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 employee's salary is increased by $3000). The interquartile range of the salaries will ____

Answer 1

Answer:

21,500

Step-by-step explanation:

Given data ( in thousand ) in this year,

28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77,

If each data is increased by $ 3000 in the next year,

So, the data for the next year,

31 34 37 38 40 44 45 45 45 50 52 54 55 55 63 64 70 75 78 80,

Since, the data is already arranged in the ascending order,

The median is 51 which is between 50 and 52,

Thus, the lower half of the Data is, 31 34 37 38 40 44 45 45 45 50,

Having median $Q_1=\frac{40+44}{2}$ = $\frac{84}{2}$ = 42,

Upper half of the data is 52 54 55 55 63 64 70 75 78 80,

Having median $Q_3=\frac{63+64}{2}=\frac{127}{2}$ = 63.5

Hence, the interquartile range = $Q_3-Q_1$

= 63.5 - 42

= 21.5

That is, the Interquartile range would be 21, 500.