Q58E Calculate the variance and stand... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 2: Q58E (page 103)

Calculate the variance and standard deviation for samples where
a.n= 10, 鈭�x² = 84, 鈭�x= 20
b.n= 40, 鈭�x² = 380, 鈭�x= 100
c.n= 20, 鈭�x² = 18, 鈭�x= 17.

Short Answer

Expert verified

Variance = 8.88, Standard Deviation = 2.98
Variance = 9.58, Standard Deviation = 3.09
Variance = 0.91, Standard Deviation = 0.95

Step by step solution

Calculating the variance and standard deviation for a

Given: n= 10, 鈭�x² = 84, 鈭�x= 20

$M e a n = \frac{鈭� x}{n} = \frac{20}{10} = 2 {\overset{炉}{x}}^{2} = 4$

$S a m p l e V a r i a n c e = \frac{鈭� x^{2} - {\overset{炉}{x}}^{2}}{n - 1} = \frac{84 - 4}{10 - 1} = \frac{80}{9} = 8.88$

localid="1662206428948" $\begin{array}{rcl} Sample standard deviation & = & \sqrt{Sample variance} \\ = & \sqrt{8.88} \\ = & 2.98 \end{array}$

Therefore, variance is 8.88 and standard deviation is 2.98.

Computing the variance and standard deviation for b

Given: n= 40, 鈭�x² = 380, 鈭�x= 100

$M e a n = \frac{鈭� x}{n} = \frac{100}{40} = 2.5 {\overset{炉}{x}}^{2} = 6.25$

$S a m p l e V a r i a n c e = \frac{鈭� x^{2} - {\overset{炉}{x}}^{2}}{n - 1} = \frac{380 - 6.25}{40 - 1} = \frac{373.75}{39} = 9.58$

$Samplestandarddeviation = \sqrt{Samplevariance} = \sqrt{9.58} = 3.09$

Therefore, variance = 9.58 and standard deviation = 3.09.

Finding the variance and standard deviation for c

Given: n= 20, 鈭�x² = 18, 鈭�x= 17.

$M e a n = \frac{鈭� x}{n} = \frac{17}{20} = 0.85 {\overset{炉}{x}}^{2} = 0.7225$

$SampleVariance = \frac{鈭� x^{2} - {\overset{炉}{x}}^{2}}{n - 1} = \frac{18 - 0.7225}{20 - 1} = \frac{17.2775}{19} = 0.91$

$Samplestandarddeviation = \sqrt{Samplevariance} = \sqrt{0.91} = 0.95$

Therefore, Variance and Standard Deviation are 0.91 and 0.95 respectively.

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91影视

Calculate the variance and standard deviation for samples where
a.n= 10, 鈭�x² = 84, 鈭�x= 20
b.n= 40, 鈭�x² = 380, 鈭�x= 100
c.n= 20, 鈭�x² = 18, 鈭�x= 17.

Short Answer

Step by step solution

Calculating the variance and standard deviation for a

Computing the variance and standard deviation for b

Finding the variance and standard deviation for c

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91影视

Calculate the variance and standard deviation for samples wherea.n= 10, 鈭�x2 = 84, 鈭�x= 20b.n= 40, 鈭�x2 = 380, 鈭�x= 100c.n= 20, 鈭�x2 = 18, 鈭�x= 17.

Short Answer

Step by step solution

Calculating the variance and standard deviation for a

Computing the variance and standard deviation for b

Finding the variance and standard deviation for c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Calculate the variance and standard deviation for samples where
a.n= 10, 鈭�x² = 84, 鈭�x= 20
b.n= 40, 鈭�x² = 380, 鈭�x= 100
c.n= 20, 鈭�x² = 18, 鈭�x= 17.