To find the square of the mode from the given scores and their corresponding frequencies, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Data We have two sets of data: - **Scores**: 4, 7, 8, 11, 13, 8 - **Frequencies**: 3, 5, 2, 7, 2, 1 ### Step 2: Create a Frequency Table To better visualize the data, we can create a frequency table that pairs each score with its frequency: | Score | Frequency | |-------|-----------| | 4 | 3 | | 7 | 5 | | 8 | 2 | | 11 | 7 | | 13 | 2 | | 8 | 1 | ### Step 3: Calculate the Total Frequency Next, we need to calculate the total frequency to understand how many total observations we have: \[ \text{Total Frequency} = 3 + 5 + 2 + 7 + 2 + 1 = 20 \] ### Step 4: Identify the Mode The mode is the value that appears most frequently in a data set. To find the mode, we look at the frequencies: - Score 4 appears 3 times. - Score 7 appears 5 times. - Score 8 appears 2 times (but note that there are two entries for 8, so we need to consider the total frequency). - Score 11 appears 7 times. - Score 13 appears 2 times. From the frequency counts, we see that: - The highest frequency is 7, which corresponds to the score of 11. Thus, the mode of the data set is **11**. ### Step 5: Calculate the Square of the Mode Now that we have identified the mode, we need to find its square: \[ \text{Square of the Mode} = 11^2 = 121 \] ### Conclusion The correct answer is **B. 121**. ### Step 6: Why Other Options Are Incorrect Let’s analyze the other options: - **A. 49**: This is \(7^2\). The score 7 is not the mode; it has a lower frequency than 11. - **C. 25**: This is \(5^2\). There is no score of 5 in the data set, making this option irrelevant. - **D. 64**: This is \(8^2\). While 8 is present in the data set, it does not have the highest frequency (which is 7 for the score of 11). ### Revision Summary - The mode is the value that appears most frequently in a data set. - The mode of the given scores is 11, as it has the highest frequency of 7. - The square of the mode (11) is calculated as \(11^2 = 121\). - The correct answer is **B. 121**; other options do not represent the mode or are irrelevant.