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Tanvi has the following data: $\newline$ $4, 5, 4, m$ $\newline$ If the range is $7$ , which number could $m$ be? $\newline$ Choices: $\newline$ $(A)$ $11$ $\newline$ $(B)$ $3$

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

Full solution

Q. Tanvi has the following data:

\newline

4, 5, 4, m

\newline

If the range is

7

, which number could

m

be?

\newline

Choices:

\newline

(A)

11

\newline

(B)

3

Understand the problem: Step $1$ : Understand the problem and the data given. $\newline$ Tanvi has numbers $4$ , $5$ , $4$ , and $m$ . The range of these numbers is $7$ . The range is the difference between the maximum and minimum values in the set.
Calculate possible values: Step $2$ : Calculate the possible values for $m$ using the range. $\text{Range} = \text{Maximum value} - \text{Minimum value} = 7.$ If $m$ is the maximum value, then $m - 4 = 7$ (since the minimum of the other numbers is $4$ ). $m = 4 + 7 = 11.$ If $m$ is the minimum value, then $5 - m = 7$ (since the maximum of the other numbers is $5$ ). $m = 5 - 7 = -2$ , which is not an option given.
Check choices: Step $3$ : Check the choices given to see which fits. $\newline$ Choices are (A) $11$ and (B) $3$ . $\newline$ From Step $2$ , $m$ could be $11$ to satisfy the range of $7$ .

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