Question

The following data set shows the number of people who attended the fitness class last week.
$6,9,12,m,5,7,$ and $14$

If the range of the data is 11, which of the following could the value(s) of m be?
(Hint: There can be more than one correct answer.)

• A. $16$
• B. $8$
• C. $13$
• D. $3$

Answer 1

Answer: (A), (D)

$3$

Given data set: $6,9,12,m,5,7,$ and $13$
Range: $11$
Since $13-5$ is not equal to $11$, we can conclude that $m$ is part of the range.
We can calculate the value of $m$ by two methods. We can assume $m$ to be the maximum value or we can assume $m$ to be the minimum value.
Let’s calculate the value of m when its value is assumed to be minimum.
Range = maximum value - minimum value
$11=14-m$
$11+m=14-m+m$
$11-11+m=14-11$
$m=3$
Now, let's calculate the value of m when its value is assumed to be maximum.
Range = maximum value - minimum value
$11=m-5$
$11+5=m-5+5$
$16=m$
So, $m$ can have two values: $3$ or $16.$