Question

Alicia records the total number of points scored in two games by 10 players on herbasketball team.28, 13, 4, 8, 15, 10, 22, 7, 11, 15Which box plot represents the data?

Answer 1

The given data are

$28,13,4,8,15,10,22,7,11,15$

We will arrange them from smallest to greatest

$4,7,8,10,11,13,15,15,22,28$

We will find the median (2nd quartile)

Since there are 10 numbers, then the median is the average of the 2 middle numbers which are in the 5th and 6th positions

$\begin{gathered} Q2(median)=\frac{11+13}{2} \\ \\ Q2(median)=\frac{24}{2}=12 \end{gathered}$

Now, we will work to find the 1st and 3rd quartiles (Q1, Q3)

The 1st quartile is the middle number of the first 5 numbers

$4,7,8,10,11$

The middle number is 8, then

$Q1=8$

The 3rd quartile is the middle number of the last 5 numbers

$13,15,15,22,28$

The middle number is 15, then

$Q3=15$

Since the smallest number is 4 and the largest number is 28, then the box plot should be as this figure

Then the answer is

The top right graph