In a continuous series, the third quartile and the quartile deviation of any data are 60 and 20 respectively. Find the coefficient of quartile deviation.

 Coefficient of Quartile Deviation (QD)=

MedianQuartile Deviation (QD)​

Given: Third quartile (Q3) = 60 Quartile deviation (QD) = 20

First, we need to find the median (Q2) using the relation between quartiles in a continuous series. In a continuous series:

$𝑄2=\frac{(𝑄1+𝑄3)}{2}$

Given Q3 = 60, we can find the median Q2

Q2=2(Q1+Q3)​=2(Q1+60)​

Also, the quartile deviation is given as 20, which is the difference between Q3 and Q1:

$𝑄𝐷=𝑄3-𝑄1$ $20=60-𝑄1$ $𝑄1=60-20=40$

Now that we have Q1 and Q3, we can find Q2:

$𝑄2=\frac{(𝑄1+𝑄3)}{2}=\frac{(40+60)}{2}=\frac{100}{2}=50$

Now, substitute the values into the formula for the coefficient of quartile deviation:

Quartile Deviation (QD)​

$\text{Coefficient of Quartile Deviation (QD)}=\frac{20}{50}=0.4$

Therefore, the coefficient of quartile deviation is 0.4.