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Chapter 4: Problem 5

Using the computation formula for the sum of squares, calculate the population standard deviation for the scores in (a) and the sample standard deviation for the scores in (b). (a) 1,3,7,2,0,4,7,3 (b) 10,8,5,0,1,1,7,9,2

Short Answer

Expert verified
The population standard deviation for scores in (a) and the sample standard deviation for scores in (b) can be computed using the formula for calculating standard deviation which involves finding the mean, calculating each score's deviation from the mean, squaring these deviations, and getting the square root of their average (for population) or their average with (n-1) in the denominator (for sample). The actual numerical answers will depend on the given data, but the key is to follow these steps correctly.

Step by step solution

01

Calculate Mean

Compute the mean (average) of each set of scores. For set (a), add all the scores and divide by 8 (the number of scores). Similarly, for set (b), sum up all scores and divide by 9.
02

Subtract the Mean and Square the Result

Subtract the mean from each score in the sets and square the outcome. This will give us the squared deviation from the mean for each score.
03

Calculate Variance

Sum all the squared deviations computed in Step 2. For set (a) which needs population standard deviation, divide this sum by the number of scores to get population variance. For set (b), since we need sample standard deviation, divide the sum of squared deviations by the number of scores minus 1 to get sample variance.
04

Square Root of Variance

Finally, compute the square root of the variances found in Step 3. This will give us the population standard deviation for set (a) and the sample standard deviation for set (b).

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Most popular questions from this chapter

Employees of Corporation A earn annual salaries described by a mean of \(\$ 90,000\) and a standard deviation of \(\$ 10,000\). (a) The majority of all salaries fall between what two values? (b) A small minority of all salaries are less than what value? (c) A small minority of all salaries are more than what value? (d) Answer parts (a), (b), and (c) for Corporation B's employees, who earn annual salaries described by a mean of \(\$ 90,000\) and a standard deviation of \(\$ 2,000\).

In what sense is the variance (a) a type of mean? (b) not a readily understood measure of variability? (c) a stepping stone to the standard deviation?

Indicate whether each of the following statements about degrees of freedom is true or false. (a) Degrees of freedom refer to the number of values free to vary in the population. (b) One degree of freedom is lost because, when expressed as a deviation from the sample mean, the final deviation in the sample fails to supply information about population variability. (c) Degrees of freedom makes sense only if we wish to estimate some unknown characteristic of a population. (d) Degrees of freedom reflect the poor quality of one or more observations.

When not interrupted artificially, the duration of human pregnancies can be described, we'll assume, by a mean of 9 months (270 days) and a standard deviation of one-half month (15 days). (a) Between what two times, in days, will a majority of babies arrive? (b) A small minority of all babies will arrive sooner than (c) A small minority of all babies will arrive later than (d) In a paternity suit, the suspected father claims that, since he was overseas during the entire 10 months prior to the baby's birth, he could not possibly be the father. Any comment?

Using the definition formula for the sum of squares, calculate the sample standard deviation for the following four scores: 1,3,4,4
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