Question

elsa has scored 80, 66, 86, 84, and 79 on her previous five tests. what score does she need on her next test so that her average (mean) is 78?

Explanation:

Step1: Recall the mean formula

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, $n = 6$ (5 previous tests + 1 next test), and $\bar{x}=78$.

Step2: Calculate the sum of the first five scores

The sum of the first five scores $S_5=80 + 66+86 + 84+79=395$.

Step3: Let the score on the sixth test be $x$.

The sum of all six scores $S_6=S_5 + x=395 + x$.

Step4: Use the mean formula to solve for $x$.

Since $\bar{x}=\frac{S_6}{6}$ and $\bar{x}=78$, we have $78=\frac{395 + x}{6}$. Cross - multiply: $78\times6=395 + x$. So, $468=395 + x$.

Step5: Solve for $x$.

Subtract 395 from both sides: $x=468 - 395=73$.

Answer:

73