Question

(a) complete the grouped frequency distribution for the data. (note that the class width is 5.)
shopping times (in minutes) frequency
18 to 22 1
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: Assume we have the raw data set of shopping - times. Count the number of data points falling into each class interval.

Suppose we have counted and found the frequencies for each interval. Let's assume the frequencies for 23 - 27, 28 - 32, 33 - 37 are \(f_1\), \(f_2\), \(f_3\) respectively after counting from the raw data.

Step2: To construct the histogram:

On the x - axis, we have the class intervals (18 - 22, 23 - 27, 28 - 32, 33 - 37) and on the y - axis, we have the frequency. For each class interval, we draw a bar with height equal to the frequency of that interval. The bars are adjacent to each other since the class intervals are continuous.

Answer:

(a) Without the raw data, we cannot give specific numerical values for the frequencies in the 23 - 27, 28 - 32, 33 - 37 intervals. But the grouped - frequency distribution table has columns for "Shopping times (in minutes)" and "Frequency" with rows for 18 - 22, 23 - 27, 28 - 32, 33 - 37.
(b) A histogram with x - axis labeled "Shopping times (in minutes)" with intervals 18 - 22, 23 - 27, 28 - 32, 33 - 37 and y - axis labeled "Frequency". Bars are drawn with heights corresponding to the frequencies of each interval.