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Joy has the following data: $\newline$ $9, m, 19, 4, 3$ $\newline$ If the median is $9$ , which number could $m$ be? $\newline$ Choices: $\newline$ (A) $1$ $\newline$ (B) $20$

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

Full solution

Q. Joy has the following data:

\newline

9, m, 19, 4, 3

\newline

If the median is

9

, which number could

m

be?

\newline

Choices:

\newline

(A)

1

\newline

(B)

20

Understand Problem and Data: Step $1$ : Understand the problem and the data given. $\newline$ We have the numbers: $9$ , $m$ , $19$ , $4$ , $3$ and the median is $9$ . We need to find the possible value of $m$ from the choices given.
Arrange Numbers in Order: Step $2$ : Arrange the numbers in ascending order to find the median. Since the median is $9$ , and there are $5$ numbers, $9$ must be the third number in the sorted list. The list sorted without $m$ known yet is $3, 4, 9, 19$ , with $m$ needing to fit in such a way that $9$ remains the median.
Determine Placement of $m$ : Step $3$ : Determine where $m$ can fit in the list. $\newline$ If $m$ is less than $9$ , it must be either less than or equal to $4$ to keep $9$ as the median. If $m$ is greater than $9$ , it must be greater than or equal to $19$ to maintain the order.
Check Given Choices: Step $4$ : Check the given choices for $m$ . $\newline$ Choice (A) $1$ : Placing $m = 1$ , the order is $1, 3, 4, 9, 19$ . Median is still $9$ . $\newline$ Choice (B) $20$ : Placing $m = 20$ , the order is $3, 4, 9, 19, 20$ . Median is still $9$ . $\newline$ Both choices keep $9$ as the median.

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