Exercise 16 Page 708

We are asked which of the given box plots represent the following data set. 18, 22, 31, 25, 30, 19, 26, 24, 35 To do that, we will make a box plot the data ourselves and then compare with the given options. To make a box plot, we need to find the five-number summary of the data set.

First, let's find the median. To do that, we first need to write the data set from least value to the greatest. 18, 22, 31, 25, 30, 19, 26, 24, 35 ⇓ 18,19,22,24, 25, 26,30,31,35 We need to find a value which splits the data set into two equal halves.

We found that the median is equal to 25. Now let's find the quartiles. The first quartile is equal to the median of the lower half.

Notice that the lower half has two middle values, 19 and 22. Therefore, the first quartile is equal to the average of these values.

We found that the first quartile is equal to 20.5. Now let's find the third quartile which is the median of the upper half.

The upper half also has two middle values. The third quartile is equal to their average.

We found the quartiles! Next, let's find the minimum and maximum values of the data set. 18,19,22,24, 25, 26,30,31, 35 We can see that the minimum value is 18 and the maximum value is 35. We found all the values from the five-number summary!

Now we are ready to draw a box plot. First, let's mark all the values from the five-number summary above the number line.

Now let's draw a straight line between the minimum values and the first quartile and another line between the third quartile and maximum value.

Next, we will draw a box around the median. The sides of the box should go through the points representing the first and third quartile.

Finally, we will finish our box plot by drawing a line inside the box going through the point representing the median.

Notice that this graph looks like the one from option A. Therefore, option A is correct.