Question

Angela is a supervisor at a department store. She developed this chart to check the dollar amount of sales made by various salespersons. $$ \begin{array}{|c|c|} \hline \text { Sales } & \text { \\# Salespersons } \\ \hline \$ 0-\$ 50 & 1 \\ \hline \$ 51-\$ 100 & 3 \\ \hline \$ 101-\$ 150 & 7 \\ \hline \$ 151-\$ 200 & 6 \\ \hline \$ 201-\$ 250 & 4 \\ \hline \end{array} $$ What is the modal class of this week's sales? A. $$0-\$ 50$$ B. $$\$ 51-\$ 100$$ C. $$\$ 101-\$ 150$$ D. $$\$ 151-\$ 200$$

Short answer

The modal class is \( \$101-\$150 \).

Step-by-step solution

- Understand the Definition

The modal class in a frequency distribution is the class interval that contains the highest frequency.

- Examine the Frequency Distribution

Review the given chart to identify the frequency (number of salespersons) for each sales range:

- Identify the Highest Frequency

Look for the highest number in the salespersons column. The frequencies are: 1, 3, 7, 6, and 4.

- Locate the Modal Class

The highest frequency is 7, which corresponds to the sales range of \( \$101-\$150 \). Therefore, this is the modal class.

Key concepts

modal class

To begin understanding the concept of the *modal class*, imagine you have a collection of data divided into different groups or intervals. The term 'modal class' refers to the interval in a frequency distribution that occurs most often. Let's say you have a table showing the number of salespersons in different sales ranges, just like Angela's chart. The modal class is simply the sales range with the most salespersons.

• For instance, if you see that 7 salespersons sold items in the \(101-\)150 range, which is the highest number compared to other ranges, this \(101-\)150 range is your modal class.
• It's important because it helps identify where the majority lies in the given data.

Always look for the class interval with the highest frequency to find the modal class.

highest frequency

When analyzing a *frequency distribution*, the 'highest frequency' is simply the biggest number in your frequency column. To find it, review each number of salespersons in the given sales ranges and identify the maximum.

• For example, Angela's chart includes frequencies like 1, 3, 7, 6, and 4.
• The highest number among these is 7.

This means 7 salespersons have made sales in a specific range, showing that this range is more frequent compared to others. Knowing the highest frequency helps you pinpoint the modal class swiftly because it identifies the range where most salespersons are active.

sales range

A *sales range* represents a particular interval in which sales amounts fall. These ranges help categorize large sets of data into smaller, manageable sections.

• For example, the sales ranges in Angela's data are \(0-\)50, \(51-\)100, \(101-\)150, \(151-\)200, and \(201-\)250.
• Each range shows the number of salespersons who made sales within those specific dollar amounts.

Using sales ranges helps support better analysis and clearer insights because you can easily see how sales are distributed and where sales activities are concentrated. By studying these ranges, you can make more informed decisions about inventory, staffing, and marketing efforts.

frequency chart

A *frequency chart* or table is a tool that helps organize data to show how often each item or range of items occurs. It lists each unique item or range, alongside a count of occurrences (frequency). In Angela's example, the frequency chart displays sales ranges on the left and the corresponding number of salespersons on the right.

• The ranges like \(0-\)50 and \(51-\)100 are the items.
• The numbers 1 and 3 next to these ranges are the frequencies.

Frequency charts are very useful in visualizing data distribution and can help identify patterns, such as the modal class, without having to go through raw data manually. They simplify the work of data analysis, making it easier to interpret numbers and make decisions based on the insights derived.