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Kelly has the following data: $\newline$ $15, 14, 1, 9, h$ $\newline$ If the median is $14$ , which number could $h$ be? $\newline$ Choices: $\newline$ $(A)$ $10$ $\newline$ $(B)$ $15$

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

Full solution

Q. Kelly has the following data:

\newline

15, 14, 1, 9, h

\newline

If the median is

14

, which number could

h

be?

\newline

Choices:

\newline

(A)

10

\newline

(B)

15

Understand Median Definition: First, let's understand what median means. The median is the middle number in a sorted list of numbers. To find which number $h$ could be, we need to sort the numbers and see where $14$ fits as the median.
Sort Numbers Without $h$ : Sort the numbers without $h$ : $1$ , $9$ , $14$ , $15$ . Since $14$ is the median, it must be in the middle of the list. With $h$ added, the list should have $5$ numbers, making the third number the median.
Check $h = 10$ : If $h$ is $10$ , the sorted list would be $1, 9, 10, 14, 15$ . Here, $10$ would be the median, which is incorrect because the median should be $14$ .
Check $h = 15$ : If $h$ is $15$ , the sorted list would be $1, 9, 14, 15, 15$ . Here, $14$ is still the median, which matches the condition given in the problem.

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