Question

What is the median of 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 11, 13?

Answer 1

Median = 4

Explanation:

1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4,
4, 5, 5, 6, 7,7, 7, 8, 8, 8, 9, 9, 10, 11, 13

There are 30 sample points and the media, `Q_2` is the middle sample poit (ie `50%` of the data lies to the left and `50%` lies to the right).

As we have an even number of samples, the median sample point would have to be estimated by averaging as it lies in-between the sample points it `x_15.5`, In the case `x_15=4` and `x_16=4`, and so `Q_2=4`.