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Anne has the following data: $\newline$ $13, 16, z, 8, 11$ $\newline$ If the median is $13$ , which number could $z$ be? $\newline$ Choices: $\newline$ $(A)$ $9$ $\newline$ $(B)$ $14$

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

Full solution

Q. Anne has the following data:

\newline

13, 16, z, 8, 11

\newline

If the median is

13

, which number could

z

be?

\newline

Choices:

\newline

(A)

9

\newline

(B)

14

Understand median concept: Understand the concept of median. The median is the middle value in a list of numbers sorted in ascending order. Since there are $5$ numbers, the median will be the third number when sorted.
Sort and analyze numbers: Sort the given numbers, excluding $z$ , and analyze the possible positions for $z$ . The sorted numbers without $z$ are $8$ , $11$ , $13$ , $16$ . To have a median of $13$ , $z$ must be placed in such a way that $13$ remains the third number in the sorted list.
Determine possible values for $z$ : Determine the possible values for $z$ . If $z$ is less than $13$ but greater than $11$ , it will not affect the position of $13$ as the median. If $z$ is greater than $13$ but less than $16$ , $13$ will still be the median. Therefore, $z$ can be any number between $11$ and $16$ , excluding $13$ itself.
Check choices for $z$ : Check the given choices for $z$ . The choices are: $\newline$ (A) $9$ $\newline$ (B) $14$ $\newline$ Since $9$ would place $z$ before $11$ , making $11$ the third number, it cannot be the median. However, $14$ fits between $13$ and $z$ $0$ , keeping $13$ as the median.

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