Question

Mario made five phone calls lasting 4,6, 8, 15, 21 minutes. After another call, the median length of the phone calls were 10 minutes. What was the mean length of the six calls?

Answer 1

Explanation

We are given that Mario made 5 phone calls which lasted 4, 6, 8, 15, and 21 minutes

We are then asked to determine the mean length of the 6 calls after another call has been made

Let the 6th call be x

So that the median of 4, 6, 8, 15, 21, and x minutes be 10

$4,6,8,\text{ x,15, 21}$

The value of x cannot be after 21 because, this will mean that x is greater than 21 minutes, which will not give us a median of 10 minutes

The median of the values is

The median

$\frac{8+x}{2}=10$

If we make x the subject of the formula

$\begin{gathered} 8+x=20 \\ x=20-8 \\ x=12\text{ minutes} \end{gathered}$

So we can then compute the mean of the six calls as

$mean=\frac{4+6+8+12+15+21}{6}=11\text{ minutes}$

The mean length of the calls is 11 minutes