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Chapter 8: Problem 3

Compute the (sample) variance and standard deviation of the data samples given in Exercises \(1-8 .\) You calculated the means in the last exercise set. Round all answers to two decimal nlaces. $$ 2,6,6,7,-1 $$

Short Answer

Expert verified
The sample variance is 11.50, and the sample standard deviation is approximately 3.39.

Step by step solution

01

Calculate the mean of the data set (already given)

As mentioned earlier, we already have the mean of the data set calculated from a previous exercise. If the mean was not given, we would simply add up all the data points and divide by the total number of data points. The mean is: \[\frac{2 + 6 + 6 + 7 - 1}{5} = \frac{20}{5} = 4\]
02

Calculate the differences between each data point and the mean

To calculate the differences, we need to subtract the mean from each data point in the data set. The differences are: \[2 - 4 = -2\] \[6 - 4 = 2\] \[6 - 4 = 2\] \[7 - 4 = 3\] \[-1 - 4 = -5\]
03

Square each difference

We need to square each difference obtained in Step 2: \[(-2)^2 = 4\] \[(2)^2 = 4\] \[(2)^2 = 4\] \[(3)^2 = 9\] \[(-5)^2 = 25\]
04

Calculate the average of the squared differences

Add the squared differences and divide by the total number of data points minus 1 (to compute sample variance): \[\frac{4 + 4 + 4 + 9 + 25}{5 - 1} = \frac{46}{4} = 11.50\] The sample variance is 11.50.
05

Compute the standard deviation

To find the standard deviation, take the square root of the variance: \[\sqrt{11.50} \approx 3.39\] The sample standard deviation is approximately 3.39. So, the sample variance is 11.50, and the sample standard deviation is approximately 3.39.

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Most popular questions from this chapter

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