Question

maria scored 72, 97, and 82 on her first three math tests. she wants to have a mean score of 82 for the quarter. how many points does she need on her last test to earn an 82 for the quarter?

Explanation:

Step1: Recall mean - score formula

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data - points and $\sum_{i = 1}^{n}x_{i}$ is the sum of the data - points. Here, $n = 4$ (three tests already taken and one more to go), and $\bar{x}=82$.

Step2: Calculate the sum of the first three scores

The scores on the first three tests are 72, 97, and 82. The sum of the first three scores $S_1=72 + 97+82=251$.

Step3: Calculate the total sum needed for four tests

Since $\bar{x}=82$ and $n = 4$, the total sum of the four scores $S$ needed is $S=\bar{x}\times n=82\times4 = 328$.

Step4: Find the score on the last test

Let the score on the last test be $x$. We know that $S=S_1 + x$. So, $x=S - S_1$. Substituting the values of $S$ and $S_1$, we get $x=328 - 251=77$.

Answer:

77