Question

1. samira’s mean quiz grade was 92. four of her grades were 80, 98, 87 and 99. what was her fifth quiz grade? tip! plug it in, plug it in and calculate mean 4 times! a. 76 b. 92 c. 96 d. 89

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 5$ and $\bar{x}=92$. Let the fifth - grade be $x$. Then $92=\frac{80 + 98+87 + 99+x}{5}$.

Step2: Cross - multiply

Multiply both sides of the equation by 5: $92\times5=80 + 98+87 + 99+x$.
$460=80 + 98+87 + 99+x$.

Step3: Calculate the sum of known grades

$80+98 + 87+99=364$.
So the equation becomes $460=364+x$.

Step4: Solve for $x$

Subtract 364 from both sides: $x=460 - 364=96$.

Answer:

C. 96