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Jon has the following data: $\newline$ $18, 8, n, 8$ $\newline$ If the mean is $13$ , which number could $n$ be? $\newline$ Choices: $\newline$ $(A)$ $30$ $\newline$ $(B)$ $18$

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

Full solution

Q. Jon has the following data:

\newline

18, 8, n, 8

\newline

If the mean is

13

, which number could

n

be?

\newline

Choices:

\newline

(A)

30

\newline

(B)

18

Calculate Mean Sum: Calculate the sum of the numbers given the mean. $\newline$ Mean formula: $\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}}$ $\newline$ Given mean = $13$ , Number of numbers = $4$ $\newline$ Sum = $\text{Mean} \times \text{Number of numbers} = 13 \times 4 = 52$
Sum Known Numbers: Sum up the known numbers and set up the equation to find $n$ . $\newline$ Known numbers: $18$ , $8$ , $8$ $\newline$ Sum of known numbers = $18 + 8 + 8 = 34$
Solve for n: Solve for n using the total sum from Step $1$ . $\newline$ Total sum = $52$ (from Step $1$ ) $\newline$ Sum of known numbers = $34$ (from Step $2$ ) $\newline$ Equation: $34 + n = 52$ $\newline$ Solve for n: $n = 52 - 34 = 18$

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