Q 20. Teacher raises A school system e... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

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 $$ 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: $z = \frac{x 鈭� m e a n}{s \tan d a r d d e v i a t i o n}$

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.