Question

here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times (in minutes)
22 19 24 34 27
25 28 18 23 28
21 26 33 37 28
send data to calculator
(a) complete the grouped frequency distribution for the data. (note that the class - width is 5.)
17.5 to 22.5 0
22.5 to 27.5 0
27.5 to 32.5 0
32.5 to 37.5 0
(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 mid - point.
frequency
shopping times (in minutes)

Explanation:

Step1: Count data in each class

For the class 17.5 - 22.5, the data values 19, 18, 21, 22 fall in this range. Count them: 4.
For the class 22.5 - 27.5, the data values 24, 25, 23, 26, 27 fall in this range. Count them: 5.
For the class 27.5 - 32.5, the data values 28, 28, 28 fall in this range. Count them: 3.
For the class 32.5 - 37.5, the data values 34, 33, 37 fall in this range. Count them: 3.

Step2: Calculate mid - points

Mid - point of 17.5 - 22.5 is $\frac{17.5 + 22.5}{2}=20$.
Mid - point of 22.5 - 27.5 is $\frac{22.5+27.5}{2}=25$.
Mid - point of 27.5 - 32.5 is $\frac{27.5 + 32.5}{2}=30$.
Mid - point of 32.5 - 37.5 is $\frac{32.5+37.5}{2}=35$.

Step3: Draw frequency polygon

Plot points with x - coordinates as mid - points (20, 25, 30, 35) and y - coordinates as frequencies (4, 5, 3, 3) and connect them with line segments.

Answer:

(a)

Class Interval	Frequency
22.5 - 27.5	5
27.5 - 32.5	3
32.5 - 37.5	3

(b) Frequency polygon is drawn with points (20, 4), (25, 5), (30, 3), (35, 3) connected by line segments.