Chapter 2: Q 20. (page 107)

Teacher raises A school system employs teachers at salaries between $$28, 000$ and $$ 60, 000$ . The teachers’ union and the school board are negotiating the form of next year’s 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’ 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 $$ 1000$ boost. There will be no change in the standard deviation.

Step by step solution

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.

Step 2. Concept

The formula used: $z = \frac{x - m e a n}{s \tan d a r d d e v i a t i o n}$

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$ ).

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.