Question

Which value in this data set is an outlier?4,5, 1, 7,4,5,8,9,6,5,4,9,7O A 1OB. 23OD9

Answer 1

The given data set is:

`4,5,1,7,4,5,8,9,6,5,4,9,7`

Rewrite the data set in ascending order:

`1,4,4,4,5,5,5,6,7,7,8,9,9`

The total number of data points is 13, therefore, the median of the data set is the 7th value.

The 7th value is 5, therefore, the median is 5.

To calculate the first quartile, Q₁, is given by the median of the first six data points.

The first six data points is:

`1,4,4,4,5,5`

Therefore, the first quartile, Q₁ is:

`Q_1=(4+4)/(2)=4`

To calculate the first quartile, Q₁, is given by the median of the first six data points.

The last set of six data points is:

`6,7,7,8,9,9`

Therefore, the first quartile, Q₃ is:

`Q_3=(7+8)/(2)=7.5`

The Interquartile Range, IQR is given by:

`IQR=Q_3-Q_1=7.5-4=3.5`

The lower outlier is given by:

`\text{ The Lower Quartile }=Q_1-1.5IQR=4-1.5(3.5)=-1.25`
`\text{ The Higher Quartile }=Q_3+1.5IQR=7.5+1.5(3.5)=12.75`

Any data point less than the lower quartile and higher than the higher quartile is an outlier.

Therefore, there is no outlier in the data set