Question

22,15,13,25,11,1830,17,20,20

what is the First quartile?
what is the median?

what is the third quartile?

Answer 1

Median = 19.5

Quartile for Q1 = 14

Quartile for Q3 = 23.5

Explanation:

Our data is

22 15 13 25 11 19 30 17 20 20

Let us first arrange the data in ascending order

11 13 15 17 19 20 20 22 25 30

As there are total 10 terms in the data , the median will be the average of the 5th and th 6th term

5th entity = 19

6th entity = 20

Average

=
`(19+20)/(2)`

Average

=
`(39)/(2)`

Median = 19.5

The Formula to find the Quartile is

Quartile For Q1

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

n=10

`(1)/(4)*(10+1)` term

`(11)/(4)` term

2.75 term

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

2nd term = 13 , third term = 15

Average =
`\rac{13+15}{2}`

= 14

Quartile For Q3

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

n=10

`(3)/(4)*(10+1)` term

`(3 * 11)/(4)` term

= 8.25

Hence the Quartile for Q3 will be the average of the 8th and 9th term

8th term = 22

9th term = 25

Average=
`(22+25)/(2)`

= 23.5

Hence Quartile for Q1 = 14

Quartile for Q3 = 23.5