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Jake has the following data: $\newline$ $12, 10, 10, p, 11$ $\newline$ If the median is $11$ , which number could $p$ be? $\newline$ Choices: $\newline$ $(A)$ $12$ $\newline$ $(B)$ $5$

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

Full solution

Q. Jake has the following data:

\newline

12, 10, 10, p, 11

\newline

If the median is

11

, which number could

p

be?

\newline

Choices:

\newline

(A)

12

\newline

(B)

5

Understand the Problem: Step $1$ : Understand the problem and the data given. $\newline$ Jake has the following numbers: $12$ , $10$ , $10$ , $p$ , $11$ . We need to find the value of $p$ such that the median of these numbers is $11$ .
Arrange Numbers: Step $2$ : Arrange the numbers in ascending order to find the median. Since the median is the middle value when the numbers are in order, and we know the median is $11$ , the sequence should be $10, 10, 11, p, 12$ or $10, 10, p, 11, 12$ .
Determine Possible Values: Step $3$ : Determine possible values for $p$ . For the median to be $11$ , $p$ must be either $11$ or a number greater than $11$ but less than $12$ . Since $12$ is already in the list and is the maximum, $p$ must be $11$ .

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