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Nathan has the following data: $\newline$ $14, 8, 8, j, 4$ $\newline$ If the mean is $8$ , which number could $j$ be? $\newline$ Choices: $\newline$ $(A)$ $6$ $\newline$ $(B)$ $16$

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

Full solution

Q. Nathan has the following data:

\newline

14, 8, 8, j, 4

\newline

If the mean is

8

, which number could

j

be?

\newline

Choices:

\newline

(A)

6

\newline

(B)

16

Calculate Mean Formula: Calculate the sum of the numbers given the mean formula. $\newline$ Mean = $\frac{\text{sum of all numbers}}{\text{total count of numbers}}$ $\newline$ $8 = \frac{14 + 8 + 8 + j + 4}{5}$
Find Total Sum: Multiply both sides by $5$ to find the total sum. $8 \times 5 = (14 + 8 + 8 + j + 4)$ $40 = 34 + j$
Solve for $j$ : Solve for $j$ . $40 = 34 + j$ $j = 40 - 34$ $j = 6$

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