Question

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

Answer 1

Answer:

Upper Quartile / Q1 = 82

Lower Quartile / Q3 = 93

Step-by-step 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

$\frac{1}{4}\times(n+1)$  term

n=8

$\frac{1}{4}\times(8+1)$  term

$\frac{9}{4}$  term

2.25 term

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

2nd term = 80 , 3rd  term = 84

Average = $\frac{80+84}{2}$

=  82

Quartile For Q3/Lower Quartile  

$\frac{3}{4}\times(n+1)$  term

n=8

$\frac{3}{4}\times(8+1)$  term

$\frac{3 \times 9}{4}$  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= $\frac{92+94}{2}$

= 93

Hence Upper Quartile / Q1 = 82

Lower Quartile / Q3 = 93