Identity Theft Identity fraud occurs when someone else’s personal information is used to open credit card accounts, apply for a job, receive benefits, and so on. The following relative frequency bar graph represents the various types of identity theft based on a study conducted by the Federal Trade Commission. If there were 10 million cases of identity fraud in a recent year, how many were credit card fraud (someone uses someone else’s credit card to make a purchase)?

Verified step by step guidance

1. Identify the relative frequency of credit card fraud from the bar graph. Observe the length of the bar corresponding to 'Credit card fraud' on the horizontal axis labeled 'Relative Frequency'.
2. Note that the relative frequency represents the proportion of total identity theft cases that are credit card fraud. From the graph, estimate this value (it appears to be approximately 0.26).
3. Understand that the total number of identity fraud cases is given as 10 million. To find the number of credit card fraud cases, multiply the total number of cases by the relative frequency of credit card fraud.
4. Set up the multiplication as: \(\text{Number of credit card fraud cases} = 10,000,000 \times \text{Relative Frequency of credit card fraud}\).
5. Perform the multiplication to find the number of credit card fraud cases (this step involves calculation, so you can compute it using the relative frequency you estimated).

Key Concepts

Relative Frequency

Relative frequency represents the proportion of times a specific event occurs compared to the total number of events. It is calculated by dividing the frequency of a particular category by the total number of observations. In this question, relative frequency helps determine the fraction of identity theft cases that are credit card fraud.

Bar Graph Interpretation

A bar graph visually displays data using bars to represent the frequency or relative frequency of categories. The length of each bar corresponds to the value it represents. Understanding how to read the bar lengths and their corresponding labels is essential to extract accurate data from the graph.

Applying Relative Frequency to Total Counts

To find the actual number of cases from relative frequency, multiply the relative frequency by the total number of cases. This converts the proportion into a concrete count, allowing practical interpretation of the data, such as estimating how many identity theft cases involved credit card fraud.