Question

20 24 26 35 18 34 32 27 24 33 37 29 24 36 31 (a) complete the grouped frequency - distribution for the data. (note that the class width is 5.) shopping times (in minutes) frequency 17.5 - 22.5 22.5 - 27.5 27.5 - 32.5 32.5 - 37.5 (b) construct a histogram for the data. frequency

Explanation:

Step1: Count data in 17.5 - 22.5

The data values in the range 17.5 - 22.5 are 20, 18. So the frequency is 2.

Step2: Count data in 22.5 - 27.5

The data values in the range 22.5 - 27.5 are 24, 26, 24, 27, 24. So the frequency is 5.

Step3: Count data in 27.5 - 32.5

The data values in the range 27.5 - 32.5 are 32, 29, 31. So the frequency is 3.

Step4: Count data in 32.5 - 37.5

The data values in the range 32.5 - 37.5 are 34, 33, 37, 36. So the frequency is 4.

Answer:

Shopping times (in minutes)	Frequency
22.5 - 27.5	5
27.5 - 32.5	3
32.5 - 37.5	4

To construct the histogram:

1. On the x - axis, label the shopping - time intervals (17.5 - 22.5, 22.5 - 27.5, 27.5 - 32.5, 32.5 - 37.5).
2. On the y - axis, label the frequency.
3. For the interval 17.5 - 22.5, draw a bar with height 2.
4. For the interval 22.5 - 27.5, draw a bar with height 5.
5. For the interval 27.5 - 32.5, draw a bar with height 3.
6. For the interval 32.5 - 37.5, draw a bar with height 4.