Question

The data set below shows the number of homework assignments required in math classes for a month:

22

23

23

21

18

4

17

15

23

20

24

15

25

16



Which of the following statements is true based on the data set?
a.There is one outlier that indicates an unusually large number of assignments required in that class.
b.There is one outlier that indicates an unusually small number of assignments required in that class.
c.There are two outliers that indicate an unusually large number of assignments required in those two classes.
d.There are two outliers that indicate an unusually small number of assignments required in those two classes.

Answer 1

The letter answer is (B)

Answer 2

There is one outlier that indicates an unusually small number of assignments required in that class.

Explanation:

Arranging the data is ascending order, we get:

4, 15, 15, 16, 17, 18, 20, 21, 22, 23, 23, 23, 24, 25

Lets divide the data in 4 equal parts to know the IQ ranges.

(4, 15, 15), 16, (17, 18, 20), (21, 22, 23), 23, (23, 24, 25)`

We can see that first interquartile range Q1 is 16

The third interquartile range Q3 is 23.

The IQR is
`23-16=7`

Lets check the interval [Q1-1.5(IQR),Q3+1.5(IQR)],

If any data lies in this interval, it will have no outliers.

[
`[16-1.5(7),23+1.5(7)]` = [5.5,33.5]

So, we can see that all the data except 4 lie in the interval [5.5,33.5].

Therefore, we can say that -

B - There is one outlier that indicates an unusually small number of assignments required in that class.