Exercise 1 Page 348

a To find if the new course will affect the median class size, let's first look at how the new student will change the dot plot. Remember, the new course has only

65

enrolled students.

Original Dot Plot	New Dot Plot

Now, we can find the median of the original

16

courses and then the new median when there are

17

courses. To determine the median, we need to find the middle value, or the mean of the two middle values, of the data when it is ordered from least to greatest.

b Now we want to know if the new course is an outlier. A data point is an outlier if one of two things is true.

The value $x$ is less than $1.5$ times the IQR below the first quartile, $x < Q_{1} - 1.5 (I Q R) .$
The value $x$ is greater than $1.5$ times the IQR above the third quartile, $x > Q_{3} + 1.5 (I Q R) .$

First, let's determine

Q_{1}

and

Q_{3}

for the

17

courses. In Part A, we found that the median is

85 .

We find

Q_{1}

and

Q_{3}

by looking for the median values of the lower and upper halves of the data.

65, 80, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90, 90, 95, 95, 100, 105

c Finally, we need to check whether or not the range increases by

40

when the

1 7^{th}

course is added. The range

R

is the difference between the

least

and the

greatest

data values.

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Exercises p.348