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Michelle has the following data: $\newline$ $10, 9, 8, b$ $\newline$ If the range is $7$ , which number could $b$ be? $\newline$ Choices: $\newline$ $(A)$ $12$ $\newline$ $(B)$ $3$

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

Full solution

Q. Michelle has the following data:

\newline

10, 9, 8, b

\newline

If the range is

7

, which number could

b

be?

\newline

Choices:

\newline

(A)

12

\newline

(B)

3

Understand the problem: Step $1$ : Understand the problem and identify the range calculation. $\newline$ We know the range of a set of numbers is the difference between the maximum and minimum values. We're given the numbers $10$ , $9$ , $8$ , and $b$ , and the range is $7$ .
Calculate possible values: Step $2$ : Calculate the possible values for $b$ using the range. $\newline$ The range is the difference between the maximum and minimum values in the dataset. Since the range is $7$ , we have two scenarios: $\newline$ $1$ . If $b$ is the maximum value, then $b - 8 = 7$ (since $8$ is the smallest of the other numbers). $\newline$ $2$ . If $b$ is the minimum value, then $10 - b = 7$ (since $10$ is the largest of the other numbers).
Solve equations: Step $3$ : Solve the equations from Step $2$ . $\newline$ $1$ . $b - 8 = 7$ leads to $b = 15$ . $\newline$ $2$ . $10 - b = 7$ leads to $b = 3$ .
Check value of $b$ : Step $4$ : Check which value of $b$ is among the choices given. $\newline$ From the calculations, $b$ could be $3$ or $15$ . However, only $3$ is listed in the choices provided (A) $12$ and (B) $3$ .

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