Question

"Construct a frequency distribution for the given data set, which represents the amount (in dollars) spent on books for a semester. Use 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies.

The data set is as follows: 428, 403, 186, 84, 303, 537, 185, 506, 246, 282, 385, 444, 471, 443, 453, 509, 160, 264, 50, 250, 210, 100, 313, 393, 218, 410, 377, 268, 358.

Which class in your frequency distribution has the greatest frequency?"

This question asks you to create a frequency distribution from the given data and identify the class with the highest frequency.

Answer 1

A frequency distribution is constructed by sorting the data, calculating range, dividing it to get class width, creating intervals, and then calculating frequencies, relative frequencies, and cumulative frequencies. The class with the highest frequency count is determined as having the greatest frequency.

Step-by-step explanation:

To construct a frequency distribution for the given set of book expenditures using 6 classes, you'll first sort the data and then determine the range. Divide the range by the number of classes to find the class width. Round up to the nearest whole dollar if necessary. Then, create equal-width intervals starting from just below the smallest value, calculate the midpoint for each class, count the number of expenditures in each class for frequency, and calculate relative and cumulative frequencies.

Here's an abbreviated outline of the process:

1. Sort the data in ascending order.
2. Find the range by subtracting the smallest value from the largest value.
3. Divide the range by 6 to get the class width, rounding up if necessary.
4. Create intervals starting from just below the smallest value, each with the class width determined in step 3.
5. Calculate the midpoint of each class, which is the average of the class limits.
6. Tally the frequencies for each class.
7. Determine relative frequencies by dividing the frequency of each class by the total number of data points.
8. Calculate cumulative frequencies by adding the frequency of a class to the sum of the frequencies of all preceding classes.

We can't complete this fully without actual calculations, but whichever class has the highest frequency count will be identified as having the "greatest frequency".