Question

The data set below has a lower quartile of 13 and an upper quartile of 37.

1, 12, 13, 15, 18, 20, 35, 37, 40, 78

Which statement is true about any outliers of the data set?

The data set does not have any outliers.

The lowest value, 1, is the only outlier.

The greatest value, 78, is the only outlier.

Both 1 and 78 are outliers.

Answer 1

its C The greatest value, 78, is the only outlier

Explanation:

Answer 2

The correct option is 3.

Explanation:

The first and third quartile of the data are 13 and 37.

The interquartile range is the difference between Q₃ and Q₁.

`\text{Interquartile Range}=Q_3-Q_1`

`\text{Interquartile Range}=37-13=24`

We have to find 1.5 (IQR),

`1.5* \text{Interquartile Range}=1.5* 24=36`

Now subtract 36 from Q₁ and add 36 in Q₃, if data lies outside the interval [Q₁-1.5(IQR),Q₃+1.5(IQR)] are called outliers.

`Q_1-36=13-36=-23`

`Q_3+36=37+36=73`

The outliers are the numbers which lies outside the range [-23,73]. Only 78 lies outside the range, therefore the correct option is 3.