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Chloe has the following data: $\newline$ $15, b, 8, 8, 19, 15$ $\newline$ If the mean is $14$ , which number could $b$ be? $\newline$ Choices: $\newline$ $(A)$ $7$ $\newline$ $(B)$ $19$

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

Full solution

Q. Chloe has the following data:

\newline

15, b, 8, 8, 19, 15

\newline

If the mean is

14

, which number could

b

be?

\newline

Choices:

\newline

(A)

7

\newline

(B)

19

Calculate Sum Excluding $b$ : Calculate the sum of the given numbers excluding $b$ and the total number of numbers. $\newline$ Sum excluding $b$ = $15 + 8 + 8 + 19 + 15 = 65$ . $\newline$ Total numbers = $6$ .
Find Total Sum for Mean: Use the mean formula to find the total sum needed for a mean of $14$ . $\newline$ Mean = Total sum / Number of numbers $\newline$ $14 = \frac{\text{Total sum}}{6}$ $\newline$ Total sum = $14 \times 6 = 84$ .
Subtract to Find $b$ : Subtract the sum excluding $b$ from the total sum to find $b$ . $b =$ Total sum $-$ Sum excluding $b$ $b = 84 - 65 = 19$ .

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