Question

Ivan was given two data sets, one without an outlier and one with an outlier.

Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61

How is the median affected by the outlier?

Answer 1

It make it 121 instead of 118 because there is an extra number and median is the middle of a data set so the number of numbers is important.

Answer 2

Median is decreased by the outlier or Outlier made median lower.

Explanation:

First we calculate median of the data without an outlier:

Data in Ascending or increasing order ,

105 , 108 , 109 , 113 , 118 , 121 , 124

Now there are 7 terms so

Median =
`(7+1)/(2)^(th)\:term` = 4th term = 113

Now we find median of the data with outlier:

Data in ascending or descending order,

61 , 105 , 108 , 109 , 113 , 118 , 121 , 124

here no of terms are 8.

So, Median =
`(((8)/(2))^(th)+((8)/(2)+1)^(th))/(2)`

=
`(4^(th)+5^(th))/(2)=(109+113)/(2)`

= 111

So, Median is decreased by the outlier or Outlier made median lower.