Question

constructing a frequency distribution and a frequency polygon
here are the shopping times (in minutes) for each of sixteen shoppers at a local grocery store.
shopping times
(in minutes)
19 21 26 32 24 34 35 28
30 29 34 16 31 33 17 26
(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)
shopping times
(in minutes) frequency
15.5 to 19.5
19.5 to 23.5
23.5 to 27.5
27.5 to 31.5
31.5 to 35.5
(b) using the classes from part (a), draw the frequency polygon for the data. note that you can add or remove classes from the figure. label each class with its midpoint.

Explanation:

Step1: Count data in each class

For \(15.5 - 19.5\): Data values \(16,17,19\). Frequency \(= 3\).

Step2: Count data in \(19.5 - 23.5\)

Data values \(21,24\). Frequency \(= 2\).

Step3: Count data in \(23.5 - 27.5\)

Data values \(26,26,28\). Frequency \(= 3\).

Step4: Count data in \(27.5 - 31.5\)

Data values \(29,30,31\). Frequency \(= 3\).

Step5: Count data in \(31.5 - 35.5\)

Data values \(32,34,34,35\). Frequency \(= 4\).

Answer:

Shopping times (in minutes)	Frequency
\(19.5 - 23.5\)	\(2\)
\(23.5 - 27.5\)	\(3\)
\(27.5 - 31.5\)	\(3\)
\(31.5 - 35.5\)	\(4\)