Question

Check the following data set for outliers.

33, 42, 44, 44, 46, 47, 49, 51

Answer 1

For the given data set

n=8

For First quartile

n/4 = 8/4=2

(n/4)+1= 3

Q1=Average of 2nd and 3rd terms =(42+44)/2

Q1=43

Q2=average of 4th and 5th terms=(44+46)/2=45

Q2=45

Q3= average of 6th and 7th terms= (47+49)/2= 48

Q3=48

Inter quartile region IQR=Q3-Q1= 48-43=5

IQR=5

For outliers we need to find Q1-1.5*IQR and Q3+1.5*IQR

1.5*IQR= 1.5*5=7.5

Lower limit = Q1-1.5*IQR = 43-7.5= 35.5

Upper limit=Q3+1.5*IQR = 48+7.5=55.5

Now compare this values from the dataset

The values which are less than 33.5 or values which are greater than 55.5 are called outliers.

We can see that 33 is less than 35.5 so it an outlier.

33--> outlier