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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 14 Mar 2009 03:01:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Mar/14/t1237021412pr407h9ql3jr8l4.htm/, Retrieved Fri, 19 Apr 2024 19:43:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39070, Retrieved Fri, 19 Apr 2024 19:43:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact239
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - Om...] [2009-03-14 09:01:51] [13980c6c3342d2be2ef42581b409ab4a] [Current]
-         [Central Tendency] [Centrummaten - Om...] [2009-05-31 08:52:04] [b66e0de983b23a707273d4ecaef43d15]
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Dataseries X:
2291180
1971664
2193270
2197733
2345324
2195121
2170583
2241521
2154945
2912568
2392562
3336621
4080642
3735329
4018383
4171360
3855698
4101316
4199346
3959646
3960841
4784025
4105467
5929558
4048642
3828808
4268127
4171816
4004783
4295447
3968177
3918480
4040260
4530715
4103330
6025506
4632308
4133863
4519182
4151573
4486595
4504699
4180443
4222193
4373727
4734738
4403232
5903985
4414074
4061816
4504697
3994176
4114925
4485120
4171230
4476075
4179369
4823185
4585751
6110454
4279575
3782118
4098678
4065616
4413733
4481214
4345018
4294488
4361269
4535031
4318397
6040168




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39070&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39070&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4051270.95833333108498.05929279237.3395707235703
Geometric Mean3930351.89394091
Harmonic Mean3786576.75300653
Quadratic Mean4153142.93368607
Winsorized Mean ( 1 / 24 )4052840.33333333107580.60588999337.6725925626183
Winsorized Mean ( 2 / 24 )4052867.44444444107367.32958932937.7476785531160
Winsorized Mean ( 3 / 24 )4049814.90277778106118.07945377438.1632887027693
Winsorized Mean ( 4 / 24 )4048497.01388889105739.92094174938.2873088785375
Winsorized Mean ( 5 / 24 )3973622.8472222291170.691412156643.5844325152544
Winsorized Mean ( 6 / 24 )3974008.5138888989752.469915423644.2774278817476
Winsorized Mean ( 7 / 24 )3974044.6805555687847.917843073545.2377788583966
Winsorized Mean ( 8 / 24 )3968679.5694444484904.639001819446.7427883340909
Winsorized Mean ( 9 / 24 )3968764.6944444482690.611999607247.9953479418353
Winsorized Mean ( 10 / 24 )4033943.3055555663109.095489256463.9201572179447
Winsorized Mean ( 11 / 24 )4098069.7916666747497.918941159786.2789335411378
Winsorized Mean ( 12 / 24 )4162598.9583333333498.1057768511124.263711687540
Winsorized Mean ( 13 / 24 )4168431.9861111131619.6091993806131.830597899760
Winsorized Mean ( 14 / 24 )4177510.2083333330096.6970956754138.802945554235
Winsorized Mean ( 15 / 24 )4179341.0416666728619.2648361743146.032438834140
Winsorized Mean ( 16 / 24 )4192964.8194444426434.1162467558158.619443914984
Winsorized Mean ( 17 / 24 )4201762.3194444424912.1666289821168.663062591924
Winsorized Mean ( 18 / 24 )4200776.3194444424668.7950296070170.28704946483
Winsorized Mean ( 19 / 24 )4186350.8333333321912.1271101059191.051777506465
Winsorized Mean ( 20 / 24 )4193478.0555555620906.4354840659200.583119908302
Winsorized Mean ( 21 / 24 )4193508.9722222220040.5341628624209.251357181553
Winsorized Mean ( 22 / 24 )4188649.1111111118179.1272379192230.409802202944
Winsorized Mean ( 23 / 24 )4191657.9583333316701.4584094362250.975564862352
Winsorized Mean ( 24 / 24 )4189034.9583333315576.0929363857268.940033642696
Trimmed Mean ( 1 / 24 )4051562.72857143103372.31281669239.1938868172175
Trimmed Mean ( 2 / 24 )4050209.9705882498340.877871368441.1854160574607
Trimmed Mean ( 3 / 24 )4048760.4393939492398.521829002643.8184546597702
Trimmed Mean ( 4 / 24 )4048365.01562585747.13119005347.2128333559296
Trimmed Mean ( 5 / 24 )4048326.6935483977588.804286865852.1766861953521
Trimmed Mean ( 6 / 24 )4066255.6166666772726.047556489455.9119566274826
Trimmed Mean ( 7 / 24 )4085341.2241379367037.744519596460.9409110257835
Trimmed Mean ( 8 / 24 )4105783.4464285760284.034098724568.107310796499
Trimmed Mean ( 9 / 24 )4128634.0925925952166.834801125379.1428904654098
Trimmed Mean ( 10 / 24 )4153229.3846153841348.9876849969100.443314749453
Trimmed Mean ( 11 / 24 )4170406.5834013.5705482876122.610079235270
Trimmed Mean ( 12 / 24 )4180270.687529810.0541430367140.230227943966
Trimmed Mean ( 13 / 24 )4182575.6956521728587.453246818146.308090459850
Trimmed Mean ( 14 / 24 )4184356.0227272727467.2848845043152.339630229993
Trimmed Mean ( 15 / 24 )4185194.2857142926380.1437740662158.649411525523
Trimmed Mean ( 16 / 24 )4185896.67525304.9416502701165.418151634241
Trimmed Mean ( 17 / 24 )4185059.6578947424411.3866640343171.438833667760
Trimmed Mean ( 18 / 24 )4183094.6388888923556.751718032177.575189014148
Trimmed Mean ( 19 / 24 )4181014.4411764722416.7820803154186.512695095872
Trimmed Mean ( 20 / 24 )4180382.521631.7531833712193.252135625029
Trimmed Mean ( 21 / 24 )4178811.0333333320761.0898796743201.280908543462
Trimmed Mean ( 22 / 24 )4177011.2857142919728.6037364826211.723614174989
Trimmed Mean ( 23 / 24 )4175546.3846153818824.4056514268221.815576116153
Trimmed Mean ( 24 / 24 )4173444.87517928.5808044182232.781664122100
Median4171295
Midrange4041059
Midmean - Weighted Average at Xnp4177055.48648649
Midmean - Weighted Average at X(n+1)p4183094.63888889
Midmean - Empirical Distribution Function4177055.48648649
Midmean - Empirical Distribution Function - Averaging4183094.63888889
Midmean - Empirical Distribution Function - Interpolation4183094.63888889
Midmean - Closest Observation4177055.48648649
Midmean - True Basic - Statistics Graphics Toolkit4183094.63888889
Midmean - MS Excel (old versions)4185059.65789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4051270.95833333 & 108498.059292792 & 37.3395707235703 \tabularnewline
Geometric Mean & 3930351.89394091 &  &  \tabularnewline
Harmonic Mean & 3786576.75300653 &  &  \tabularnewline
Quadratic Mean & 4153142.93368607 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4052840.33333333 & 107580.605889993 & 37.6725925626183 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4052867.44444444 & 107367.329589329 & 37.7476785531160 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4049814.90277778 & 106118.079453774 & 38.1632887027693 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4048497.01388889 & 105739.920941749 & 38.2873088785375 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3973622.84722222 & 91170.6914121566 & 43.5844325152544 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3974008.51388889 & 89752.4699154236 & 44.2774278817476 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3974044.68055556 & 87847.9178430735 & 45.2377788583966 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3968679.56944444 & 84904.6390018194 & 46.7427883340909 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3968764.69444444 & 82690.6119996072 & 47.9953479418353 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4033943.30555556 & 63109.0954892564 & 63.9201572179447 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4098069.79166667 & 47497.9189411597 & 86.2789335411378 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4162598.95833333 & 33498.1057768511 & 124.263711687540 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4168431.98611111 & 31619.6091993806 & 131.830597899760 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4177510.20833333 & 30096.6970956754 & 138.802945554235 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4179341.04166667 & 28619.2648361743 & 146.032438834140 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4192964.81944444 & 26434.1162467558 & 158.619443914984 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4201762.31944444 & 24912.1666289821 & 168.663062591924 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4200776.31944444 & 24668.7950296070 & 170.28704946483 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4186350.83333333 & 21912.1271101059 & 191.051777506465 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4193478.05555556 & 20906.4354840659 & 200.583119908302 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4193508.97222222 & 20040.5341628624 & 209.251357181553 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4188649.11111111 & 18179.1272379192 & 230.409802202944 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4191657.95833333 & 16701.4584094362 & 250.975564862352 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4189034.95833333 & 15576.0929363857 & 268.940033642696 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4051562.72857143 & 103372.312816692 & 39.1938868172175 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4050209.97058824 & 98340.8778713684 & 41.1854160574607 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4048760.43939394 & 92398.5218290026 & 43.8184546597702 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4048365.015625 & 85747.131190053 & 47.2128333559296 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4048326.69354839 & 77588.8042868658 & 52.1766861953521 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4066255.61666667 & 72726.0475564894 & 55.9119566274826 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4085341.22413793 & 67037.7445195964 & 60.9409110257835 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4105783.44642857 & 60284.0340987245 & 68.107310796499 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4128634.09259259 & 52166.8348011253 & 79.1428904654098 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4153229.38461538 & 41348.9876849969 & 100.443314749453 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4170406.58 & 34013.5705482876 & 122.610079235270 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4180270.6875 & 29810.0541430367 & 140.230227943966 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4182575.69565217 & 28587.453246818 & 146.308090459850 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4184356.02272727 & 27467.2848845043 & 152.339630229993 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4185194.28571429 & 26380.1437740662 & 158.649411525523 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4185896.675 & 25304.9416502701 & 165.418151634241 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4185059.65789474 & 24411.3866640343 & 171.438833667760 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4183094.63888889 & 23556.751718032 & 177.575189014148 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4181014.44117647 & 22416.7820803154 & 186.512695095872 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4180382.5 & 21631.7531833712 & 193.252135625029 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4178811.03333333 & 20761.0898796743 & 201.280908543462 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4177011.28571429 & 19728.6037364826 & 211.723614174989 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4175546.38461538 & 18824.4056514268 & 221.815576116153 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4173444.875 & 17928.5808044182 & 232.781664122100 \tabularnewline
Median & 4171295 &  &  \tabularnewline
Midrange & 4041059 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4177055.48648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4183094.63888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4177055.48648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4183094.63888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4183094.63888889 &  &  \tabularnewline
Midmean - Closest Observation & 4177055.48648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4183094.63888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4185059.65789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39070&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]4051270.95833333[/C][C]108498.059292792[/C][C]37.3395707235703[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3930351.89394091[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3786576.75300653[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4153142.93368607[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4052840.33333333[/C][C]107580.605889993[/C][C]37.6725925626183[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4052867.44444444[/C][C]107367.329589329[/C][C]37.7476785531160[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4049814.90277778[/C][C]106118.079453774[/C][C]38.1632887027693[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4048497.01388889[/C][C]105739.920941749[/C][C]38.2873088785375[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3973622.84722222[/C][C]91170.6914121566[/C][C]43.5844325152544[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3974008.51388889[/C][C]89752.4699154236[/C][C]44.2774278817476[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3974044.68055556[/C][C]87847.9178430735[/C][C]45.2377788583966[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3968679.56944444[/C][C]84904.6390018194[/C][C]46.7427883340909[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3968764.69444444[/C][C]82690.6119996072[/C][C]47.9953479418353[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4033943.30555556[/C][C]63109.0954892564[/C][C]63.9201572179447[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4098069.79166667[/C][C]47497.9189411597[/C][C]86.2789335411378[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4162598.95833333[/C][C]33498.1057768511[/C][C]124.263711687540[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4168431.98611111[/C][C]31619.6091993806[/C][C]131.830597899760[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4177510.20833333[/C][C]30096.6970956754[/C][C]138.802945554235[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4179341.04166667[/C][C]28619.2648361743[/C][C]146.032438834140[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4192964.81944444[/C][C]26434.1162467558[/C][C]158.619443914984[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4201762.31944444[/C][C]24912.1666289821[/C][C]168.663062591924[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4200776.31944444[/C][C]24668.7950296070[/C][C]170.28704946483[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4186350.83333333[/C][C]21912.1271101059[/C][C]191.051777506465[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4193478.05555556[/C][C]20906.4354840659[/C][C]200.583119908302[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4193508.97222222[/C][C]20040.5341628624[/C][C]209.251357181553[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4188649.11111111[/C][C]18179.1272379192[/C][C]230.409802202944[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4191657.95833333[/C][C]16701.4584094362[/C][C]250.975564862352[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4189034.95833333[/C][C]15576.0929363857[/C][C]268.940033642696[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4051562.72857143[/C][C]103372.312816692[/C][C]39.1938868172175[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4050209.97058824[/C][C]98340.8778713684[/C][C]41.1854160574607[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4048760.43939394[/C][C]92398.5218290026[/C][C]43.8184546597702[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4048365.015625[/C][C]85747.131190053[/C][C]47.2128333559296[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4048326.69354839[/C][C]77588.8042868658[/C][C]52.1766861953521[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4066255.61666667[/C][C]72726.0475564894[/C][C]55.9119566274826[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4085341.22413793[/C][C]67037.7445195964[/C][C]60.9409110257835[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4105783.44642857[/C][C]60284.0340987245[/C][C]68.107310796499[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4128634.09259259[/C][C]52166.8348011253[/C][C]79.1428904654098[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4153229.38461538[/C][C]41348.9876849969[/C][C]100.443314749453[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4170406.58[/C][C]34013.5705482876[/C][C]122.610079235270[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4180270.6875[/C][C]29810.0541430367[/C][C]140.230227943966[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4182575.69565217[/C][C]28587.453246818[/C][C]146.308090459850[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4184356.02272727[/C][C]27467.2848845043[/C][C]152.339630229993[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4185194.28571429[/C][C]26380.1437740662[/C][C]158.649411525523[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4185896.675[/C][C]25304.9416502701[/C][C]165.418151634241[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4185059.65789474[/C][C]24411.3866640343[/C][C]171.438833667760[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4183094.63888889[/C][C]23556.751718032[/C][C]177.575189014148[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4181014.44117647[/C][C]22416.7820803154[/C][C]186.512695095872[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4180382.5[/C][C]21631.7531833712[/C][C]193.252135625029[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4178811.03333333[/C][C]20761.0898796743[/C][C]201.280908543462[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4177011.28571429[/C][C]19728.6037364826[/C][C]211.723614174989[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4175546.38461538[/C][C]18824.4056514268[/C][C]221.815576116153[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4173444.875[/C][C]17928.5808044182[/C][C]232.781664122100[/C][/ROW]
[ROW][C]Median[/C][C]4171295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4041059[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4177055.48648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4183094.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4177055.48648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4183094.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4183094.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4177055.48648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4183094.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4185059.65789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39070&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4051270.95833333108498.05929279237.3395707235703
Geometric Mean3930351.89394091
Harmonic Mean3786576.75300653
Quadratic Mean4153142.93368607
Winsorized Mean ( 1 / 24 )4052840.33333333107580.60588999337.6725925626183
Winsorized Mean ( 2 / 24 )4052867.44444444107367.32958932937.7476785531160
Winsorized Mean ( 3 / 24 )4049814.90277778106118.07945377438.1632887027693
Winsorized Mean ( 4 / 24 )4048497.01388889105739.92094174938.2873088785375
Winsorized Mean ( 5 / 24 )3973622.8472222291170.691412156643.5844325152544
Winsorized Mean ( 6 / 24 )3974008.5138888989752.469915423644.2774278817476
Winsorized Mean ( 7 / 24 )3974044.6805555687847.917843073545.2377788583966
Winsorized Mean ( 8 / 24 )3968679.5694444484904.639001819446.7427883340909
Winsorized Mean ( 9 / 24 )3968764.6944444482690.611999607247.9953479418353
Winsorized Mean ( 10 / 24 )4033943.3055555663109.095489256463.9201572179447
Winsorized Mean ( 11 / 24 )4098069.7916666747497.918941159786.2789335411378
Winsorized Mean ( 12 / 24 )4162598.9583333333498.1057768511124.263711687540
Winsorized Mean ( 13 / 24 )4168431.9861111131619.6091993806131.830597899760
Winsorized Mean ( 14 / 24 )4177510.2083333330096.6970956754138.802945554235
Winsorized Mean ( 15 / 24 )4179341.0416666728619.2648361743146.032438834140
Winsorized Mean ( 16 / 24 )4192964.8194444426434.1162467558158.619443914984
Winsorized Mean ( 17 / 24 )4201762.3194444424912.1666289821168.663062591924
Winsorized Mean ( 18 / 24 )4200776.3194444424668.7950296070170.28704946483
Winsorized Mean ( 19 / 24 )4186350.8333333321912.1271101059191.051777506465
Winsorized Mean ( 20 / 24 )4193478.0555555620906.4354840659200.583119908302
Winsorized Mean ( 21 / 24 )4193508.9722222220040.5341628624209.251357181553
Winsorized Mean ( 22 / 24 )4188649.1111111118179.1272379192230.409802202944
Winsorized Mean ( 23 / 24 )4191657.9583333316701.4584094362250.975564862352
Winsorized Mean ( 24 / 24 )4189034.9583333315576.0929363857268.940033642696
Trimmed Mean ( 1 / 24 )4051562.72857143103372.31281669239.1938868172175
Trimmed Mean ( 2 / 24 )4050209.9705882498340.877871368441.1854160574607
Trimmed Mean ( 3 / 24 )4048760.4393939492398.521829002643.8184546597702
Trimmed Mean ( 4 / 24 )4048365.01562585747.13119005347.2128333559296
Trimmed Mean ( 5 / 24 )4048326.6935483977588.804286865852.1766861953521
Trimmed Mean ( 6 / 24 )4066255.6166666772726.047556489455.9119566274826
Trimmed Mean ( 7 / 24 )4085341.2241379367037.744519596460.9409110257835
Trimmed Mean ( 8 / 24 )4105783.4464285760284.034098724568.107310796499
Trimmed Mean ( 9 / 24 )4128634.0925925952166.834801125379.1428904654098
Trimmed Mean ( 10 / 24 )4153229.3846153841348.9876849969100.443314749453
Trimmed Mean ( 11 / 24 )4170406.5834013.5705482876122.610079235270
Trimmed Mean ( 12 / 24 )4180270.687529810.0541430367140.230227943966
Trimmed Mean ( 13 / 24 )4182575.6956521728587.453246818146.308090459850
Trimmed Mean ( 14 / 24 )4184356.0227272727467.2848845043152.339630229993
Trimmed Mean ( 15 / 24 )4185194.2857142926380.1437740662158.649411525523
Trimmed Mean ( 16 / 24 )4185896.67525304.9416502701165.418151634241
Trimmed Mean ( 17 / 24 )4185059.6578947424411.3866640343171.438833667760
Trimmed Mean ( 18 / 24 )4183094.6388888923556.751718032177.575189014148
Trimmed Mean ( 19 / 24 )4181014.4411764722416.7820803154186.512695095872
Trimmed Mean ( 20 / 24 )4180382.521631.7531833712193.252135625029
Trimmed Mean ( 21 / 24 )4178811.0333333320761.0898796743201.280908543462
Trimmed Mean ( 22 / 24 )4177011.2857142919728.6037364826211.723614174989
Trimmed Mean ( 23 / 24 )4175546.3846153818824.4056514268221.815576116153
Trimmed Mean ( 24 / 24 )4173444.87517928.5808044182232.781664122100
Median4171295
Midrange4041059
Midmean - Weighted Average at Xnp4177055.48648649
Midmean - Weighted Average at X(n+1)p4183094.63888889
Midmean - Empirical Distribution Function4177055.48648649
Midmean - Empirical Distribution Function - Averaging4183094.63888889
Midmean - Empirical Distribution Function - Interpolation4183094.63888889
Midmean - Closest Observation4177055.48648649
Midmean - True Basic - Statistics Graphics Toolkit4183094.63888889
Midmean - MS Excel (old versions)4185059.65789474
Number of observations72



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')