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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 12 Dec 2016 22:19:09 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481577606gyiq7hbwp90t0ki.htm/, Retrieved Sat, 04 May 2024 00:31:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298995, Retrieved Sat, 04 May 2024 00:31:20 +0000

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

-       [Central Tendency] [Central tendency ...] [2016-12-12 21:19:09] [e6dc02234f5305f92311fb16bc25f73e] [Current]

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Dataseries X:

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-3.144
-3.193
1.047
1.038
-1.134
-0.08485
-0.6671
1.324
1.423
1.472
-4.003
-2.891
1.623
2.798
-0.0211
-0.9951
-4.347
-0.5589
2.897
4.139
2.883
-2.993
1.271
-1.688
0.9789
1.109
-2.021
4.974
-1.196
1.09
-1.255
-4.021
-0.2052
-1.91
1.09
-0.9193
4.09
1.04
-3.43
-0.0211
-2.455
0.3824
-4.658
-0.9193
-0.738
-1.913
2.672
1.906
0.6228
2.271
1.795
-0.8605
-0.8605
-1.627
-3.08
-0.6764
0.8254
-0.9716
-0.03037
-0.4242
1.715
-0.0211
0.03766
-0.6269
-3.132
-0.2668
3.081
0.7051
0.7453
-0.91
-2.144
-0.2547
-2.91
0.07788
3.512
1.312
3.807
1.939
-1.913
-0.002562
-0.1867
-0.1867
-0.1846
-1.488
-2.021
-1.094
1.028
-1.377
-0.2547
0.8443
-1.298
-0.196
3.058
0.9882
-1.144
-0.1415
2.979
-6.436
0.7659
-3.403
1.09
0.8471
0.33
1.038
3.906
-0.1034
4.745
1.736
2.847
3.847
-0.8605
-3.972
0.1395
-0.6885
-2.094
-0.6885
-2.386
-0.7351
2.253
-1.738
0.02839
3.189
-0.1034
-1.972
-0.2052
3.09
-1.144
-3.187
-0.0211
-2.854
2.462
0.8657
-3.87
0.9479
1.979
3.038
-2.123
1.213
-4.103
-1.146
2.764
2.663
2.151
1.213
1.763
2.13
1.222
1.866
0.1602
2.979
-0.2547
-1.972
1.078
-0.1436
1.423
-0.337
-1.134
2.038
-1.278
0.3236
-1.116
-1.406
0.7453
-0.9531
-0.3865
-1.021
-1.962

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298995&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298995&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.48383e-05	0.161256	0.00015403
Geometric Mean	NaN
Harmonic Mean	-0.270275
Quadratic Mean	2.07764
Winsorized Mean ( 1 / 55 )	0.00930029	0.15878	0.0585733
Winsorized Mean ( 2 / 55 )	0.00576735	0.156911	0.0367556
Winsorized Mean ( 3 / 55 )	0.00927035	0.156058	0.0594034
Winsorized Mean ( 4 / 55 )	0.00682723	0.155067	0.0440276
Winsorized Mean ( 5 / 55 )	0.00559969	0.154717	0.0361931
Winsorized Mean ( 6 / 55 )	0.00527634	0.15433	0.0341888
Winsorized Mean ( 7 / 55 )	-0.00281349	0.15189	-0.0185232
Winsorized Mean ( 8 / 55 )	0.00279131	0.146694	0.0190281
Winsorized Mean ( 9 / 55 )	-0.00108893	0.145799	-0.00746873
Winsorized Mean ( 10 / 55 )	0.010947	0.144003	0.076019
Winsorized Mean ( 11 / 55 )	0.00982723	0.143756	0.0683604
Winsorized Mean ( 12 / 55 )	0.0114799	0.143161	0.080189
Winsorized Mean ( 13 / 55 )	0.00782125	0.142456	0.0549029
Winsorized Mean ( 14 / 55 )	0.0121805	0.14188	0.0858507
Winsorized Mean ( 15 / 55 )	0.0126296	0.139941	0.0902499
Winsorized Mean ( 16 / 55 )	0.0192404	0.138754	0.138666
Winsorized Mean ( 17 / 55 )	0.0175099	0.138054	0.126833
Winsorized Mean ( 18 / 55 )	0.0162165	0.1369	0.118455
Winsorized Mean ( 19 / 55 )	0.0577434	0.130926	0.441038
Winsorized Mean ( 20 / 55 )	0.0549889	0.128615	0.427548
Winsorized Mean ( 21 / 55 )	0.0842883	0.125101	0.673761
Winsorized Mean ( 22 / 55 )	0.0605757	0.121583	0.498226
Winsorized Mean ( 23 / 55 )	0.0382644	0.118085	0.324039
Winsorized Mean ( 24 / 55 )	0.0461686	0.11666	0.395752
Winsorized Mean ( 25 / 55 )	0.0308991	0.114942	0.268824
Winsorized Mean ( 26 / 55 )	0.0352584	0.113763	0.309928
Winsorized Mean ( 27 / 55 )	0.0203841	0.112132	0.181787
Winsorized Mean ( 28 / 55 )	0.0121686	0.110888	0.109738
Winsorized Mean ( 29 / 55 )	0.0137314	0.109239	0.1257
Winsorized Mean ( 30 / 55 )	0.00780328	0.108613	0.0718451
Winsorized Mean ( 31 / 55 )	0.000935018	0.107775	0.00867563
Winsorized Mean ( 32 / 55 )	0.0202883	0.102901	0.197163
Winsorized Mean ( 33 / 55 )	0.0238452	0.101234	0.235546
Winsorized Mean ( 34 / 55 )	0.0307674	0.099409	0.309503
Winsorized Mean ( 35 / 55 )	0.0554979	0.0960789	0.577629
Winsorized Mean ( 36 / 55 )	0.0533422	0.0923341	0.577708
Winsorized Mean ( 37 / 55 )	0.0263123	0.0883577	0.297792
Winsorized Mean ( 38 / 55 )	0.0331386	0.08556	0.387314
Winsorized Mean ( 39 / 55 )	0.0378093	0.0851237	0.444169
Winsorized Mean ( 40 / 55 )	0.0196057	0.0823157	0.238177
Winsorized Mean ( 41 / 55 )	0.0311446	0.0806951	0.385954
Winsorized Mean ( 42 / 55 )	0.0334081	0.0785682	0.425211
Winsorized Mean ( 43 / 55 )	0.0213063	0.0773328	0.275514
Winsorized Mean ( 44 / 55 )	0.018935	0.0771113	0.245554
Winsorized Mean ( 45 / 55 )	0.0216296	0.0768669	0.281391
Winsorized Mean ( 46 / 55 )	-0.00701708	0.0742316	-0.0945295
Winsorized Mean ( 47 / 55 )	-0.00729851	0.0732858	-0.0995898
Winsorized Mean ( 48 / 55 )	-0.000975162	0.0727113	-0.0134114
Winsorized Mean ( 49 / 55 )	0.020444	0.0707921	0.288789
Winsorized Mean ( 50 / 55 )	0.0246057	0.0697803	0.352616
Winsorized Mean ( 51 / 55 )	0.0223153	0.0682915	0.326765
Winsorized Mean ( 52 / 55 )	0.0258961	0.0675906	0.383132
Winsorized Mean ( 53 / 55 )	0.0359883	0.0666017	0.540351
Winsorized Mean ( 54 / 55 )	0.0359883	0.0666017	0.540351
Winsorized Mean ( 55 / 55 )	0.0357578	0.066039	0.541465
Trimmed Mean ( 1 / 55 )	0.00888575	0.155545	0.0571266
Trimmed Mean ( 2 / 55 )	0.00846103	0.15205	0.0556465
Trimmed Mean ( 3 / 55 )	0.00985806	0.149332	0.0660142
Trimmed Mean ( 4 / 55 )	0.0100638	0.146733	0.0685861
Trimmed Mean ( 5 / 55 )	0.0109245	0.144226	0.0757458
Trimmed Mean ( 6 / 55 )	0.0120719	0.141604	0.0852513
Trimmed Mean ( 7 / 55 )	0.0133082	0.13885	0.0958457
Trimmed Mean ( 8 / 55 )	0.0158553	0.136341	0.116292
Trimmed Mean ( 9 / 55 )	0.0176856	0.134528	0.131464
Trimmed Mean ( 10 / 55 )	0.0200554	0.132704	0.151129
Trimmed Mean ( 11 / 55 )	0.0211045	0.130989	0.161117
Trimmed Mean ( 12 / 55 )	0.0223017	0.129159	0.172669
Trimmed Mean ( 13 / 55 )	0.0233698	0.127247	0.183658
Trimmed Mean ( 14 / 55 )	0.0248068	0.125253	0.198054
Trimmed Mean ( 15 / 55 )	0.0259062	0.123149	0.210365
Trimmed Mean ( 16 / 55 )	0.0270011	0.12108	0.223001
Trimmed Mean ( 17 / 55 )	0.0276101	0.118956	0.232105
Trimmed Mean ( 18 / 55 )	0.0283675	0.116707	0.243066
Trimmed Mean ( 19 / 55 )	0.0292415	0.114368	0.255678
Trimmed Mean ( 20 / 55 )	0.0272689	0.112445	0.242508
Trimmed Mean ( 21 / 55 )	0.0254172	0.110573	0.229868
Trimmed Mean ( 22 / 55 )	0.021611	0.108865	0.198512
Trimmed Mean ( 23 / 55 )	0.0191665	0.107337	0.178564
Trimmed Mean ( 24 / 55 )	0.0180012	0.105992	0.169836
Trimmed Mean ( 25 / 55 )	0.0180012	0.104637	0.172035
Trimmed Mean ( 26 / 55 )	0.0154795	0.103298	0.149853
Trimmed Mean ( 27 / 55 )	0.0143553	0.101921	0.140847
Trimmed Mean ( 28 / 55 )	0.0140194	0.100543	0.139437
Trimmed Mean ( 29 / 55 )	0.0141206	0.0991226	0.142456
Trimmed Mean ( 30 / 55 )	0.0141416	0.0976917	0.144757
Trimmed Mean ( 31 / 55 )	0.0144776	0.096149	0.150575
Trimmed Mean ( 32 / 55 )	0.0151859	0.0944992	0.160699
Trimmed Mean ( 33 / 55 )	0.0149223	0.0931187	0.16025
Trimmed Mean ( 34 / 55 )	0.0144661	0.0917221	0.157717
Trimmed Mean ( 35 / 55 )	0.0136407	0.0903198	0.151027
Trimmed Mean ( 36 / 55 )	0.0115384	0.0890501	0.129572
Trimmed Mean ( 37 / 55 )	0.0094532	0.0879668	0.107463
Trimmed Mean ( 38 / 55 )	0.00861701	0.0871095	0.0989216
Trimmed Mean ( 39 / 55 )	0.00740616	0.0863799	0.0857393
Trimmed Mean ( 40 / 55 )	0.00590975	0.0855678	0.0690651
Trimmed Mean ( 41 / 55 )	0.00523704	0.0848914	0.061691
Trimmed Mean ( 42 / 55 )	0.00396564	0.0842453	0.0470725
Trimmed Mean ( 43 / 55 )	0.00396564	0.0836808	0.0473901
Trimmed Mean ( 44 / 55 )	0.00159681	0.0831214	0.0192106
Trimmed Mean ( 45 / 55 )	0.000742182	0.0824629	0.00900019
Trimmed Mean ( 46 / 55 )	-0.00029136	0.0816906	-0.00356663
Trimmed Mean ( 47 / 55 )	4.31233e-05	0.081043	0.000532104
Trimmed Mean ( 48 / 55 )	0.000410535	0.080351	0.00510927
Trimmed Mean ( 49 / 55 )	0.000480406	0.0795645	0.00603794
Trimmed Mean ( 50 / 55 )	0.000480406	0.0788202	0.00609496
Trimmed Mean ( 51 / 55 )	-0.00182695	0.0780158	-0.0234177
Trimmed Mean ( 52 / 55 )	-0.00308178	0.0772	-0.0399194
Trimmed Mean ( 53 / 55 )	-0.00460741	0.076266	-0.0604123
Trimmed Mean ( 54 / 55 )	-0.00677546	0.0752251	-0.0900691
Trimmed Mean ( 55 / 55 )	-0.00909565	0.0739163	-0.123053
Median	-0.1034
Midrange	-0.731
Midmean - Weighted Average at Xnp	-0.0103197
Midmean - Weighted Average at X(n+1)p	0.00523704
Midmean - Empirical Distribution Function	0.00523704
Midmean - Empirical Distribution Function - Averaging	0.00523704
Midmean - Empirical Distribution Function - Interpolation	0.00396564
Midmean - Closest Observation	-0.0103197
Midmean - True Basic - Statistics Graphics Toolkit	0.00523704
Midmean - MS Excel (old versions)	0.00523704
Number of observations	167

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.48383e-05 & 0.161256 & 0.00015403 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.270275 &  &  \tabularnewline
Quadratic Mean & 2.07764 &  &  \tabularnewline
Winsorized Mean ( 1 / 55 ) & 0.00930029 & 0.15878 & 0.0585733 \tabularnewline
Winsorized Mean ( 2 / 55 ) & 0.00576735 & 0.156911 & 0.0367556 \tabularnewline
Winsorized Mean ( 3 / 55 ) & 0.00927035 & 0.156058 & 0.0594034 \tabularnewline
Winsorized Mean ( 4 / 55 ) & 0.00682723 & 0.155067 & 0.0440276 \tabularnewline
Winsorized Mean ( 5 / 55 ) & 0.00559969 & 0.154717 & 0.0361931 \tabularnewline
Winsorized Mean ( 6 / 55 ) & 0.00527634 & 0.15433 & 0.0341888 \tabularnewline
Winsorized Mean ( 7 / 55 ) & -0.00281349 & 0.15189 & -0.0185232 \tabularnewline
Winsorized Mean ( 8 / 55 ) & 0.00279131 & 0.146694 & 0.0190281 \tabularnewline
Winsorized Mean ( 9 / 55 ) & -0.00108893 & 0.145799 & -0.00746873 \tabularnewline
Winsorized Mean ( 10 / 55 ) & 0.010947 & 0.144003 & 0.076019 \tabularnewline
Winsorized Mean ( 11 / 55 ) & 0.00982723 & 0.143756 & 0.0683604 \tabularnewline
Winsorized Mean ( 12 / 55 ) & 0.0114799 & 0.143161 & 0.080189 \tabularnewline
Winsorized Mean ( 13 / 55 ) & 0.00782125 & 0.142456 & 0.0549029 \tabularnewline
Winsorized Mean ( 14 / 55 ) & 0.0121805 & 0.14188 & 0.0858507 \tabularnewline
Winsorized Mean ( 15 / 55 ) & 0.0126296 & 0.139941 & 0.0902499 \tabularnewline
Winsorized Mean ( 16 / 55 ) & 0.0192404 & 0.138754 & 0.138666 \tabularnewline
Winsorized Mean ( 17 / 55 ) & 0.0175099 & 0.138054 & 0.126833 \tabularnewline
Winsorized Mean ( 18 / 55 ) & 0.0162165 & 0.1369 & 0.118455 \tabularnewline
Winsorized Mean ( 19 / 55 ) & 0.0577434 & 0.130926 & 0.441038 \tabularnewline
Winsorized Mean ( 20 / 55 ) & 0.0549889 & 0.128615 & 0.427548 \tabularnewline
Winsorized Mean ( 21 / 55 ) & 0.0842883 & 0.125101 & 0.673761 \tabularnewline
Winsorized Mean ( 22 / 55 ) & 0.0605757 & 0.121583 & 0.498226 \tabularnewline
Winsorized Mean ( 23 / 55 ) & 0.0382644 & 0.118085 & 0.324039 \tabularnewline
Winsorized Mean ( 24 / 55 ) & 0.0461686 & 0.11666 & 0.395752 \tabularnewline
Winsorized Mean ( 25 / 55 ) & 0.0308991 & 0.114942 & 0.268824 \tabularnewline
Winsorized Mean ( 26 / 55 ) & 0.0352584 & 0.113763 & 0.309928 \tabularnewline
Winsorized Mean ( 27 / 55 ) & 0.0203841 & 0.112132 & 0.181787 \tabularnewline
Winsorized Mean ( 28 / 55 ) & 0.0121686 & 0.110888 & 0.109738 \tabularnewline
Winsorized Mean ( 29 / 55 ) & 0.0137314 & 0.109239 & 0.1257 \tabularnewline
Winsorized Mean ( 30 / 55 ) & 0.00780328 & 0.108613 & 0.0718451 \tabularnewline
Winsorized Mean ( 31 / 55 ) & 0.000935018 & 0.107775 & 0.00867563 \tabularnewline
Winsorized Mean ( 32 / 55 ) & 0.0202883 & 0.102901 & 0.197163 \tabularnewline
Winsorized Mean ( 33 / 55 ) & 0.0238452 & 0.101234 & 0.235546 \tabularnewline
Winsorized Mean ( 34 / 55 ) & 0.0307674 & 0.099409 & 0.309503 \tabularnewline
Winsorized Mean ( 35 / 55 ) & 0.0554979 & 0.0960789 & 0.577629 \tabularnewline
Winsorized Mean ( 36 / 55 ) & 0.0533422 & 0.0923341 & 0.577708 \tabularnewline
Winsorized Mean ( 37 / 55 ) & 0.0263123 & 0.0883577 & 0.297792 \tabularnewline
Winsorized Mean ( 38 / 55 ) & 0.0331386 & 0.08556 & 0.387314 \tabularnewline
Winsorized Mean ( 39 / 55 ) & 0.0378093 & 0.0851237 & 0.444169 \tabularnewline
Winsorized Mean ( 40 / 55 ) & 0.0196057 & 0.0823157 & 0.238177 \tabularnewline
Winsorized Mean ( 41 / 55 ) & 0.0311446 & 0.0806951 & 0.385954 \tabularnewline
Winsorized Mean ( 42 / 55 ) & 0.0334081 & 0.0785682 & 0.425211 \tabularnewline
Winsorized Mean ( 43 / 55 ) & 0.0213063 & 0.0773328 & 0.275514 \tabularnewline
Winsorized Mean ( 44 / 55 ) & 0.018935 & 0.0771113 & 0.245554 \tabularnewline
Winsorized Mean ( 45 / 55 ) & 0.0216296 & 0.0768669 & 0.281391 \tabularnewline
Winsorized Mean ( 46 / 55 ) & -0.00701708 & 0.0742316 & -0.0945295 \tabularnewline
Winsorized Mean ( 47 / 55 ) & -0.00729851 & 0.0732858 & -0.0995898 \tabularnewline
Winsorized Mean ( 48 / 55 ) & -0.000975162 & 0.0727113 & -0.0134114 \tabularnewline
Winsorized Mean ( 49 / 55 ) & 0.020444 & 0.0707921 & 0.288789 \tabularnewline
Winsorized Mean ( 50 / 55 ) & 0.0246057 & 0.0697803 & 0.352616 \tabularnewline
Winsorized Mean ( 51 / 55 ) & 0.0223153 & 0.0682915 & 0.326765 \tabularnewline
Winsorized Mean ( 52 / 55 ) & 0.0258961 & 0.0675906 & 0.383132 \tabularnewline
Winsorized Mean ( 53 / 55 ) & 0.0359883 & 0.0666017 & 0.540351 \tabularnewline
Winsorized Mean ( 54 / 55 ) & 0.0359883 & 0.0666017 & 0.540351 \tabularnewline
Winsorized Mean ( 55 / 55 ) & 0.0357578 & 0.066039 & 0.541465 \tabularnewline
Trimmed Mean ( 1 / 55 ) & 0.00888575 & 0.155545 & 0.0571266 \tabularnewline
Trimmed Mean ( 2 / 55 ) & 0.00846103 & 0.15205 & 0.0556465 \tabularnewline
Trimmed Mean ( 3 / 55 ) & 0.00985806 & 0.149332 & 0.0660142 \tabularnewline
Trimmed Mean ( 4 / 55 ) & 0.0100638 & 0.146733 & 0.0685861 \tabularnewline
Trimmed Mean ( 5 / 55 ) & 0.0109245 & 0.144226 & 0.0757458 \tabularnewline
Trimmed Mean ( 6 / 55 ) & 0.0120719 & 0.141604 & 0.0852513 \tabularnewline
Trimmed Mean ( 7 / 55 ) & 0.0133082 & 0.13885 & 0.0958457 \tabularnewline
Trimmed Mean ( 8 / 55 ) & 0.0158553 & 0.136341 & 0.116292 \tabularnewline
Trimmed Mean ( 9 / 55 ) & 0.0176856 & 0.134528 & 0.131464 \tabularnewline
Trimmed Mean ( 10 / 55 ) & 0.0200554 & 0.132704 & 0.151129 \tabularnewline
Trimmed Mean ( 11 / 55 ) & 0.0211045 & 0.130989 & 0.161117 \tabularnewline
Trimmed Mean ( 12 / 55 ) & 0.0223017 & 0.129159 & 0.172669 \tabularnewline
Trimmed Mean ( 13 / 55 ) & 0.0233698 & 0.127247 & 0.183658 \tabularnewline
Trimmed Mean ( 14 / 55 ) & 0.0248068 & 0.125253 & 0.198054 \tabularnewline
Trimmed Mean ( 15 / 55 ) & 0.0259062 & 0.123149 & 0.210365 \tabularnewline
Trimmed Mean ( 16 / 55 ) & 0.0270011 & 0.12108 & 0.223001 \tabularnewline
Trimmed Mean ( 17 / 55 ) & 0.0276101 & 0.118956 & 0.232105 \tabularnewline
Trimmed Mean ( 18 / 55 ) & 0.0283675 & 0.116707 & 0.243066 \tabularnewline
Trimmed Mean ( 19 / 55 ) & 0.0292415 & 0.114368 & 0.255678 \tabularnewline
Trimmed Mean ( 20 / 55 ) & 0.0272689 & 0.112445 & 0.242508 \tabularnewline
Trimmed Mean ( 21 / 55 ) & 0.0254172 & 0.110573 & 0.229868 \tabularnewline
Trimmed Mean ( 22 / 55 ) & 0.021611 & 0.108865 & 0.198512 \tabularnewline
Trimmed Mean ( 23 / 55 ) & 0.0191665 & 0.107337 & 0.178564 \tabularnewline
Trimmed Mean ( 24 / 55 ) & 0.0180012 & 0.105992 & 0.169836 \tabularnewline
Trimmed Mean ( 25 / 55 ) & 0.0180012 & 0.104637 & 0.172035 \tabularnewline
Trimmed Mean ( 26 / 55 ) & 0.0154795 & 0.103298 & 0.149853 \tabularnewline
Trimmed Mean ( 27 / 55 ) & 0.0143553 & 0.101921 & 0.140847 \tabularnewline
Trimmed Mean ( 28 / 55 ) & 0.0140194 & 0.100543 & 0.139437 \tabularnewline
Trimmed Mean ( 29 / 55 ) & 0.0141206 & 0.0991226 & 0.142456 \tabularnewline
Trimmed Mean ( 30 / 55 ) & 0.0141416 & 0.0976917 & 0.144757 \tabularnewline
Trimmed Mean ( 31 / 55 ) & 0.0144776 & 0.096149 & 0.150575 \tabularnewline
Trimmed Mean ( 32 / 55 ) & 0.0151859 & 0.0944992 & 0.160699 \tabularnewline
Trimmed Mean ( 33 / 55 ) & 0.0149223 & 0.0931187 & 0.16025 \tabularnewline
Trimmed Mean ( 34 / 55 ) & 0.0144661 & 0.0917221 & 0.157717 \tabularnewline
Trimmed Mean ( 35 / 55 ) & 0.0136407 & 0.0903198 & 0.151027 \tabularnewline
Trimmed Mean ( 36 / 55 ) & 0.0115384 & 0.0890501 & 0.129572 \tabularnewline
Trimmed Mean ( 37 / 55 ) & 0.0094532 & 0.0879668 & 0.107463 \tabularnewline
Trimmed Mean ( 38 / 55 ) & 0.00861701 & 0.0871095 & 0.0989216 \tabularnewline
Trimmed Mean ( 39 / 55 ) & 0.00740616 & 0.0863799 & 0.0857393 \tabularnewline
Trimmed Mean ( 40 / 55 ) & 0.00590975 & 0.0855678 & 0.0690651 \tabularnewline
Trimmed Mean ( 41 / 55 ) & 0.00523704 & 0.0848914 & 0.061691 \tabularnewline
Trimmed Mean ( 42 / 55 ) & 0.00396564 & 0.0842453 & 0.0470725 \tabularnewline
Trimmed Mean ( 43 / 55 ) & 0.00396564 & 0.0836808 & 0.0473901 \tabularnewline
Trimmed Mean ( 44 / 55 ) & 0.00159681 & 0.0831214 & 0.0192106 \tabularnewline
Trimmed Mean ( 45 / 55 ) & 0.000742182 & 0.0824629 & 0.00900019 \tabularnewline
Trimmed Mean ( 46 / 55 ) & -0.00029136 & 0.0816906 & -0.00356663 \tabularnewline
Trimmed Mean ( 47 / 55 ) & 4.31233e-05 & 0.081043 & 0.000532104 \tabularnewline
Trimmed Mean ( 48 / 55 ) & 0.000410535 & 0.080351 & 0.00510927 \tabularnewline
Trimmed Mean ( 49 / 55 ) & 0.000480406 & 0.0795645 & 0.00603794 \tabularnewline
Trimmed Mean ( 50 / 55 ) & 0.000480406 & 0.0788202 & 0.00609496 \tabularnewline
Trimmed Mean ( 51 / 55 ) & -0.00182695 & 0.0780158 & -0.0234177 \tabularnewline
Trimmed Mean ( 52 / 55 ) & -0.00308178 & 0.0772 & -0.0399194 \tabularnewline
Trimmed Mean ( 53 / 55 ) & -0.00460741 & 0.076266 & -0.0604123 \tabularnewline
Trimmed Mean ( 54 / 55 ) & -0.00677546 & 0.0752251 & -0.0900691 \tabularnewline
Trimmed Mean ( 55 / 55 ) & -0.00909565 & 0.0739163 & -0.123053 \tabularnewline
Median & -0.1034 &  &  \tabularnewline
Midrange & -0.731 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.0103197 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.00523704 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.00523704 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.00523704 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.00396564 &  &  \tabularnewline
Midmean - Closest Observation & -0.0103197 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.00523704 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.00523704 &  &  \tabularnewline
Number of observations & 167 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298995&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]2.48383e-05[/C][C]0.161256[/C][C]0.00015403[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.270275[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.07764[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 55 )[/C][C]0.00930029[/C][C]0.15878[/C][C]0.0585733[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 55 )[/C][C]0.00576735[/C][C]0.156911[/C][C]0.0367556[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 55 )[/C][C]0.00927035[/C][C]0.156058[/C][C]0.0594034[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 55 )[/C][C]0.00682723[/C][C]0.155067[/C][C]0.0440276[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 55 )[/C][C]0.00559969[/C][C]0.154717[/C][C]0.0361931[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 55 )[/C][C]0.00527634[/C][C]0.15433[/C][C]0.0341888[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 55 )[/C][C]-0.00281349[/C][C]0.15189[/C][C]-0.0185232[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 55 )[/C][C]0.00279131[/C][C]0.146694[/C][C]0.0190281[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 55 )[/C][C]-0.00108893[/C][C]0.145799[/C][C]-0.00746873[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 55 )[/C][C]0.010947[/C][C]0.144003[/C][C]0.076019[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 55 )[/C][C]0.00982723[/C][C]0.143756[/C][C]0.0683604[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 55 )[/C][C]0.0114799[/C][C]0.143161[/C][C]0.080189[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 55 )[/C][C]0.00782125[/C][C]0.142456[/C][C]0.0549029[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 55 )[/C][C]0.0121805[/C][C]0.14188[/C][C]0.0858507[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 55 )[/C][C]0.0126296[/C][C]0.139941[/C][C]0.0902499[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 55 )[/C][C]0.0192404[/C][C]0.138754[/C][C]0.138666[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 55 )[/C][C]0.0175099[/C][C]0.138054[/C][C]0.126833[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 55 )[/C][C]0.0162165[/C][C]0.1369[/C][C]0.118455[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 55 )[/C][C]0.0577434[/C][C]0.130926[/C][C]0.441038[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 55 )[/C][C]0.0549889[/C][C]0.128615[/C][C]0.427548[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 55 )[/C][C]0.0842883[/C][C]0.125101[/C][C]0.673761[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 55 )[/C][C]0.0605757[/C][C]0.121583[/C][C]0.498226[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 55 )[/C][C]0.0382644[/C][C]0.118085[/C][C]0.324039[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 55 )[/C][C]0.0461686[/C][C]0.11666[/C][C]0.395752[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 55 )[/C][C]0.0308991[/C][C]0.114942[/C][C]0.268824[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 55 )[/C][C]0.0352584[/C][C]0.113763[/C][C]0.309928[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 55 )[/C][C]0.0203841[/C][C]0.112132[/C][C]0.181787[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 55 )[/C][C]0.0121686[/C][C]0.110888[/C][C]0.109738[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 55 )[/C][C]0.0137314[/C][C]0.109239[/C][C]0.1257[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 55 )[/C][C]0.00780328[/C][C]0.108613[/C][C]0.0718451[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 55 )[/C][C]0.000935018[/C][C]0.107775[/C][C]0.00867563[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 55 )[/C][C]0.0202883[/C][C]0.102901[/C][C]0.197163[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 55 )[/C][C]0.0238452[/C][C]0.101234[/C][C]0.235546[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 55 )[/C][C]0.0307674[/C][C]0.099409[/C][C]0.309503[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 55 )[/C][C]0.0554979[/C][C]0.0960789[/C][C]0.577629[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 55 )[/C][C]0.0533422[/C][C]0.0923341[/C][C]0.577708[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 55 )[/C][C]0.0263123[/C][C]0.0883577[/C][C]0.297792[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 55 )[/C][C]0.0331386[/C][C]0.08556[/C][C]0.387314[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 55 )[/C][C]0.0378093[/C][C]0.0851237[/C][C]0.444169[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 55 )[/C][C]0.0196057[/C][C]0.0823157[/C][C]0.238177[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 55 )[/C][C]0.0311446[/C][C]0.0806951[/C][C]0.385954[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 55 )[/C][C]0.0334081[/C][C]0.0785682[/C][C]0.425211[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 55 )[/C][C]0.0213063[/C][C]0.0773328[/C][C]0.275514[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 55 )[/C][C]0.018935[/C][C]0.0771113[/C][C]0.245554[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 55 )[/C][C]0.0216296[/C][C]0.0768669[/C][C]0.281391[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 55 )[/C][C]-0.00701708[/C][C]0.0742316[/C][C]-0.0945295[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 55 )[/C][C]-0.00729851[/C][C]0.0732858[/C][C]-0.0995898[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 55 )[/C][C]-0.000975162[/C][C]0.0727113[/C][C]-0.0134114[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 55 )[/C][C]0.020444[/C][C]0.0707921[/C][C]0.288789[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 55 )[/C][C]0.0246057[/C][C]0.0697803[/C][C]0.352616[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 55 )[/C][C]0.0223153[/C][C]0.0682915[/C][C]0.326765[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 55 )[/C][C]0.0258961[/C][C]0.0675906[/C][C]0.383132[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 55 )[/C][C]0.0359883[/C][C]0.0666017[/C][C]0.540351[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 55 )[/C][C]0.0359883[/C][C]0.0666017[/C][C]0.540351[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 55 )[/C][C]0.0357578[/C][C]0.066039[/C][C]0.541465[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 55 )[/C][C]0.00888575[/C][C]0.155545[/C][C]0.0571266[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 55 )[/C][C]0.00846103[/C][C]0.15205[/C][C]0.0556465[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 55 )[/C][C]0.00985806[/C][C]0.149332[/C][C]0.0660142[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 55 )[/C][C]0.0100638[/C][C]0.146733[/C][C]0.0685861[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 55 )[/C][C]0.0109245[/C][C]0.144226[/C][C]0.0757458[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 55 )[/C][C]0.0120719[/C][C]0.141604[/C][C]0.0852513[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 55 )[/C][C]0.0133082[/C][C]0.13885[/C][C]0.0958457[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 55 )[/C][C]0.0158553[/C][C]0.136341[/C][C]0.116292[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 55 )[/C][C]0.0176856[/C][C]0.134528[/C][C]0.131464[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 55 )[/C][C]0.0200554[/C][C]0.132704[/C][C]0.151129[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 55 )[/C][C]0.0211045[/C][C]0.130989[/C][C]0.161117[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 55 )[/C][C]0.0223017[/C][C]0.129159[/C][C]0.172669[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 55 )[/C][C]0.0233698[/C][C]0.127247[/C][C]0.183658[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 55 )[/C][C]0.0248068[/C][C]0.125253[/C][C]0.198054[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 55 )[/C][C]0.0259062[/C][C]0.123149[/C][C]0.210365[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 55 )[/C][C]0.0270011[/C][C]0.12108[/C][C]0.223001[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 55 )[/C][C]0.0276101[/C][C]0.118956[/C][C]0.232105[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 55 )[/C][C]0.0283675[/C][C]0.116707[/C][C]0.243066[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 55 )[/C][C]0.0292415[/C][C]0.114368[/C][C]0.255678[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 55 )[/C][C]0.0272689[/C][C]0.112445[/C][C]0.242508[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 55 )[/C][C]0.0254172[/C][C]0.110573[/C][C]0.229868[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 55 )[/C][C]0.021611[/C][C]0.108865[/C][C]0.198512[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 55 )[/C][C]0.0191665[/C][C]0.107337[/C][C]0.178564[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 55 )[/C][C]0.0180012[/C][C]0.105992[/C][C]0.169836[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 55 )[/C][C]0.0180012[/C][C]0.104637[/C][C]0.172035[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 55 )[/C][C]0.0154795[/C][C]0.103298[/C][C]0.149853[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 55 )[/C][C]0.0143553[/C][C]0.101921[/C][C]0.140847[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 55 )[/C][C]0.0140194[/C][C]0.100543[/C][C]0.139437[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 55 )[/C][C]0.0141206[/C][C]0.0991226[/C][C]0.142456[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 55 )[/C][C]0.0141416[/C][C]0.0976917[/C][C]0.144757[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 55 )[/C][C]0.0144776[/C][C]0.096149[/C][C]0.150575[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 55 )[/C][C]0.0151859[/C][C]0.0944992[/C][C]0.160699[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 55 )[/C][C]0.0149223[/C][C]0.0931187[/C][C]0.16025[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 55 )[/C][C]0.0144661[/C][C]0.0917221[/C][C]0.157717[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 55 )[/C][C]0.0136407[/C][C]0.0903198[/C][C]0.151027[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 55 )[/C][C]0.0115384[/C][C]0.0890501[/C][C]0.129572[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 55 )[/C][C]0.0094532[/C][C]0.0879668[/C][C]0.107463[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 55 )[/C][C]0.00861701[/C][C]0.0871095[/C][C]0.0989216[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 55 )[/C][C]0.00740616[/C][C]0.0863799[/C][C]0.0857393[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 55 )[/C][C]0.00590975[/C][C]0.0855678[/C][C]0.0690651[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 55 )[/C][C]0.00523704[/C][C]0.0848914[/C][C]0.061691[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 55 )[/C][C]0.00396564[/C][C]0.0842453[/C][C]0.0470725[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 55 )[/C][C]0.00396564[/C][C]0.0836808[/C][C]0.0473901[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 55 )[/C][C]0.00159681[/C][C]0.0831214[/C][C]0.0192106[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 55 )[/C][C]0.000742182[/C][C]0.0824629[/C][C]0.00900019[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 55 )[/C][C]-0.00029136[/C][C]0.0816906[/C][C]-0.00356663[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 55 )[/C][C]4.31233e-05[/C][C]0.081043[/C][C]0.000532104[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 55 )[/C][C]0.000410535[/C][C]0.080351[/C][C]0.00510927[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 55 )[/C][C]0.000480406[/C][C]0.0795645[/C][C]0.00603794[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 55 )[/C][C]0.000480406[/C][C]0.0788202[/C][C]0.00609496[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 55 )[/C][C]-0.00182695[/C][C]0.0780158[/C][C]-0.0234177[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 55 )[/C][C]-0.00308178[/C][C]0.0772[/C][C]-0.0399194[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 55 )[/C][C]-0.00460741[/C][C]0.076266[/C][C]-0.0604123[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 55 )[/C][C]-0.00677546[/C][C]0.0752251[/C][C]-0.0900691[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 55 )[/C][C]-0.00909565[/C][C]0.0739163[/C][C]-0.123053[/C][/ROW]
[ROW][C]Median[/C][C]-0.1034[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.731[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.0103197[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.00523704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.00523704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.00523704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.00396564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.0103197[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.00523704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.00523704[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]167[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298995&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	2.48383e-05	0.161256	0.00015403
Geometric Mean	NaN
Harmonic Mean	-0.270275
Quadratic Mean	2.07764
Winsorized Mean ( 1 / 55 )	0.00930029	0.15878	0.0585733
Winsorized Mean ( 2 / 55 )	0.00576735	0.156911	0.0367556
Winsorized Mean ( 3 / 55 )	0.00927035	0.156058	0.0594034
Winsorized Mean ( 4 / 55 )	0.00682723	0.155067	0.0440276
Winsorized Mean ( 5 / 55 )	0.00559969	0.154717	0.0361931
Winsorized Mean ( 6 / 55 )	0.00527634	0.15433	0.0341888
Winsorized Mean ( 7 / 55 )	-0.00281349	0.15189	-0.0185232
Winsorized Mean ( 8 / 55 )	0.00279131	0.146694	0.0190281
Winsorized Mean ( 9 / 55 )	-0.00108893	0.145799	-0.00746873
Winsorized Mean ( 10 / 55 )	0.010947	0.144003	0.076019
Winsorized Mean ( 11 / 55 )	0.00982723	0.143756	0.0683604
Winsorized Mean ( 12 / 55 )	0.0114799	0.143161	0.080189
Winsorized Mean ( 13 / 55 )	0.00782125	0.142456	0.0549029
Winsorized Mean ( 14 / 55 )	0.0121805	0.14188	0.0858507
Winsorized Mean ( 15 / 55 )	0.0126296	0.139941	0.0902499
Winsorized Mean ( 16 / 55 )	0.0192404	0.138754	0.138666
Winsorized Mean ( 17 / 55 )	0.0175099	0.138054	0.126833
Winsorized Mean ( 18 / 55 )	0.0162165	0.1369	0.118455
Winsorized Mean ( 19 / 55 )	0.0577434	0.130926	0.441038
Winsorized Mean ( 20 / 55 )	0.0549889	0.128615	0.427548
Winsorized Mean ( 21 / 55 )	0.0842883	0.125101	0.673761
Winsorized Mean ( 22 / 55 )	0.0605757	0.121583	0.498226
Winsorized Mean ( 23 / 55 )	0.0382644	0.118085	0.324039
Winsorized Mean ( 24 / 55 )	0.0461686	0.11666	0.395752
Winsorized Mean ( 25 / 55 )	0.0308991	0.114942	0.268824
Winsorized Mean ( 26 / 55 )	0.0352584	0.113763	0.309928
Winsorized Mean ( 27 / 55 )	0.0203841	0.112132	0.181787
Winsorized Mean ( 28 / 55 )	0.0121686	0.110888	0.109738
Winsorized Mean ( 29 / 55 )	0.0137314	0.109239	0.1257
Winsorized Mean ( 30 / 55 )	0.00780328	0.108613	0.0718451
Winsorized Mean ( 31 / 55 )	0.000935018	0.107775	0.00867563
Winsorized Mean ( 32 / 55 )	0.0202883	0.102901	0.197163
Winsorized Mean ( 33 / 55 )	0.0238452	0.101234	0.235546
Winsorized Mean ( 34 / 55 )	0.0307674	0.099409	0.309503
Winsorized Mean ( 35 / 55 )	0.0554979	0.0960789	0.577629
Winsorized Mean ( 36 / 55 )	0.0533422	0.0923341	0.577708
Winsorized Mean ( 37 / 55 )	0.0263123	0.0883577	0.297792
Winsorized Mean ( 38 / 55 )	0.0331386	0.08556	0.387314
Winsorized Mean ( 39 / 55 )	0.0378093	0.0851237	0.444169
Winsorized Mean ( 40 / 55 )	0.0196057	0.0823157	0.238177
Winsorized Mean ( 41 / 55 )	0.0311446	0.0806951	0.385954
Winsorized Mean ( 42 / 55 )	0.0334081	0.0785682	0.425211
Winsorized Mean ( 43 / 55 )	0.0213063	0.0773328	0.275514
Winsorized Mean ( 44 / 55 )	0.018935	0.0771113	0.245554
Winsorized Mean ( 45 / 55 )	0.0216296	0.0768669	0.281391
Winsorized Mean ( 46 / 55 )	-0.00701708	0.0742316	-0.0945295
Winsorized Mean ( 47 / 55 )	-0.00729851	0.0732858	-0.0995898
Winsorized Mean ( 48 / 55 )	-0.000975162	0.0727113	-0.0134114
Winsorized Mean ( 49 / 55 )	0.020444	0.0707921	0.288789
Winsorized Mean ( 50 / 55 )	0.0246057	0.0697803	0.352616
Winsorized Mean ( 51 / 55 )	0.0223153	0.0682915	0.326765
Winsorized Mean ( 52 / 55 )	0.0258961	0.0675906	0.383132
Winsorized Mean ( 53 / 55 )	0.0359883	0.0666017	0.540351
Winsorized Mean ( 54 / 55 )	0.0359883	0.0666017	0.540351
Winsorized Mean ( 55 / 55 )	0.0357578	0.066039	0.541465
Trimmed Mean ( 1 / 55 )	0.00888575	0.155545	0.0571266
Trimmed Mean ( 2 / 55 )	0.00846103	0.15205	0.0556465
Trimmed Mean ( 3 / 55 )	0.00985806	0.149332	0.0660142
Trimmed Mean ( 4 / 55 )	0.0100638	0.146733	0.0685861
Trimmed Mean ( 5 / 55 )	0.0109245	0.144226	0.0757458
Trimmed Mean ( 6 / 55 )	0.0120719	0.141604	0.0852513
Trimmed Mean ( 7 / 55 )	0.0133082	0.13885	0.0958457
Trimmed Mean ( 8 / 55 )	0.0158553	0.136341	0.116292
Trimmed Mean ( 9 / 55 )	0.0176856	0.134528	0.131464
Trimmed Mean ( 10 / 55 )	0.0200554	0.132704	0.151129
Trimmed Mean ( 11 / 55 )	0.0211045	0.130989	0.161117
Trimmed Mean ( 12 / 55 )	0.0223017	0.129159	0.172669
Trimmed Mean ( 13 / 55 )	0.0233698	0.127247	0.183658
Trimmed Mean ( 14 / 55 )	0.0248068	0.125253	0.198054
Trimmed Mean ( 15 / 55 )	0.0259062	0.123149	0.210365
Trimmed Mean ( 16 / 55 )	0.0270011	0.12108	0.223001
Trimmed Mean ( 17 / 55 )	0.0276101	0.118956	0.232105
Trimmed Mean ( 18 / 55 )	0.0283675	0.116707	0.243066
Trimmed Mean ( 19 / 55 )	0.0292415	0.114368	0.255678
Trimmed Mean ( 20 / 55 )	0.0272689	0.112445	0.242508
Trimmed Mean ( 21 / 55 )	0.0254172	0.110573	0.229868
Trimmed Mean ( 22 / 55 )	0.021611	0.108865	0.198512
Trimmed Mean ( 23 / 55 )	0.0191665	0.107337	0.178564
Trimmed Mean ( 24 / 55 )	0.0180012	0.105992	0.169836
Trimmed Mean ( 25 / 55 )	0.0180012	0.104637	0.172035
Trimmed Mean ( 26 / 55 )	0.0154795	0.103298	0.149853
Trimmed Mean ( 27 / 55 )	0.0143553	0.101921	0.140847
Trimmed Mean ( 28 / 55 )	0.0140194	0.100543	0.139437
Trimmed Mean ( 29 / 55 )	0.0141206	0.0991226	0.142456
Trimmed Mean ( 30 / 55 )	0.0141416	0.0976917	0.144757
Trimmed Mean ( 31 / 55 )	0.0144776	0.096149	0.150575
Trimmed Mean ( 32 / 55 )	0.0151859	0.0944992	0.160699
Trimmed Mean ( 33 / 55 )	0.0149223	0.0931187	0.16025
Trimmed Mean ( 34 / 55 )	0.0144661	0.0917221	0.157717
Trimmed Mean ( 35 / 55 )	0.0136407	0.0903198	0.151027
Trimmed Mean ( 36 / 55 )	0.0115384	0.0890501	0.129572
Trimmed Mean ( 37 / 55 )	0.0094532	0.0879668	0.107463
Trimmed Mean ( 38 / 55 )	0.00861701	0.0871095	0.0989216
Trimmed Mean ( 39 / 55 )	0.00740616	0.0863799	0.0857393
Trimmed Mean ( 40 / 55 )	0.00590975	0.0855678	0.0690651
Trimmed Mean ( 41 / 55 )	0.00523704	0.0848914	0.061691
Trimmed Mean ( 42 / 55 )	0.00396564	0.0842453	0.0470725
Trimmed Mean ( 43 / 55 )	0.00396564	0.0836808	0.0473901
Trimmed Mean ( 44 / 55 )	0.00159681	0.0831214	0.0192106
Trimmed Mean ( 45 / 55 )	0.000742182	0.0824629	0.00900019
Trimmed Mean ( 46 / 55 )	-0.00029136	0.0816906	-0.00356663
Trimmed Mean ( 47 / 55 )	4.31233e-05	0.081043	0.000532104
Trimmed Mean ( 48 / 55 )	0.000410535	0.080351	0.00510927
Trimmed Mean ( 49 / 55 )	0.000480406	0.0795645	0.00603794
Trimmed Mean ( 50 / 55 )	0.000480406	0.0788202	0.00609496
Trimmed Mean ( 51 / 55 )	-0.00182695	0.0780158	-0.0234177
Trimmed Mean ( 52 / 55 )	-0.00308178	0.0772	-0.0399194
Trimmed Mean ( 53 / 55 )	-0.00460741	0.076266	-0.0604123
Trimmed Mean ( 54 / 55 )	-0.00677546	0.0752251	-0.0900691
Trimmed Mean ( 55 / 55 )	-0.00909565	0.0739163	-0.123053
Median	-0.1034
Midrange	-0.731
Midmean - Weighted Average at Xnp	-0.0103197
Midmean - Weighted Average at X(n+1)p	0.00523704
Midmean - Empirical Distribution Function	0.00523704
Midmean - Empirical Distribution Function - Averaging	0.00523704
Midmean - Empirical Distribution Function - Interpolation	0.00396564
Midmean - Closest Observation	-0.0103197
Midmean - True Basic - Statistics Graphics Toolkit	0.00523704
Midmean - MS Excel (old versions)	0.00523704
Number of observations	167

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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
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