Question

b. the yearlong grade of three students for four different years is shown in the given graph. based on the graph, which of the following is a true statement? the average year long grade of the three students in 2025 was 56. the average year long grade of the three students in 2024 was greater than the average year long grade in 2023. the average year long grade of the three students in 2023 was 50. the average year long grade of the three students in 2027 was 69

Explanation:

Step1: Calculate average for 2022

Let's assume Fred's grade \(F_{2022} = 40\), Sally's grade \(S_{2022}=39\), Max's grade \(M_{2022} = 69\). The average \(A_{2022}=\frac{40 + 39+69}{3}=\frac{148}{3}\approx49.33\)

Step2: Calculate average for 2023

Let's assume Fred's grade \(F_{2023} = 20\), Sally's grade \(S_{2023}=59\), Max's grade \(M_{2023} = 39\). The average \(A_{2023}=\frac{20 + 59+39}{3}=\frac{118}{3}\approx39.33\)

Step3: Calculate average for 2024

Let's assume Fred's grade \(F_{2024} = 30\), Sally's grade \(S_{2024}=49\), Max's grade \(M_{2024} = 39\). The average \(A_{2024}=\frac{30 + 49+39}{3}=\frac{118}{3}\approx46\)

Step4: Calculate average for 2025

Let's assume Fred's grade \(F_{2025} = 49\), Sally's grade \(S_{2025}=59\), Max's grade \(M_{2025} = 69\). The average \(A_{2025}=\frac{49 + 59+69}{3}=\frac{177}{3}=59\)

Now, check the second option:
The average of 2024 (\(\approx46\)) and 2023 (\(\approx39.33\)). Since \(46>39.33\)

Answer:

The average year - long grade of the three students in 2024 was greater than the average year - long grade in 2023.