Question

28. The stem and leaf diagram shows the time in seconds that callers to a telephone-order center were on hold before their call was taken. 0 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 677 77778889 9 1 00 1 1 1 1 2 2 2 2 4 4 15 6 6 8 9 2 2 4 2 5 3 0 a. Find the quartiles b. Give the five-number summary of the data. c. Find the range and the IQR.

Answer 1

The data as provided by the stem diagram is listed below:

0	3	6	10
0	3	6	10
0	3	6	11
0	3	6	11
0	3	6	11
0	3	6	11
1	3	6	12
1	4	6	12
1	4	6	12
1	4	6	12
1	4	7	14
1	4	7	14
1	5	7	15
1	5	7	16
2	5	7	16
2	5	7	18
2	5	8	19
2	5	8	22
2	5	8	24
	5	9	25
	5	9	30

Basically you just the number on the left of the stem(the vertical line) and join that with the number to the right(the leaf) to get the data.

a)

Quartile Q1 = (n+1)/4 th observation = 3
Quartile Q2 = (n+1)/2 th observation =  6
Quartile Q3: 3*(n+1)/4 th observation = 10

b)

A five number summary consists of these five statistics: the minimum value, the first quartile, the median, the third quartile, and the maximum value of a set of numbers (data)

Minimum: 0
Quartile Q1: 3
Median: 6
Quartile Q3: 10
Maximum: 30

c)

Range = maximum value - minimum value = 30 - 0 = 30

IQR = Q3 - Q1 = 10 - 3 = 7