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Terrence has the following data: $\newline$ $10, 14, c, 10$ $\newline$ If the mean is $12$ , which number could $c$ be? $\newline$ Choices: $\newline$ $(A)$ $14$ $\newline$ $(B)$ $2$

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Mean, median, mode, and range: find the missing number

Full solution

Q. Terrence has the following data:

\newline

10, 14, c, 10

\newline

If the mean is

12

, which number could

c

be?

\newline

Choices:

\newline

(A)

14

\newline

(B)

2

Arrange data and include unknown: Arrange the given data and include the unknown $c$ : $10$ , $14$ , $c$ , $10$ .
Calculate mean of data set: Calculate the mean of the data set. The formula for the mean is $(\text{sum of all items}) / (\text{number of items})$ . Here, $(10 + 14 + c + 10) / 4 = 12$ .
Solve for unknown: Solve for $c$ : $(34 + c) / 4 = 12$ . Multiply both sides by $4$ to clear the fraction: $34 + c = 48$ .
Subtract to isolate unknown: Subtract $34$ from both sides to isolate $c$ : $c = 48 - 34$ .
Calculate unknown: Calculate $c$ : $c = 14$ .

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