Question

here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times
(in minutes)
20 27 25 26 28
18 20 23 37 34
20 33 36 32 22
(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.

Explanation:

Step1: Count the number of data points in each class

• For the class \(18 - 22\): The data points are \(18,20,20,20,22\). So the frequency is \(5\).
• For the class \(23 - 27\): The data points are \(23,25,26,27\). So the frequency is \(4\).
• For the class \(28 - 32\): The data points are \(28,32\). So the frequency is \(2\).
• For the class \(33 - 37\): The data points are \(33,34,36,37\). So the frequency is \(4\).

Answer:

Shopping times (in minutes)	Frequency
\(23 - 27\)	\(4\)
\(28 - 32\)	\(2\)
\(33 - 37\)	\(4\)

For the histogram:

• The bar for the class \(18 - 22\) has a height of \(5\).
• The bar for the class \(23 - 27\) has a height of \(4\).
• The bar for the class \(28 - 32\) has a height of \(2\).
• The bar for the class \(33 - 37\) has a height of \(4\).