33 )12574.7676767677282.93196199835744.4444932553810
Winsorized Mean ( 14 / 33 )12570.2424242424282.20059141919444.5436430909885
Winsorized Mean ( 15 / 33 )12482.6666666667267.92292256272146.5905139704666
Winsorized Mean ( 16 / 33 )12475.3939393939265.06397745747147.0655954802293
Winsorized Mean ( 17 / 33 )12446.2020202020260.46861934903847.7838829541443
Winsorized Mean ( 18 / 33 )12436.3838383838256.15485023501348.5502571080496
Winsorized Mean ( 19 / 33 )12433.3131313131254.40664376742348.8718098992713
Winsorized Mean ( 20 / 33 )12420.5858585859252.35410296212449.2188782064307
Winsorized Mean ( 21 / 33 )12419.9494949495251.96707810039749.2919534908474
Winsorized Mean ( 22 / 33 )12402.1717171717248.98761373929749.8103963121532
Winsorized Mean ( 23 / 33 )12384.5151515152243.83737976845050.7900600116176
Winsorized Mean ( 24 / 33 )12379.1818181818242.65139887019551.016321668947
Winsorized Mean ( 25 / 33 )12383.4747474747240.25301647226651.5434724995608
Winsorized Mean ( 26 / 33 )12369.5555555556238.267347847251.914606291283
Winsorized Mean ( 27 / 33 )12384.8282828283235.99867973751252.4783795256958
Winsorized Mean ( 28 / 33 )12308.1818181818225.31206392925054.6272649743543
Winsorized Mean ( 29 / 33 )12271.5656565657219.57913171766255.8867573642863
Winsorized Mean ( 30 / 33 )12269.4444444444217.67891710218056.3648726655742
Winsorized Mean ( 31 / 33 )12214.0202020202209.84521097838458.2049032478438
Winsorized Mean ( 32 / 33 )12212.4040404040208.34643220128958.6158539475507
Winsorized Mean ( 33 / 33 )12206.0707070707205.59599234955259.369205438198
Trimmed Mean ( 1 / 33 )12727.4329896907325.81556930791439.0633050984209
Trimmed Mean ( 2 / 33 )12687.3473684211321.17069128121939.5034407336749
Trimmed Mean ( 3 / 33 )12648.8817204301317.25770346666839.8694234441467
Trimmed Mean ( 4 / 33 )12610.5274725275313.50506257318040.2243184496706
Trimmed Mean ( 5 / 33 )12569.0112359551310.09150042355140.5332336384170
Trimmed Mean ( 6 / 33 )12525.7011494253306.1313887683540.9160955360363
Trimmed Mean ( 7 / 33 )12487.2941176471303.23955217119841.1796351374282
Trimmed Mean ( 8 / 33 )12447.0963855422300.21021218470841.4612690719659
Trimmed Mean ( 9 / 33 )12404.5802469136296.7993964754841.7944928265324
Trimmed Mean ( 10 / 33 )12360.2025316456292.90993039194842.1979634323294
Trimmed Mean ( 11 / 33 )12317.2597402597289.36816667708142.566049616664
Trimmed Mean ( 12 / 33 )12276.32286.28350162190842.8816887122375
Trimmed Mean ( 13 / 33 )12233.4794520548282.71710122723043.2710982071874
Trimmed Mean ( 14 / 33 )12196.8732394366280.73561026176443.4461208111930
Trimmed Mean ( 15 / 33 )12158.6086956522278.30058070617543.688765092765
Trimmed Mean ( 16 / 33 )12126.6865671642277.46568334022643.7051761543229
Trimmed Mean ( 17 / 33 )12093.4923076923276.60697968962743.7208501436301
Trimmed Mean ( 18 / 33 )12060.8888888889275.97982323371143.7020675916415
Trimmed Mean ( 19 / 33 )12027.0327868852275.51029551162643.6536600730325
Trimmed Mean ( 20 / 33 )11991.1525423729274.82104885110043.6325841579543
Trimmed Mean ( 21 / 33 )11953.8596491228273.91281729378343.6411109462680
Trimmed Mean ( 22 / 33 )11913.9090909091272.44454570918743.7296663799842
Trimmed Mean ( 23 / 33 )11872.4528301887270.70850915229643.8569621153263
Trimmed Mean ( 24 / 33 )11829.2352941176268.94505538176843.9838363167749
Trimmed Mean ( 25 / 33 )11782.9387755102266.44523184243244.2227421148909
Trimmed Mean ( 26 / 33 )11732.3404255319263.14266869068944.5854732868226
Trimmed Mean ( 27 / 33 )11732.3404255319258.78721318092345.3358582957869
Trimmed Mean ( 28 / 33 )11618.1860465116252.90613479830845.9387276460379
Trimmed Mean ( 29 / 33 )11558.6829268293247.20542568199246.7573998221968
Trimmed Mean ( 30 / 33 )11496.2820512821240.41686117506647.8181188918805
Trimmed Mean ( 31 / 33 )11427.3243243243230.94448344898149.4808282651566
Trimmed Mean ( 32 / 33 )11355.5428571429219.61780530768351.7059299505968
Trimmed Mean ( 33 / 33 )11275.2121212121203.06466706583955.5252289043292
Median10812
Midrange14625.5
Midmean - Weighted Average at Xnp11752.16
Midmean - Weighted Average at X(n+1)p11829.2352941176
Midmean - Empirical Distribution Function11829.2352941176
Midmean - Empirical Distribution Function - Averaging11829.2352941176
Midmean - Empirical Distribution Function - Interpolation11782.9387755102
Midmean - Closest Observation11752.16
Midmean - True Basic - Statistics Graphics Toolkit11829.2352941176
Midmean - MS Excel (old versions)11829.2352941176
Number of observations99


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')