Question

here are the shopping times (in minutes) for each of sixteen shoppers at a local grocery store.
shopping times (in minutes)
31 20 32 34 16 24 35 29
20 33 21 23 30 33 25 26
(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)
shopping times (in minutes) frequency
16 to 19
20 to 23
24 to 27
28 to 31
32 to 35
(b) construct a histogram for the data.
frequency
6
5
4
3
2
1
0
16 to 19 20 to 23 24 to 27 28 to 31 32 to 35 shopping times (in minutes)

Explanation:

Step1: Count data in 16 - 19

The data values in the range 16 - 19 are 16. So the frequency is 1.

Step2: Count data in 20 - 23

The data values in the range 20 - 23 are 20, 20, 21, 23. So the frequency is 4.

Step3: Count data in 24 - 27

The data values in the range 24 - 27 are 24, 25, 26. So the frequency is 3.

Step4: Count data in 28 - 31

The data values in the range 28 - 31 are 29, 30, 31. So the frequency is 3.

Step5: Count data in 32 - 35

The data values in the range 32 - 35 are 32, 33, 33, 34, 35. So the frequency is 5.

Answer:

Shopping times (in minutes)	Frequency
20 to 23	4
24 to 27	3
28 to 31	3
32 to 35	5

For part (b), to construct the histogram:

• For the interval 16 - 19, draw a bar with height 1.
• For the interval 20 - 23, draw a bar with height 4.
• For the interval 24 - 27, draw a bar with height 3.
• For the interval 28 - 31, draw a bar with height 3.
• For the interval 32 - 35, draw a bar with height 5.

The x - axis represents the shopping - time intervals and the y - axis represents the frequency.