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Nicole has the following data: $\newline$ $13, 10, s, 13, 13, 10$ $\newline$ If the mean is $12$ , which number could $s$ be? $\newline$ Choices: $\newline$ $(A)$ $13$ $\newline$ $(B)$ $31$

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

Full solution

Q. Nicole has the following data:

\newline

13, 10, s, 13, 13, 10

\newline

If the mean is

12

, which number could

s

be?

\newline

Choices:

\newline

(A)

13

\newline

(B)

31

Calculate sum and set equation: Step $1$ : Calculate the sum of the known numbers and set up the equation for the mean. $\newline$ Given numbers: $13, 10, s, 13, 13, 10$ . Mean = $12$ . $\newline$ Sum of known numbers = $13 + 10 + 13 + 13 + 10 = 59$ . $\newline$ Mean equation: $(59 + s) / 6 = 12$
Solve for s: Step $2$ : Solve for s. $\newline$ Multiply both sides by $6$ to eliminate the fraction: $\newline$ $(59 + s) = 12 \times 6$ $\newline$ $59 + s = 72$
Isolate $s$ : Step $3$ : Isolate $s$ . $s = 72 - 59$ $s = 13$

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