Question

Which values are outliers ?

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

select all correct answers

Answer 1

5.8 0.8 5.9 6.1 and 10.9 are all correct answers.

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Answer 2

0.8 and 1.1 are outliers of the given data set.

Explanation:

The given data set is

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

Arrange the data set in ascending order

0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9

Divide the data in four equal parts.

(0.8, 1.1), 4.9,( 5.2, 5.8), 5.9,( 6.1, 6.1), 7.4, (10.2, 10.9)

From the above division we get,

`Q_1=4.9`

`Median=5.9`

`Q_3=7.4`

The interquartile range of the data is

`IQR=Q_3-Q_1`

`IQR=7.4-4.9=2.5`

If all the data elements lies in the interval [Q₁-1.5(IQR),Q_3+1.5(IQR)], then the data set has no outliers.

`[Q_1-1.5(IQR),Q_3-1.5(IQR)]=[4.9-1.5(2.5),7.4-1.5(2.5)]=[1.15,11.15]`

Since all the elements lie in the interval [1.15,11.15] except 0.8 and 1.1, therefore 0.8 and 1.1 are outliers.