Question

if the mean of five values is 9.6 and four of the values are 14, 9, 6, and 12, find the fifth value.
the fifth value is \boxed{}.

Explanation:

Step1: Recall the mean formula

The formula for the mean $\bar{x}$ of a set of $n$ numbers $x_1, x_2, \dots, x_n$ is $\bar{x}=\frac{x_1 + x_2+\dots+x_n}{n}$. Here, $n = 5$, $\bar{x}=9.6$, and four of the numbers are $14, 9, 6, 12$. Let the fifth number be $x$.

Step2: Substitute into the mean formula

Substitute the known values into the formula: $9.6=\frac{14 + 9+6 + 12+x}{5}$.

Step3: Multiply both sides by 5

Multiply both sides of the equation by 5 to get rid of the denominator: $9.6\times5=14 + 9+6 + 12+x$. Calculate the left - hand side: $9.6\times5 = 48$. Calculate the sum of the known numbers on the right - hand side: $14+9 + 6+12=41$. So the equation becomes $48=41 + x$.

Step4: Solve for x

Subtract 41 from both sides of the equation: $x=48 - 41=7$.

Answer:

7