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Chapter 8: Problem 4

Compute the (sample) variance and standard deviation of the given data sample. (You calculated the means in the Section 8.3 exercises. Round all answers to two decimal places.) 3,1,6,-3,0,5

Short Answer

Expert verified
The sample variance of the given data is 11.2, and the sample standard deviation is approximately 3.35 (rounded to two decimal places).

Step by step solution

01

Calculate the mean

Add up all the data points and divide the sum by the total number of data points to find the mean: \[ \text{mean} = \frac{3+1+6-3+0+5}{6} = \frac{12}{6} = 2 \]
02

Compute the squared deviations from the mean

Subtract the mean from each data point, square the result, and create a list of squared deviations: \[ (3-2)^2 = 1 \\ (1-2)^2 = 1 \\ (6-2)^2 = 16 \\ (-3-2)^2 = 25 \\ (0-2)^2 = 4 \\ (5-2)^2 = 9 \] The squared deviations are: 1, 1, 16, 25, 4, and 9.
03

Calculate the average squared deviation (sample variance)

Add up the squared deviations and divide by the total number of data points minus 1 (since it is a sample) to find the sample variance: \[ \text{sample variance} = \frac{1+1+16+25+4+9}{6-1} = \frac{56}{5} = 11.2 \] The sample variance of the given data is 11.2.
04

Compute the standard deviation

Take the square root of the sample variance to find the standard deviation: \[ \text{standard deviation} = \sqrt{11.2} \approx 3.35 \] The sample standard deviation of the given data is approximately 3.35 (rounded to two decimal places).

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Most popular questions from this chapter

Following is a sample of the day-byday change, rounded to the nearest 100 points, in the Dow Jones Industrial Average during 10 successive business days around the start of the financial crisis in October \(2008:^{20}\) $$ -100,400,-200,-500,200,-300,-200,900,-100,200 $$ Compute the mean and median of the given sample. Fill in the blank: There were as many days with a change in the Dow above \(\quad\) points as there were with changes below that.

Explain how you can use a sample to estimate an expected value.

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\- Find an algebraic formula for the population standard deviation of a sample \(\\{x, y\\}\) of two scores \((x \leq y)\).
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