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Chapter 2: Q 20. (page 107)

Teacher raises A school system employs teachers at salaries between \(28,000 and \)60,000. The teachers鈥� union and the school board are negotiating the form of next year鈥檚 increase in the salary schedule.

(a) If every teacher is given a flat \(1000 raise, what will this do to the mean salary? To the median salary? Explain your answers.

(b) What would a flat\)1000 raise do to the extremes and quartiles of the salary distribution? To the standard deviation of teachers鈥� salaries? Explain your answers.

Short Answer

Expert verified

Part (a) The mean and median salaries will both rise by$1000

Part (b) The extremes and quartiles will each see a $1000boost. There will be no change in the standard deviation.

Step by step solution

01

Step 1. Given

It's a known that teachers in the school system earn between $28,000 and $60,000 The teachers' union and the school board are also working on the details of next year's pay raise.

02

Step 2. Concept

The formula used: z=x鈭�meanstandarddeviation

03

Step 3. Explanation

Teacher salaries range from $28,000 to $60,000 each year.

If every teacher receives a $1000 raise, the mean and median incomes will both rise by $1000 (the salary distribution will only shift by $1000).

04

Step 1. Explanation

The extremes and quartiles will each see a $1000 boost. There will be no change in the standard deviation. Nothing has transpired to change the distribution's variability. The Centre has moved, but the spread has remained the same.

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