Question

A Walgreens manager compared the numbers of hours different pharmaceutical technicians worked over one week. The table shows the number of hours worked per technician.
Hours per server: 20, 21, 14, 21, 21, 12, 18, 23, 20, 23, 12

Construct a dot plot to represent the data, and determine which of the following is correct.

A.Q1 is 13
B.Q3 is 21.5
C.The interquartile range is 9
D. The data has no outliers

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

The given data is

20, 21, 14, 21, 21, 12, 18, 23, 20, 23, 12

Arrange the data in ascending order.

12, 12, 14, 18, 20, 20, 21, 21, 21, 23, 23

Find the number that divides the data in two equal parts.

(12, 12, 14, 18, 20), 20,( 21, 21, 21, 23, 23)

Divide each parenthesis in two parts.

(12, 12), 14,( 18, 20), 20,( 21, 21), 21, (23, 23)

It means first quartile is 14, median is 20 and third quartile is 21.

$Q_1=14$

$Median=20$

$Q_3=21$

Therefore option A and B are incorrect.

The interquartile range is

$IQR=\text{Maximum value}-\text{Minimum value}$

$IQR=23-12=11$

The interquartile range is 9. Therefore option C is incorrect.

If the data lies outside the interval $[Q_1-1.5\times IQR,Q_3+1.5\times IQR]$, then it has outliers.

$[Q_1-1.5\times IQR,Q_3+1.5\times IQR]=[14-1.5\times 11,21+1.5\times 11]=[-2.5,37.5]$

All the data lie in the interval [-2.5,37.5], therefore data has no outliers and option D is correct.

Answer 2

It is D because all the numbers range from 12 to 23, with no number being extremely low or high compared this range.