Question

A manufacturer of computers has lowered prices for her product. A sample of 16 stores selected randomly indicate the following sales (in units) during the past week:

0, 10, 2, 10, 3, 10, 3, 10, 6, 6, 8, 8, 4, 4, 5, 6

Find the median, Q1 and Q3.

median=6; Q1=4; Q3=10

median=6; Q1=3.5; Q3=9

median=6; Q1=3; Q3=10

median=6; Q1=3; Q3=8

Answer 1

If we order the values then we have the sample as:

0, 2, 3, 3, 4, 4, 5, 6, 6, 6, 8, 8, 10, 10, 10, 10.

Hence, the median is = $\frac{X_{(8)} + X_{(9)}}{2}$ = (6 + 6)/2 = 6.

[$X_{(i)}$ is that value below which (i -1) observations lie].

The first quartile = (3 + 4)/2 = 3.5.

The third quartile = (8 + 10)/2 = 9.

Thus, median = 6, Q1 = 3.5, Q3 = 9. (Ans).