Question

A random sample of 30 customers at the grand opening of a new clothing store gave the following information about the age of each customer.

(a) Construct a frequency distribution of this data using 5

Answer 1

To construct a frequency distribution of the age data for the 30 customers with 5 classes, the range of ages is determined, and then the class width is calculated using
`\(\text{Class Width} = \frac{{\text{Range of Ages}}}{{\text{Number of Classes}}}\)`. The frequency distribution divides the ages into 5 classes with corresponding frequencies for each class.

Step-by-step explanation:

To begin constructing the frequency distribution, first, determine the range of ages by finding the difference between the maximum and minimum ages among the 30 customers. Then, calculate the class width by dividing the range of ages by the number of desired classes, which in this case is 5. The class width is crucial as it determines the size of each age interval or class.

Next, organize the ages into intervals or classes based on the calculated class width. The lowest age value will serve as the starting point, and subsequent classes will increment by the class width until the maximum age value is reached. Count the number of occurrences of ages falling within each interval to determine the frequency for each class.

For instance, if the age range is 20 to 60, the class width would be
`\(\frac{{60 - 20}}{5} = 8\)`. The frequency distribution might be presented as follows: Class 1 (20-28) - Frequency, Class 2 (29-37) - Frequency, Class 3 (38-46) - Frequency, Class 4 (47-55) - Frequency, and Class 5 (56-64) - Frequency. This distribution provides a clear overview of the distribution of ages among the 30 customers, aiding in analyzing age demographics at the store's opening.