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Suppose the following data set represents the starting salaries for the population of teachers from nine states:

$31,184
$43,839
$35,358
$31,606
$33,549
$39,196
$35,541
$34,972
$39,674
Part A: Calculate the mean of the data set.
Part B: Calculate the five-number summary.
Part C: Calculate the standard deviation of this data set.

User OhJeez
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1 Answer

5 votes

Final answer:

The mean starting salary is $37,093.22. The five-number summary is $31,184, $33,549, $35,358, $39,196, and $43,839. The standard deviation is approximately $3,900.09.

Step-by-step explanation:

To calculate the mean of a data set, you add up all the values and divide by the number of values. In this case, the sum of the salaries is $333,839. To get the mean, you divide that by 9 (the number of teachers). So the mean starting salary is $37,093.22.

To calculate the five-number summary, you need to find the minimum, first quartile, median, third quartile, and maximum. The minimum is $31,184, the first quartile is $33,549, the median is $35,358, the third quartile is $39,196, and the maximum is $43,839.

To calculate the standard deviation, you need to find the variance first. Subtract the mean from each salary, square the result, add up all the squared differences, and divide by the number of values. The variance is $15,218,583. To get the standard deviation, you take the square root of the variance, which is approximately $3,900.09.

User Jaroslav Urban
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