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Roger has the following data: $\newline$ $17, 20, j, 20, 18$ $\newline$ If the median is $18$ , which number could $j$ be? $\newline$ Choices: $\newline$ $(A)$ $20$ $\newline$ $(B)$ $13$

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

Full solution

Q. Roger has the following data:

\newline

17, 20, j, 20, 18

\newline

If the median is

18

, which number could

j

be?

\newline

Choices:

\newline

(A)

20

\newline

(B)

13

Understand Problem and Data: Step $1$ : Understand the problem and the given data. $\newline$ Roger has the numbers $17$ , $20$ , $j$ , $20$ , $18$ , and we need to find the value of $j$ that makes $18$ the median.
Analyze Choices for $j$ : Step $2$ : Analyze the choices for $j$ . Choices are (A) $20$ or (B) $13$ .
Order with $j = 20$ : Step $3$ : Determine the order of numbers if $j = 20$ . $\newline$ Ordering the numbers with $j$ as $20$ gives: $17, 18, 20, 20, 20$ . Here, the median (middle value) is $20$ .
Order with $j = 13$ : Step $4$ : Determine the order of numbers if $j = 13$ . $\newline$ Ordering the numbers with $j$ as $13$ gives: $13, 17, 18, 20, 20$ . Here, the median (middle value) is $18$ .

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