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Hannah has the following data: $\newline$ $q, 4, 8, 8, 3$ $\newline$ If the median is $4$ , which number could $q$ be? $\newline$ Choices: $\newline$ (A) $8$ $\newline$ (B) $3$

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

Full solution

Q. Hannah has the following data:

\newline

q, 4, 8, 8, 3

\newline

If the median is

4

, which number could

q

be?

\newline

Choices:

\newline

(A)

8

\newline

(B)

3

Understand Median Definition: First, let's understand what a median is: it's the middle value of a data set when it's arranged in order. Since there are $5$ numbers in the data set, the median will be the third number when they are sorted.
Sort Numbers Excluding $q$ : Let's sort the numbers we know, excluding $q$ for now: $3, 4, 8, 8$ . If the median is $4$ , $q$ must be a number that, when added, still allows $4$ to be the middle number.
Determine Possible Values for $q$ : If $q$ is less than or equal to $4$ , the sorted list would look like this if $q = 3$ : $3, 3, 4, 8, 8$ . Here, $4$ is still the median. If $q = 8$ , the sorted list would be: $3, 4, 8, 8, 8$ , where $8$ becomes the median, which is incorrect.

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