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Stanley has the following data: $\newline$ $3, 1, v, 5, 1, 5$ $\newline$ If the range is $4$ , which number could $v$ be? $\newline$ Choices: $\newline$ $(A)$ $6$ $\newline$ $(B)$ $1$

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

Full solution

Q. Stanley has the following data:

\newline

3, 1, v, 5, 1, 5

\newline

If the range is

4

, which number could

v

be?

\newline

Choices:

\newline

(A)

6

\newline

(B)

1

Arrange Data in Ascending Order: Arrange the data set excluding $v$ in ascending order: $1, 1, 3, 5, 5$ .
Calculate Range Excluding $v$ : Calculate the range without $v$ : $5 - 1 = 4$ .
Determine Possible Values for $v$ : Since the range of the data set including $v$ must also be $4$ , $v$ must be a value that does not increase or decrease the current range.
Check $v = 6$ : Check if $v = 6$ affects the range: New data set would be $1, 1, 3, 5, 5, 6$ . New range = $6 - 1 = 5$ , which is not equal to $4$ .
Check $v = 1$ : Check if $v = 1$ affects the range: New data set would be $1, 1, 1, 3, 5, 5$ . New range = $5 - 1 = 4$ , which is equal to $4$ .

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