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Jayla has the following data: $\newline$ $1, 1, 8, 2, n$ $\newline$ If the median is $2$ , which number could $n$ be? $\newline$ Choices: $\newline$ $(A)$ $20$ $\newline$ $(B)$ $1$

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

Full solution

Q. Jayla has the following data:

\newline

1, 1, 8, 2, n

\newline

If the median is

2

, which number could

n

be?

\newline

Choices:

\newline

(A)

20

\newline

(B)

1

Arrange Data in Order: Arrange the data set in ascending order including $n$ . Since the median is $2$ , $n$ must be positioned in a way that does not affect the middle value.
Position $n$ for Median: Possible orders are $1, 1, 2, 8, n$ or $1, 1, 2, n, 8$ . Since the median is $2$ , $n$ must be greater than or equal to $2$ to keep $2$ as the median.
Compare Choices: $20$ vs $1$ : Comparing the choices given: (A) $20$ and (B) $1$ . If $n = 1$ , the order would be $1, 1, 1, 2, 8$ , making $1$ the median, which is incorrect.
Verify Median with $n=20$ : If $n = 20$ , the order would be $1, 1, 2, 8, 20$ . The median remains $2$ , which is correct.

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