Question

here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times (in minutes)
32 18 29 27 37
35 35 23 28 35
33 19 22 20 24
(a) complete the grouped frequency distribution for the data. (note that the class width is 5.)
shopping times (in minutes) frequency
18 to 22
23 to 27
28 to 32
33 to 37
(b) construct a histogram for the data.
frequency
6
5
4
3
2
1
0
18 to 22 23 to 27 28 to 32 33 to 37
shopping times (in minutes)

Explanation:

Step1: Count data in 18 - 22

Count numbers in the range 18 - 22 from the data set {32, 18, 29, 27, 37, 35, 35, 23, 28, 35, 33, 19, 22, 20, 24}. The numbers are 18, 19, 22, 20, so the frequency is 4.

Step2: Count data in 23 - 27

Count numbers in the range 23 - 27. The numbers are 23, 27, 24, so the frequency is 3.

Step3: Count data in 28 - 32

Count numbers in the range 28 - 32. The numbers are 29, 28, 32, so the frequency is 3.

Step4: Count data in 33 - 37

Count numbers in the range 33 - 37. The numbers are 37, 35, 35, 35, 33, so the frequency is 5.

Answer:

Shopping times (in minutes)	Frequency
23 to 27	3
28 to 32	3
33 to 37	5

For part (b), to construct the histogram:

• On the x - axis, label the intervals 18 to 22, 23 to 27, 28 to 32, 33 to 37.
• On the y - axis, label the frequency from 0 to 6.
• Draw a bar for each interval with height corresponding to the frequency:
• For the interval 18 to 22, the bar height is 4.
• For the interval 23 to 27, the bar height is 3.
• For the interval 28 to 32, the bar height is 3.
• For the interval 33 to 37, the bar height is 5.