Question

A sample was taken of the salaries of 20 employees from a large company. The following are the salaries (in thousands of dollars) for this year (the data are ordered): 28, 31, 34, 35, 37, 41, 42, 42, 42, 47, 49, 51, 52, 52, 60, 61, 67, 72, 75, 77. Suppose each employee in the company receives a $3000 raise for next year (each employees salary is increased by $3000). The interquartile range of the salaries will

A) increase by $3000. B) be multiplied by $3000. C) be unchanged.

Answer 1

From the given information

X=salary of employee in the large company.

Interquartile range = Q3 - Q1

Q3= third quartile

Q1= first quartile

Each employee in the company receives $3000 raise in the next year.

Now the new salary is

Y=x+3000

Q1*=Q1+3000

Q3*=Q3+3000

Interquartile range=(Q3*-Q1*)

=(Q3+3000)-(Q1+3000)

=Q3-Q1

Hence Interquartile range of the salaries remains unchanged.