Question

current avg: 76 59 new test score: 82 82 new average ① ②

Explanation:

Step1: Calculate new average for the first case

The formula for average is $\frac{\text{Sum of values}}{\text{Number of values}}$. Initially, assume the number of tests for the first current average of 76 is \(n\). The sum of scores is \(76n\). After adding a new score of 82, the new sum is \(76n + 82\) and the new number of tests is \(n+1\). Let's assume \(n = 1\) (since the problem doesn't specify the number of previous tests, and for simplicity, when calculating the change in average, the relative change can be shown. Mathematically, \(\text{New Average}_1=\frac{76\times1 + 82}{1 + 1}=\frac{76+82}{2}=\frac{158}{2}=79\)

Step2: Calculate new average for the second case

For the second current average of 59, assume the number of tests is \(m\). The sum of scores is \(59m\). After adding a new score of 82, the new sum is \(59m+82\) and the new number of tests is \(m + 1\). Let's assume \(m=1\) (for the same simplicity reason as above). Then \(\text{New Average}_2=\frac{59\times1+82}{1 + 1}=\frac{59 + 82}{2}=\frac{141}{2}=70.5\)

Answer:

1. \(79\)
2. \(70.5\)