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Brad has the following data: $\newline$ $c, 9, 6, 7, 2$ $\newline$ If the median is $7$ , which number could $c$ be? $\newline$ Choices: $\newline$ (A) $9$ $\newline$ (B) $2$

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

Full solution

Q. Brad has the following data:

\newline

c, 9, 6, 7, 2

\newline

If the median is

7

, which number could

c

be?

\newline

Choices:

\newline

(A)

9

\newline

(B)

2

Identify Data Set & Requirement: Step $1$ : Identify the data set and the requirement for the median. $\newline$ Data set: $c, 9, 6, 7, 2$ . The median is given as $7$ .
Determine Possible Values: Step $2$ : Determine the possible values for $c$ that would place $7$ as the median. $\newline$ To have $7$ as the median, the numbers must be arranged so that two numbers are less than $7$ and two are greater when $c$ is included.
Sort & Analyze Positions: Step $3$ : Sort the given numbers excluding $c$ and analyze the positions. $\newline$ Sorting the numbers: $2, 6, 7, 9$ . Here, $7$ is already the median without $c$ .
Insert & Check Median: Step $4$ : Insert each choice for $c$ into the sorted list and check if $7$ remains the median. $\newline$ Inserting (A) $9$ : $2, 6, 7, 9, 9$ . Median is still $7$ . $\newline$ Inserting (B) $2$ : $2, 2, 6, 7, 9$ . Median shifts to $6$ .

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