What is the effect on the median when the outlier is removed from the following set of data?

Question

23, 76, 79, 76, 77, 74, 75

Answer 1

First, arrange the data set in increasing order:

 

23, 74, 75, 76, 76, 77, 79

 

The median is the middle value, 76.  Now remove the outlier, 23:

 

74, 75, 76, 76, 77, 79

 

Since there are now an even number of data points, there is no exact middle value.  So take the mean of the two values closest to the middle to get the median:

 

(76+76)/2 = 152/2 = 76

 

For this data set, the median remains unchanged when the outlier is removed.