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Activity 2 #1

The document calculates various statistical measures for a sample of size 15, including the sample mean (3.79), median (3.6), trimmed mean (3.68), variance (0.943), and standard deviation (0.971). A dot plot of the data is also presented. Both the sample mean and trimmed mean are approximately the same.

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Jireh Rivera
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65 views2 pages

Activity 2 #1

The document calculates various statistical measures for a sample of size 15, including the sample mean (3.79), median (3.6), trimmed mean (3.68), variance (0.943), and standard deviation (0.971). A dot plot of the data is also presented. Both the sample mean and trimmed mean are approximately the same.

Uploaded by

Jireh Rivera
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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A. Sample size is the number of measurements recorded.

n = 15

B. Sample mean

x̄ = (Σ xi) / n

= (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15

= 56.8/15

x̄ = 3.79

C. Sample Median

Ascending order of the data:

2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6

Sample media if n is odd:

x̄ = x(n+1)/2

= x(15+1)/2

= x(16/2)

= x(8)

x̄ = 3.6

D. Dot plot for the given data.

2.5 Dot Plot


2
1.5
1
0.5
0
2.5 2.8 2.9 3 3.3 3.4 3.6 3.7 4 4.4 4.8 5.2 5.6

Driving time
E. Trimmed Mean

1. eliminate the largest 20% and smallest 20%

2. compute average of the remaining

x̄tr(20) = (2.9+ 3.0 + 3.3 + 3.4 + 3.6 + 3.7 + 4.0 + 4.4 + 4.8)/9

= 33.1/9

x̄tr(20) = 3.68

F. Based on the computations above, the sample mean is 3.79 while the trimmed mean is 3.68.
Hence, both values are approximately the same.

G. Sample Variance (s2) and Sample Standard Deviation (s)

s2 = [Σ(xi- x̄)2]/n-1

= [(3.4-3.79)2 + (2.5-3.79)2 + (4.8-3.79)2 + (2.9-3.79)2 + (3.6-3.79)2 + (2.8-3.79)2 + (3.3-3.79)2

+ (5.6-3.79)2 + (3.7-3.79)2 + (2.8-3.79)2 + (4.4-3.79)2 + (4.0-3.79)2 + (5.2-3.79)2 + (3.0-3.79)2

+ (4.8-3.79)2] / (15-1)

= 13.2/14

s2 = 0.943;

s = √s2

= √0.943

s = 0.971

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