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Bryan has the following data: $\newline$ $3, 3, 3, 8, r$ $\newline$ If the range is $5$ , which number could $r$ be? $\newline$ Choices: $\newline$ (A) $12$ $\newline$ (B) $3$

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

Full solution

Q. Bryan has the following data:

\newline

3, 3, 3, 8, r

\newline

If the range is

5

, which number could

r

be?

\newline

Choices:

\newline

(A)

12

\newline

(B)

3

Calculate Range: Calculate the current range of the data set without $r$ . The range is the difference between the maximum and minimum values in the set. Current values are $3$ , $3$ , $3$ , and $8$ .
Determine Suitable $r$ : Since the current range is already $5$ , adding $r$ should not increase or decrease this range. Thus, $r$ must be a value that does not exceed the current maximum ( $8$ ) or fall below the current minimum ( $3$ ).
Check Given Choices: Check the given choices for $r$ : $\newline$ (A) $12$ $\newline$ (B) $3$ $\newline$ If $r = 12$ , the new range would be $12 - 3 = 9$ , which is not equal to $5$ . $\newline$ If $r = 3$ , the range remains $3$ to $8$ , which is $5$ .

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