Question

in late august of last year, pie dee restaurant sponsored its first pizza - eating contest. for the contest, the number of slices of cheese pizza eaten by each contestant were counted. the histogram below summarizes the data. use the histogram to answer each of the questions. (a) what is the class width? (b) how many contestants ate 20 or fewer pizza slices? (c) how many contestants ate from 21 to 25 pizza slices?

Explanation:

Step1: Find class - width

The class intervals are 6 - 10, 11 - 15, 16 - 20, 21 - 25. The class - width is calculated as the difference between the upper and lower limits of a class. For example, for the class 6 - 10, the class - width is \(10 - 6=5\).

Step2: Find number of contestants who ate 20 or fewer slices

We need to sum the frequencies of the classes 6 - 10, 11 - 15, and 16 - 20. Let's assume the frequencies of the classes 6 - 10, 11 - 15, and 16 - 20 are \(f_1\), \(f_2\), and \(f_3\) respectively. The number of contestants who ate 20 or fewer slices is \(f_1 + f_2 + f_3\).

Step3: Find number of contestants who ate from 21 to 25 slices

The number of contestants who ate from 21 to 25 slices is the frequency of the class 21 - 25. Let's assume this frequency is \(f_4\).

Answer:

(a) The class - width is 5.
(b) Sum the frequencies of the 6 - 10, 11 - 15, and 16 - 20 classes to get the number of contestants who ate 20 or fewer slices.
(c) The frequency of the 21 - 25 class gives the number of contestants who ate from 21 to 25 slices.