Question

At one hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows.

23	2	5	14	25	36	27	42	12	8
7	23	29	26	28	11	20	31	8	36

Make a box-and-whisker plot of the data. (Select the correct graph.)

    

Find the interquartile range. (Enter an exact number.)
IQR =

Answer 1

Solution: Let us use table to calculate the required output.

Number	Data(in months)
1	2	Minimum value=2
2	5
3	7
4	8
5	8
		1st quartile=(8+11)/2=9.5
6	11
7	12
8	14
9	20
10	23
		Median=23
11	23
12	25
13	26
14	27
15	28
		3rd quartile=(28+29)/2=28.5
16	29
17	31
18	36
19	36
20	42	Maximum value=42

Step 1: Arrange the given data in ascending order.

2

5

7

8

8

11

12

14

20

23

23

25

26

27

28

29

31

36

36

42

Step 2: Find the median.

Median is the mean of the middle two numbers.

Median=(23+23)/2=23

Step 3: Find the first and third quartile.

The first quartile is the median of the data points to the left of the median(check in the first table)

1st quartile=(8+11)/2=9.5

The third quartile is the median of the data points to the right of the median(check in the first table)

3rd quartile=(28+29)/2=28.5

Step 4: Find minimum and maximum value

Minimum value=2

Maximum value=42

Step 5: Let us make the box plot for the above data set. I have drawn on the sheet of paper and the same is uploaded.

Step 6: IQR=Q3-Q1=28.5-9.5= 19