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 median amount of sales? A. $$\$ 51-\$ 100$$ B. $$\$ 101-\$ 150$$ C. $$\$ 151-\$ 200$$ D. $$\$ 201-\$ 250$$

Short answer

B. \$ 101-\$ 150$$

Step-by-step solution

List all sales without ranges

Convert the ranges into individual sales records. The chart shows how many salespersons fell into each range, which means the number of occurrences for each sale range must be expanded individually. List the sales first without considering the specific range, just to count the total number of salespersons.

Organize the list in ascending order

Sort the list of all sales occurrences in ascending order. This helps to identify the middle value easily when finding the median.

Calculate the total number of salespersons

Sum up the total number of salespersons to determine if the count is even or odd. This will help determine how to find the median. The total number is 1 + 3 + 7 + 6 + 4 = 21.

Determine the position of the median

Since the total number of salespersons is 21, which is odd, the median value will be at position (21 + 1) / 2, which is the 11th value in the ordered list.

Identify the median range

Locate the 11th value in the sorted list. This value falls into the range of $$\$ 101-\$ 150$$ as there are 7 people in this range which starts from the 5th to the 11th value. Hence, the 11th value is within this range.

Key concepts

headline of the respective core concept

Interpreting data from a chart can be useful in various scenarios, including business and academics. Angela's chart shows different ranges of sales figures and the number of salespersons achieving these figures.
To make sense of the data, you need to understand the specific details provided, such as the exact number of salespersons performing within each sales range. The value of this approach is ensuring you're interpreting all the information correctly. When you do this accurately, you can determine statistics like totals, averages, and medians that offer greater insight into performance.

headline of the respective core concept

Median calculation involves finding the middle value in a sorted list. For Angela's chart, each sales range needs to be broken down into individual data points.
Here's how you can do it step-by-step:
1. Convert the ranges into individual sales records, expanding each range by the number of salespersons falling into it.
2. For example, if 7 salespersons fell within the \(101-\)150 range, you would list this range seven times.
3. List all sales values, sort them in ascending order, then find the middle value. In total, if there are 21 salespersons, the median will be the 11th value in this ordered list. Given Angela’s data, the 11th value falls in the \(101-\)150 range.

headline of the respective core concept

A frequency distribution organizes data to show the number of times each value or range of values occurs.
In Angela's chart, sales values are matched with the number of salespersons achieving them. This helps convey key information quickly and clearly. For example:

• 1 salesperson achieved \(0-\)50 sales
• 3 achieved \(51-\)100
• 7 achieved \(101-\)150
• 6 achieved \(151-\)200
• 4 achieved \(201-\)250

This type of visualization makes it easy to identify where most sales are clustered.

headline of the respective core concept

The GED math section often requires understanding how to read diagrams and charts, especially when calculating medians or interpreting data.
For your GED, you will need to identify the middle value of a data set after organizing it in a particular order. This involves steps like counting total items, determining if the count is even or odd, sorting data, and picking the median. Summing up frequency distributions and listing out individual data points specifically for finding medians are essential skills. Practice similar problems, as they enhance your confidence and ability to tackle various exam questions.