Question

The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 30 years because they are either 1.5 times the interquartile range (IQR) greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50 years

Answer 1

Only 60 is an identified outlier

Explanation:

Given

Age group: 40 to 50

`Min = 60`
`Q_1 = 70`
`Median= 73`

`Q_3 = 76`
`Max = 85`

Conditions for outlier

`Value > Q_3 + 1.5 * IQR`

`Value < Q_1 - 1.5 * IQR`

See attachment for complete question

Required

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

`IQR = Q_3 - Q_1`

Where:

`Q_3 = 76` and
`Q_1 = 70`

So:

`IQR = 76 - 70`

`IQR = 6`

Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)

Testing 60

Condition 1

`Value > Q_3 + 1.5 * IQR`

`60 > 76 + 1.5 * 6`

`60 > 76 + 9`

`60 > 85` --- False

Condition 2

`Value < Q_1 - 1.5 * IQR`

`60 < 70 - 1.5 * 6`

`60 < 70 - 9`

`60 < 61` --- True

Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years

Testing 62

Condition 1

`Value > Q_3 + 1.5 * IQR`

`62> 76 + 1.5 * 6`

`62 > 76 + 9`

`62 > 85` --- False

Condition 2

`Value < Q_1 - 1.5 * IQR`

`62 < 70 - 1.5 * 6`

`62 < 70 - 9`

`62 < 61` --- False

Because both conditions are false, then 62 is not an outlier of group 40 - 50 years

Testing 84

Condition 1

`Value > Q_3 + 1.5 * IQR`

`84> 76 + 1.5 * 6`

`84 > 76 + 9`

`84 > 85` --- False

Condition 2

`Value < Q_1 - 1.5 * IQR`

`84 < 70 - 1.5 * 6`

`84 < 70 - 9`

`84 < 61` --- False

Because both conditions are false, then 84 is not an outlier of group 40 - 50 years