Question

Cookies Using the same frequency distribution from Exercise 1, identify the class boundaries of the first class and identify the class limits of the first class.

Chocolate Chips	Frequency
18-20	6
21-23	11
24-26	18
27-29	4
30-31	1

Short answer

The class limits of the first class are 18 and 20.

The class boundaries of the first class are 17.5 and 20.5.

Step-by-step solution

Given information

A frequency distribution is known for the frequencies of chocolate chips found in a cookie.

Chocolate chips	Frequency
18-20	6
21-23	11
24-26	18
27-29	4
30-32	1

Class boundaries and class limits

For a discontinuous frequency distribution, the minimum value included in the interval is the lower class limit, and the maximum value included in the interval is the upper-class limit.

The class boundaries are the central values that create a gap between each successive class interval.

Identify the class limits

The first class interval is equal to 18-20.

The minimum value included in this interval is equal to 18.

Therefore, the lower class limit is equal to 18.

The maximum value included in this interval is equal to 21.

Therefore, the upper-class limit is equal to 21.

Compute the class boundaries

The gap between the first two class intervals is equal to:

$21-20=1$

The middle value is calculated as shown below:

$$\begin{gathered} \frac{Gap}{2}=\frac{1}{2} \\ =0.5 \end{gathered}$$

Subtracting a value equal to 0.5 from the lower class limit of the first class will result in the lower class boundary of the first class interval.

$18-0.5=17.5$

Therefore, the value of the lower class boundary is equal to 17.5.

Adding a value equal to 0.5 to the upper class limit of the first class will result in the upper class boundary of the first class interval.

$20+0.5=20.5$

Therefore, the value of the upper class boundary is equal to 20.5.