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Marshall has the following data: $\newline$ $2, 2, 18, c$ $\newline$ If the range is $16$ , which number could $c$ be? $\newline$ Choices: $\newline$ $(A)$ $13$ $\newline$ $(B)$ $20$

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

Full solution

Q. Marshall has the following data:

\newline

2, 2, 18, c

\newline

If the range is

16

, which number could

c

be?

\newline

Choices:

\newline

(A)

13

\newline

(B)

20

Identify Data and Range: Step $1$ : Identify the given data and the range. $\newline$ Data: $2, 2, 18, c$ $\newline$ Range given: $16$
Calculate Possible Values: Step $2$ : Calculate the possible values for $c$ using the range formula. $\text{Range} = \text{Maximum value} - \text{Minimum value}$ $16 = \text{Max}(2, 2, 18, c) - \text{Min}(2, 2, 18, c)$
Substitute Values into Equation: Step $3$ : Since the maximum value without $c$ is $18$ , and the minimum value is $2$ , substitute these into the range equation. $\newline$ $16 = 18 - \min(2, c)$ $\newline$ $\min(2, c)$ must be $2$ for the range to remain $16$ .
Solve for $c$ : Step $4$ : Solve for $c$ . $16 = 18 - 2$ $c$ must be greater than or equal to $18$ to maintain $2$ as the minimum value.
Check Choices for $c$ : Step $5$ : Check the choices given for $c$ . Choices are (A) $13$ and (B) $20$ . Since $c$ must be greater than or equal to $18$ , the only possible choice is (B) $20$ .

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