Question

The table below shows data from a survey about the amount of time, in hours, high school students spent reading and the amount of time spent watching videos each week (without reading):

Reading Video
3 1
3 2
4 3
5 4
6 6
7 7
10 8
12 8
14 9
30 15

Which response best describes outliers in these data sets?
A, Reading has a suspected outlier in the 30-hour value.
B. Reading has a suspected outlier in the 30-hour value, and video has a possible outlier in the 15-hour value.
C. Neither data set has suspected outliers.
D. The range of data is too small to identify outliers.

Answer 1

The correct option is: A,B

Explanation:

" An outlier is a odd value which on removing from the data leads to the less mean as calculated mean on including that value ".

There are total 10 data points.

• The table for reading is given as:

3 3 4 5 6 7 10 12 14 30

The mean of this data is given by:

`(3+3+4+5+6+7+10+12+14+30)/(10)=(94)/(10)=9.4`

Also the mean after omitting the odd value i.e. 30 we get:

`(3+3+4+5+6+7+10+12+14)/(9)=(64)/(9)=7.11`

Hence, there is a change in its mean;

Hence the outlier for reading is 30.

• The table for Video is given by:

1 2 3 4 6 7 8 8 9 15

The possible maximum value here is 15 so we will check whether it is an outlier or not.

The mean of this data is given by:

`(1+2+3+4+6+7+8+8+9+15)/(10)=(63)/(10)=6.3`

Also the mean after omitting the odd value i.e. 15 we get:

`(1+2+3+4+6+7+8+8+9)/(9)=(48)/(9)=5.33`

Hence, there is a change in its mean hence 15 is an outlier.

Hence option A and B are true.

Answer 2

Reading: 3, 3, 4, 5, 6, 7, 10, 12, 14, 30
Video: 1, 2, 3, 4, 6, 7, 8, 8, 9, 15

Reading Video
Minimum 3 1
1st quartile 4 3
Median 6.5 6.5
3rd quartile 12 8
Maximum 30 15
IQR 8 5
Outliers 30 no outliers

A, Reading has a suspected outlier in the 30-hour value.