Question

set be equal 20. In a school system, teachers start at a salary of $25,200 and have a top salary of $51,800. The teachers' union is bargaining with the school district for next year's salary increment. a. If every teacher is given a $1000 raise, what happens to each of the following? i. Mean ii. Median iii. Extremes iv. Quartiles v. Standard deviation vi. IQR b. If every teacher received a 5% raise, what does this do to the following? i. Mean ii. Standard deviation​

Answer 1

a. If every teacher is given a $1000 raise:

i. The mean salary of the teachers will increase by $1000.

ii. The median salary will also increase by $1000.

iii. The extremes of the salary range will remain the same.

iv. The quartiles will shift up by $1000.

v. The standard deviation of the salaries will not be affected.

vi. The interquartile range (IQR) will remain the same.

b. If every teacher received a 5% raise:

i. The mean salary of the teachers will increase by 5% of the current mean salary.

ii. The standard deviation of the salaries will increase, since the relative difference between the salaries will become larger.

Note: To calculate the new mean salary, you can use the formula:

New mean salary = Old mean salary * (1 + percentage raise)

So, if the old mean salary is $38,500, and every teacher receives a 5% raise, the new mean salary would be:

New mean salary = $38,500 * (1 + 0.05) = $40,425

This means the mean salary of the teachers will increase by $1,925.

To calculate the new standard deviation, you can use the formula:

New standard deviation = Old standard deviation * square root(1 + percentage raise)

So, if the old standard deviation is $7,000, and every teacher receives a 5% raise, the new standard deviation would be:

New standard deviation = $7,000 * square root(1 + 0.05) = $7,266

This means the standard deviation of the salaries will increase by $266.