Question

asa received scores of 72, 97, and 82 on her last three math tests. she needs a mean test score of 82 to qualify for the math team. what is the first step in determining how many points she needs on her next test to qualify for the team?
find the sum of all the numbers in the problem, 72+97+82+82.
find the average score for the three tests that asa has taken.
determine the total number of points that she needs on the last test.
determine how many total points are needed to have an average of 82.

Explanation:

Step1: Recall the formula for the mean

The formula for the mean (average) of \(n\) numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{x_1 + x_2+\cdots+x_n}{n}\). Here, \(n = 4\) (three past tests + one future test), and \(\bar{x}=82\). We can rewrite the formula as \(x_1 + x_2+x_3+x_4=n\times\bar{x}\). The first step is to find the total number of points needed for an average of 82. Using the formula \(n\times\bar{x}\), with \(n = 4\) and \(\bar{x}=82\), we calculate \(4\times82\).

Answer:

Determine how many total points are needed to have an average of 82.