Question

What is the upper and lower quartile of 84-84 92 92 95 94 80-72

Answer 1

Upper Quartile / Q1 = 82

Lower Quartile / Q3 = 93

Explanation:

The data we are given with is :

84 84 92 92 95 94 80 72

Let us first arrange the data in ascending order

72 80 84 84 92 92 94 95

The Formula to find the Quartile is

Quartile For Q1/Upper

`(1)/(4)*(n+1)` term

n=8

`(1)/(4)*(8+1)` term

`(9)/(4)` term

2.25 term

This means that Quartile for Q1 is average of 2nd and 3rd term

2nd term = 80 , 3rd term = 84

Average =
`(80+84)/(2)`

= 82

Quartile For Q3/Lower Quartile

`(3)/(4)*(n+1)` term

n=8

`(3)/(4)*(8+1)` term

`(3 * 9)/(4)` term

= 6.75

Hence the Quartile for Q3 will be the average of the 6th and 7th term

6th term = 92

7th term = 94

Average=
`(92+94)/(2)`

= 93

Hence Upper Quartile / Q1 = 82

Lower Quartile / Q3 = 93