Question

Calculate ¯ x x¯ (x-bar) and the median for the data shown, to two decimal places x 16.7 2.2 2.1 7.9 1.6 14.5 21.5 19 26.9 29 7.2 28.3 6.3 23.9 25.6 16.1 6.4 15.2 19.1 4.5 22.5 13.7 11.4 16.9 ¯ x x¯ = Median

Answer 1

Solution :

We are given a data of sample size n = 24

16.7,2.2,2.1,7.9,1.6,14.5,21.5,19,26.9,29,7.2,28.3,6.3,23.9,25.6,16.1,6.4,15.2,19.1,4.5,22.5,13.7,11.4,16.9

Using this, first we find sample mean()

=   

= (16.7 + 2.2.......+ 16.9)/24

= 14.94

The Median =

Arrange all data in ascending order -

1.6, 2.1, 2.2, 4.5, 6.3, 6.4, 7.2, 7.9, 11.4, 13.7, 14.5, 15.2, 16.1, 16.7, 16.9, 19, 19.1, 21.5, 22.5, 23.9, 25.6, 26.9, 28.3, 29

Now, n + 1/ 2 = 24 + 1/ 2 =   12.5

The median = 12.5^th observation

= 15.2 + 16.1 /2

= 15.65

The Median = 15.65