Question

Teacher raises A school system employs teachers at salaries between $\backslash (38,000$ and Page Number: $107\backslash )70,000$ The teachers’ union and school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a $\$1000$ raise. What effect will these raises have on each of the following characteristics of the resulting distribution of salary?

a. Shape

b. Mean and median

c. Standard deviation and interquartile range (IQR)

Short answer

Part (a) No change.

Part (b) Mean = It will be increased by$3$

Median = No effect

Part (c) No change in standard deviation.

No change in the interquartile range.

Step-by-step solution

Part (a) Step 1: Given information

Teachers in a school system can earn anywhere from $\$38,000$ to $\$70,000$ per year. The teachers' union and the school board are currently negotiating the structure of next year's compensation rise. Assume that each teacher receives a $\$1,000$ raise.

Part (a) Step 2: Explanation

Changes to each teacher's salary are being made here, with each teacher's salary being increased by $\$1000$ Changes in salary indicate a change in origin, but the change in origin has no effect on the form of the distribution.

Part (b) Step 1: Explanation

Changes are being made to each teacher's salary, with each teacher's income being increased by $\$1000$ Changes in the salaries of all teachers indicate a change in origin, and a change in origin indicates an increase or decrease in the mean by the same amount, thus the mean will increase by $\$1000$, but there will be no influence on the data's median, so the median will remain the middle term.

Part (c) Step 1: Explanation

Changes are being made to each teacher's salary, with each teacher's income being increased by $\$1000$ Changes in the salaries of all instructors indicate a change in origin, and when there is a change in origin, the measures of dispersion such as standard and interquartile range have no influence.