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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 19 Apr 2008 06:26:51 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/19/t12086093778zxt3f4jomi5jv8.htm/, Retrieved Thu, 16 May 2024 21:30:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10264, Retrieved Thu, 16 May 2024 21:30:08 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

221

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [US dollar in Euro...] [2008-04-19 12:26:51] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10264&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10264&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.03442361111111	0.0157056759490028	65.8630430469814
Geometric Mean	1.02615511339297
Harmonic Mean	1.01812349322224
Quadratic Mean	1.04285456966550
Winsorized Mean ( 1 / 24 )	1.0338625	0.0155581558850723	66.4514809876643
Winsorized Mean ( 2 / 24 )	1.03293194444444	0.0153234205590863	67.4087055472707
Winsorized Mean ( 3 / 24 )	1.03318611111111	0.0152794360851321	67.6193876105458
Winsorized Mean ( 4 / 24 )	1.03290277777778	0.0150587912770914	68.5913469927105
Winsorized Mean ( 5 / 24 )	1.03152777777778	0.0147618737150776	69.8778351371606
Winsorized Mean ( 6 / 24 )	1.03165277777778	0.0146521595149512	70.409605950923
Winsorized Mean ( 7 / 24 )	1.03173055555556	0.01462411529618	70.5499467598601
Winsorized Mean ( 8 / 24 )	1.03205277777778	0.0144394387129541	71.4745772529156
Winsorized Mean ( 9 / 24 )	1.03199027777778	0.0143126156581727	72.1035415485709
Winsorized Mean ( 10 / 24 )	1.03168472222222	0.0141524465581976	72.8979768960609
Winsorized Mean ( 11 / 24 )	1.02989722222222	0.0136909085886252	75.2248994692649
Winsorized Mean ( 12 / 24 )	1.02993055555556	0.0136280151132436	75.5745093469025
Winsorized Mean ( 13 / 24 )	1.0260125	0.0126423083894643	81.1570536323134
Winsorized Mean ( 14 / 24 )	1.0265375	0.0125444724432360	81.8318589837159
Winsorized Mean ( 15 / 24 )	1.02643333333333	0.0123329345830731	83.2270151454553
Winsorized Mean ( 16 / 24 )	1.0247	0.0120237112506028	85.2232708057281
Winsorized Mean ( 17 / 24 )	1.02408611111111	0.0118643416554347	86.3163031588865
Winsorized Mean ( 18 / 24 )	1.01991111111111	0.0110514645705079	92.2874162609056
Winsorized Mean ( 19 / 24 )	1.01811666666667	0.0105516638283337	96.4887323203743
Winsorized Mean ( 20 / 24 )	1.01792222222222	0.0100792420253336	100.991941622568
Winsorized Mean ( 21 / 24 )	1.01754305555556	0.00973624804146028	104.510798330374
Winsorized Mean ( 22 / 24 )	1.01454861111111	0.00787891815562481	128.767502221967
Winsorized Mean ( 23 / 24 )	1.01410138888889	0.007733905872913	131.124092477082
Winsorized Mean ( 24 / 24 )	1.01430138888889	0.0071990646380604	140.893496569877
Trimmed Mean ( 1 / 24 )	1.03264857142857	0.0153219919001489	67.3964963666726
Trimmed Mean ( 2 / 24 )	1.03136323529412	0.0150373034693575	68.5869801986635
Trimmed Mean ( 3 / 24 )	1.03050757575758	0.0148418493105993	69.4325588538108
Trimmed Mean ( 4 / 24 )	1.029503125	0.0146211229715150	70.4120420165869
Trimmed Mean ( 5 / 24 )	1.02851612903226	0.0144286604058774	71.2828564884164
Trimmed Mean ( 6 / 24 )	1.02779333333333	0.0142800512482793	71.9740647609494
Trimmed Mean ( 7 / 24 )	1.02699482758621	0.0141192423012143	72.7372479115176
Trimmed Mean ( 8 / 24 )	1.026125	0.0139194947031926	73.7185524245103
Trimmed Mean ( 9 / 24 )	1.02513703703704	0.0137074485600286	74.7868600453021
Trimmed Mean ( 10 / 24 )	1.02408269230769	0.0134634650932215	76.0638279385661
Trimmed Mean ( 11 / 24 )	1.022988	0.0131850377910350	77.5870358669408
Trimmed Mean ( 12 / 24 )	1.02204583333333	0.0129301324083978	79.0437252343632
Trimmed Mean ( 13 / 24 )	1.02101739130435	0.0126083456389866	80.9794893429342
Trimmed Mean ( 14 / 24 )	1.02038863636364	0.0124098611372218	82.2240172618137
Trimmed Mean ( 15 / 24 )	1.01963571428571	0.0121572860061914	83.8703402853599
Trimmed Mean ( 16 / 24 )	1.01882	0.0118590489089826	85.9107680404538
Trimmed Mean ( 17 / 24 )	1.01812368421053	0.0115246624251808	88.3430374486264
Trimmed Mean ( 18 / 24 )	1.01742222222222	0.0110994881271302	91.6638867098174
Trimmed Mean ( 19 / 24 )	1.01712941176471	0.0107283833395542	94.8073329944019
Trimmed Mean ( 20 / 24 )	1.0170125	0.0103359513408766	98.3956354339562
Trimmed Mean ( 21 / 24 )	1.01690333333333	0.00990216913811548	102.695007442265
Trimmed Mean ( 22 / 24 )	1.016825	0.0093641068989986	108.587504496424
Trimmed Mean ( 23 / 24 )	1.01711153846154	0.0091869980481164	110.712066458975
Trimmed Mean ( 24 / 24 )	1.01750416666667	0.0089198960950573	114.071302605250
Median	1.01625
Midrange	1.09655
Midmean - Weighted Average at Xnp	1.01440810810811
Midmean - Weighted Average at X(n+1)p	1.01742222222222
Midmean - Empirical Distribution Function	1.01440810810811
Midmean - Empirical Distribution Function - Averaging	1.01742222222222
Midmean - Empirical Distribution Function - Interpolation	1.01742222222222
Midmean - Closest Observation	1.01440810810811
Midmean - True Basic - Statistics Graphics Toolkit	1.01742222222222
Midmean - MS Excel (old versions)	1.01812368421053
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.03442361111111 & 0.0157056759490028 & 65.8630430469814 \tabularnewline
Geometric Mean & 1.02615511339297 &  &  \tabularnewline
Harmonic Mean & 1.01812349322224 &  &  \tabularnewline
Quadratic Mean & 1.04285456966550 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.0338625 & 0.0155581558850723 & 66.4514809876643 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.03293194444444 & 0.0153234205590863 & 67.4087055472707 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.03318611111111 & 0.0152794360851321 & 67.6193876105458 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.03290277777778 & 0.0150587912770914 & 68.5913469927105 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.03152777777778 & 0.0147618737150776 & 69.8778351371606 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.03165277777778 & 0.0146521595149512 & 70.409605950923 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.03173055555556 & 0.01462411529618 & 70.5499467598601 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.03205277777778 & 0.0144394387129541 & 71.4745772529156 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.03199027777778 & 0.0143126156581727 & 72.1035415485709 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.03168472222222 & 0.0141524465581976 & 72.8979768960609 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.02989722222222 & 0.0136909085886252 & 75.2248994692649 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.02993055555556 & 0.0136280151132436 & 75.5745093469025 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.0260125 & 0.0126423083894643 & 81.1570536323134 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.0265375 & 0.0125444724432360 & 81.8318589837159 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.02643333333333 & 0.0123329345830731 & 83.2270151454553 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.0247 & 0.0120237112506028 & 85.2232708057281 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.02408611111111 & 0.0118643416554347 & 86.3163031588865 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.01991111111111 & 0.0110514645705079 & 92.2874162609056 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.01811666666667 & 0.0105516638283337 & 96.4887323203743 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.01792222222222 & 0.0100792420253336 & 100.991941622568 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.01754305555556 & 0.00973624804146028 & 104.510798330374 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.01454861111111 & 0.00787891815562481 & 128.767502221967 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.01410138888889 & 0.007733905872913 & 131.124092477082 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.01430138888889 & 0.0071990646380604 & 140.893496569877 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.03264857142857 & 0.0153219919001489 & 67.3964963666726 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.03136323529412 & 0.0150373034693575 & 68.5869801986635 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.03050757575758 & 0.0148418493105993 & 69.4325588538108 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.029503125 & 0.0146211229715150 & 70.4120420165869 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.02851612903226 & 0.0144286604058774 & 71.2828564884164 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.02779333333333 & 0.0142800512482793 & 71.9740647609494 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.02699482758621 & 0.0141192423012143 & 72.7372479115176 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.026125 & 0.0139194947031926 & 73.7185524245103 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.02513703703704 & 0.0137074485600286 & 74.7868600453021 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.02408269230769 & 0.0134634650932215 & 76.0638279385661 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.022988 & 0.0131850377910350 & 77.5870358669408 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.02204583333333 & 0.0129301324083978 & 79.0437252343632 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.02101739130435 & 0.0126083456389866 & 80.9794893429342 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.02038863636364 & 0.0124098611372218 & 82.2240172618137 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.01963571428571 & 0.0121572860061914 & 83.8703402853599 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.01882 & 0.0118590489089826 & 85.9107680404538 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.01812368421053 & 0.0115246624251808 & 88.3430374486264 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.01742222222222 & 0.0110994881271302 & 91.6638867098174 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.01712941176471 & 0.0107283833395542 & 94.8073329944019 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.0170125 & 0.0103359513408766 & 98.3956354339562 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.01690333333333 & 0.00990216913811548 & 102.695007442265 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.016825 & 0.0093641068989986 & 108.587504496424 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.01711153846154 & 0.0091869980481164 & 110.712066458975 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.01750416666667 & 0.0089198960950573 & 114.071302605250 \tabularnewline
Median & 1.01625 &  &  \tabularnewline
Midrange & 1.09655 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.01440810810811 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.01742222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.01440810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.01742222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.01742222222222 &  &  \tabularnewline
Midmean - Closest Observation & 1.01440810810811 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.01742222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.01812368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10264&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]1.03442361111111[/C][C]0.0157056759490028[/C][C]65.8630430469814[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.02615511339297[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.01812349322224[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.04285456966550[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.0338625[/C][C]0.0155581558850723[/C][C]66.4514809876643[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.03293194444444[/C][C]0.0153234205590863[/C][C]67.4087055472707[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.03318611111111[/C][C]0.0152794360851321[/C][C]67.6193876105458[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.03290277777778[/C][C]0.0150587912770914[/C][C]68.5913469927105[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.03152777777778[/C][C]0.0147618737150776[/C][C]69.8778351371606[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.03165277777778[/C][C]0.0146521595149512[/C][C]70.409605950923[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.03173055555556[/C][C]0.01462411529618[/C][C]70.5499467598601[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.03205277777778[/C][C]0.0144394387129541[/C][C]71.4745772529156[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.03199027777778[/C][C]0.0143126156581727[/C][C]72.1035415485709[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.03168472222222[/C][C]0.0141524465581976[/C][C]72.8979768960609[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.02989722222222[/C][C]0.0136909085886252[/C][C]75.2248994692649[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.02993055555556[/C][C]0.0136280151132436[/C][C]75.5745093469025[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.0260125[/C][C]0.0126423083894643[/C][C]81.1570536323134[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.0265375[/C][C]0.0125444724432360[/C][C]81.8318589837159[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.02643333333333[/C][C]0.0123329345830731[/C][C]83.2270151454553[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.0247[/C][C]0.0120237112506028[/C][C]85.2232708057281[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.02408611111111[/C][C]0.0118643416554347[/C][C]86.3163031588865[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.01991111111111[/C][C]0.0110514645705079[/C][C]92.2874162609056[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.01811666666667[/C][C]0.0105516638283337[/C][C]96.4887323203743[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.01792222222222[/C][C]0.0100792420253336[/C][C]100.991941622568[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.01754305555556[/C][C]0.00973624804146028[/C][C]104.510798330374[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.01454861111111[/C][C]0.00787891815562481[/C][C]128.767502221967[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.01410138888889[/C][C]0.007733905872913[/C][C]131.124092477082[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.01430138888889[/C][C]0.0071990646380604[/C][C]140.893496569877[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.03264857142857[/C][C]0.0153219919001489[/C][C]67.3964963666726[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.03136323529412[/C][C]0.0150373034693575[/C][C]68.5869801986635[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.03050757575758[/C][C]0.0148418493105993[/C][C]69.4325588538108[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.029503125[/C][C]0.0146211229715150[/C][C]70.4120420165869[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.02851612903226[/C][C]0.0144286604058774[/C][C]71.2828564884164[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.02779333333333[/C][C]0.0142800512482793[/C][C]71.9740647609494[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.02699482758621[/C][C]0.0141192423012143[/C][C]72.7372479115176[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.026125[/C][C]0.0139194947031926[/C][C]73.7185524245103[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.02513703703704[/C][C]0.0137074485600286[/C][C]74.7868600453021[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.02408269230769[/C][C]0.0134634650932215[/C][C]76.0638279385661[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.022988[/C][C]0.0131850377910350[/C][C]77.5870358669408[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.02204583333333[/C][C]0.0129301324083978[/C][C]79.0437252343632[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.02101739130435[/C][C]0.0126083456389866[/C][C]80.9794893429342[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.02038863636364[/C][C]0.0124098611372218[/C][C]82.2240172618137[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.01963571428571[/C][C]0.0121572860061914[/C][C]83.8703402853599[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.01882[/C][C]0.0118590489089826[/C][C]85.9107680404538[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.01812368421053[/C][C]0.0115246624251808[/C][C]88.3430374486264[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.01742222222222[/C][C]0.0110994881271302[/C][C]91.6638867098174[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.01712941176471[/C][C]0.0107283833395542[/C][C]94.8073329944019[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.0170125[/C][C]0.0103359513408766[/C][C]98.3956354339562[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.01690333333333[/C][C]0.00990216913811548[/C][C]102.695007442265[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.016825[/C][C]0.0093641068989986[/C][C]108.587504496424[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.01711153846154[/C][C]0.0091869980481164[/C][C]110.712066458975[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.01750416666667[/C][C]0.0089198960950573[/C][C]114.071302605250[/C][/ROW]
[ROW][C]Median[/C][C]1.01625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.09655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.01440810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.01742222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.01440810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.01742222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.01742222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.01440810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.01742222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.01812368421053[/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=10264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10264&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.03442361111111	0.0157056759490028	65.8630430469814
Geometric Mean	1.02615511339297
Harmonic Mean	1.01812349322224
Quadratic Mean	1.04285456966550
Winsorized Mean ( 1 / 24 )	1.0338625	0.0155581558850723	66.4514809876643
Winsorized Mean ( 2 / 24 )	1.03293194444444	0.0153234205590863	67.4087055472707
Winsorized Mean ( 3 / 24 )	1.03318611111111	0.0152794360851321	67.6193876105458
Winsorized Mean ( 4 / 24 )	1.03290277777778	0.0150587912770914	68.5913469927105
Winsorized Mean ( 5 / 24 )	1.03152777777778	0.0147618737150776	69.8778351371606
Winsorized Mean ( 6 / 24 )	1.03165277777778	0.0146521595149512	70.409605950923
Winsorized Mean ( 7 / 24 )	1.03173055555556	0.01462411529618	70.5499467598601
Winsorized Mean ( 8 / 24 )	1.03205277777778	0.0144394387129541	71.4745772529156
Winsorized Mean ( 9 / 24 )	1.03199027777778	0.0143126156581727	72.1035415485709
Winsorized Mean ( 10 / 24 )	1.03168472222222	0.0141524465581976	72.8979768960609
Winsorized Mean ( 11 / 24 )	1.02989722222222	0.0136909085886252	75.2248994692649
Winsorized Mean ( 12 / 24 )	1.02993055555556	0.0136280151132436	75.5745093469025
Winsorized Mean ( 13 / 24 )	1.0260125	0.0126423083894643	81.1570536323134
Winsorized Mean ( 14 / 24 )	1.0265375	0.0125444724432360	81.8318589837159
Winsorized Mean ( 15 / 24 )	1.02643333333333	0.0123329345830731	83.2270151454553
Winsorized Mean ( 16 / 24 )	1.0247	0.0120237112506028	85.2232708057281
Winsorized Mean ( 17 / 24 )	1.02408611111111	0.0118643416554347	86.3163031588865
Winsorized Mean ( 18 / 24 )	1.01991111111111	0.0110514645705079	92.2874162609056
Winsorized Mean ( 19 / 24 )	1.01811666666667	0.0105516638283337	96.4887323203743
Winsorized Mean ( 20 / 24 )	1.01792222222222	0.0100792420253336	100.991941622568
Winsorized Mean ( 21 / 24 )	1.01754305555556	0.00973624804146028	104.510798330374
Winsorized Mean ( 22 / 24 )	1.01454861111111	0.00787891815562481	128.767502221967
Winsorized Mean ( 23 / 24 )	1.01410138888889	0.007733905872913	131.124092477082
Winsorized Mean ( 24 / 24 )	1.01430138888889	0.0071990646380604	140.893496569877
Trimmed Mean ( 1 / 24 )	1.03264857142857	0.0153219919001489	67.3964963666726
Trimmed Mean ( 2 / 24 )	1.03136323529412	0.0150373034693575	68.5869801986635
Trimmed Mean ( 3 / 24 )	1.03050757575758	0.0148418493105993	69.4325588538108
Trimmed Mean ( 4 / 24 )	1.029503125	0.0146211229715150	70.4120420165869
Trimmed Mean ( 5 / 24 )	1.02851612903226	0.0144286604058774	71.2828564884164
Trimmed Mean ( 6 / 24 )	1.02779333333333	0.0142800512482793	71.9740647609494
Trimmed Mean ( 7 / 24 )	1.02699482758621	0.0141192423012143	72.7372479115176
Trimmed Mean ( 8 / 24 )	1.026125	0.0139194947031926	73.7185524245103
Trimmed Mean ( 9 / 24 )	1.02513703703704	0.0137074485600286	74.7868600453021
Trimmed Mean ( 10 / 24 )	1.02408269230769	0.0134634650932215	76.0638279385661
Trimmed Mean ( 11 / 24 )	1.022988	0.0131850377910350	77.5870358669408
Trimmed Mean ( 12 / 24 )	1.02204583333333	0.0129301324083978	79.0437252343632
Trimmed Mean ( 13 / 24 )	1.02101739130435	0.0126083456389866	80.9794893429342
Trimmed Mean ( 14 / 24 )	1.02038863636364	0.0124098611372218	82.2240172618137
Trimmed Mean ( 15 / 24 )	1.01963571428571	0.0121572860061914	83.8703402853599
Trimmed Mean ( 16 / 24 )	1.01882	0.0118590489089826	85.9107680404538
Trimmed Mean ( 17 / 24 )	1.01812368421053	0.0115246624251808	88.3430374486264
Trimmed Mean ( 18 / 24 )	1.01742222222222	0.0110994881271302	91.6638867098174
Trimmed Mean ( 19 / 24 )	1.01712941176471	0.0107283833395542	94.8073329944019
Trimmed Mean ( 20 / 24 )	1.0170125	0.0103359513408766	98.3956354339562
Trimmed Mean ( 21 / 24 )	1.01690333333333	0.00990216913811548	102.695007442265
Trimmed Mean ( 22 / 24 )	1.016825	0.0093641068989986	108.587504496424
Trimmed Mean ( 23 / 24 )	1.01711153846154	0.0091869980481164	110.712066458975
Trimmed Mean ( 24 / 24 )	1.01750416666667	0.0089198960950573	114.071302605250
Median	1.01625
Midrange	1.09655
Midmean - Weighted Average at Xnp	1.01440810810811
Midmean - Weighted Average at X(n+1)p	1.01742222222222
Midmean - Empirical Distribution Function	1.01440810810811
Midmean - Empirical Distribution Function - Averaging	1.01742222222222
Midmean - Empirical Distribution Function - Interpolation	1.01742222222222
Midmean - Closest Observation	1.01440810810811
Midmean - True Basic - Statistics Graphics Toolkit	1.01742222222222
Midmean - MS Excel (old versions)	1.01812368421053
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code