Question

dwayne had a test average of 82.8 last semester. his first four test grades were 88, 77, 78, and 86. use the formula $overline{x}=\frac{x_1 + x_2+cdots+x_n}{n}$ to find his score on the fifth test.

Explanation:

Step1: Substitute known values into the formula

Let the fifth - test score be \(x_5\). We know that \(\bar{x}=82.8\), \(n = 5\), \(x_1 = 88\), \(x_2=77\), \(x_3 = 78\), \(x_4 = 86\).
The formula for the mean \(\bar{x}=\frac{x_1 + x_2+x_3+x_4+x_5}{n}\) becomes \(82.8=\frac{88 + 77+78+86+x_5}{5}\).

Step2: Solve the equation for \(x_5\)

First, multiply both sides of the equation by \(5\):
\(82.8\times5=(88 + 77+78+86+x_5)\).
Calculate \(82.8\times5 = 414\) and \(88 + 77+78+86=329\).
The equation is \(414=329+x_5\).
Then, subtract \(329\) from both sides: \(x_5=414 - 329\).

Answer:

\(85\)