12.36 Raising pay. A school system employs teachers at salaries between $40,000 and $70,000. The teachers’ union and the school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a flat $3000 raise.
(a) How much will the mean salary increase? The median salary?
(b) Will a flat $3000 raise increase the variability as measured by the distance between the quartiles? Explain.
(c) Will a flat $3000 raise increase the variability as measured by the standard deviation of the salaries? Explain.