Question

Find the interquartile range of the data set: 19, 8, 22, 16, 11, 10, 13

Answer 1

IQR = 9

Explanation:

First, arrange the data in ascending order.

8 , 10 , 11 , 13 , 16 , 19 , 22

Now, let us find the lower quartile using the below formula.

`\sf Q_1=(1)/(4)\;(n+1)`

n is the number of data.

`\sf Q_1=(1)/(4)\;(n+1)\\\\\sf Q_1=(1)/(4)\;(7+1)\\\\\sf Q_1=2nd \:data`

Q₁ = 10

Now, let us find the upper quartile using the below formula.

`\sf Q_3=(3)/(4)\;(n+1)`

`\sf Q_3=(3)/(4)\;(n+1)\\\\\sf Q_3=(3)/(4)\;(7+1)\\\\\sf Q_3=6th \:data`

Q₃ = 19

Now let us find the interquartile range.

IQR = Q₃ - Q₁

IQR = 19 - 10

IQR = 9