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Jasper has the following data: $\newline$ $7, 8, 7, r, 9$ $\newline$ If the median is $8$ , which number could $r$ be? $\newline$ Choices: $\newline$ $(A)$ $3$ $\newline$ $(B)$ $9$

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

Full solution

Q. Jasper has the following data:

\newline

7, 8, 7, r, 9

\newline

If the median is

8

, which number could

r

be?

\newline

Choices:

\newline

(A)

3

\newline

(B)

9

Understand the problem: Step $1$ : Understand the problem and the data given. $\newline$ Jasper has the numbers $7$ , $8$ , $7$ , $r$ , $9$ and we know the median is $8$ . The median is the middle value when all numbers are arranged in order.
Arrange numbers without r: Step $2$ : Arrange the numbers in order without $r$ . The numbers without $r$ , sorted, are $7, 7, 8, 9$ . Since the median is $8$ , $r$ must be placed in such a way that $8$ remains the median.
Determine possible positions: Step $3$ : Determine possible positions for $r$ . If $r$ is less than $8$ , the sequence could be $7, 7, r, 8, 9$ . If $r$ is greater than $8$ , the sequence could be $7, 7, 8, 9, r$ . Since $8$ needs to be the third number to be the median, $r$ must be either less than $7$ or greater than $r$ $0$ .

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