# Quartile Deviation

What is dispersion?

Dispersion means scatterings, variability, deviation or fluctuation of data.

Write the various measures of dispersion.

The various measures of dispersion are:
1. An absolute measure of dispersion: It includes range, quartile deviation, mean deviation, standard deviation.
2. A relative measure of dispersion: It includes coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of standard deviation and coefficient of variation.

Define quartile deviation and write the formula to calculate quartile deviation.

Half of the difference between upper quartile (Q3) and lower quartile (Q1) is called quartile deviation. It is also called as semi-interquartile range. Its formula is:
Quartile deviation (QD) = $\frac{Q_3 - Q_1}{2}$

What do you mean by coefficient of quartile deviation?

The relative measure based on lower and upper quartile is coefficient of quartile deviation. It is given by:
Coefficient of Quartile deviation = $\frac{Q_3 - Q_1}{Q_3 + Q_1}$

Write the difference between quartile deviation and the coefficient of quartile deviation.

Quartile deviation is a half of the difference between upper quartile (Q3) and lower quartile (Q1) whereas coefficient of quartile deviation is the relative measure based on lower and upper quartile.
Formula to calculate quartile deviation is $\frac{Q_3 - Q_1}{2}$ and coefficient of quartile deviation is $\frac{Q_3 - Q_1}{Q_3 + Q_1}$

In Continuous data, the first quartile and third quartile are 40 and 60 respectively, find the quartile deviation.

Here,
First quartile(Q1) = 40
Third quartile(Q3) = 60
Quartile deviation(QD) = ?

Now, we know,
QD = $\frac{Q_3 - Q_1}{2}$ = $\frac{60 - 40}{2}$ ∴ QD = 10

In a continuous series, the lower quartile is 25 and its quartile deviation is 10, find the upper quartile.

Here,
Lower quartile(Q1) = 25
Quartile deviation(QD) = 10
Upper quartile(Q3) = ?

Now, we know, QD = $\frac{Q_3 - Q_1}{2}$ or, 10 = $\frac{Q_3 - 25}{2}$
or, 20 + 25 = Q3
∴ Q3 = 45

In a continuous series, the coefficient of quartile deviation is $\frac 12$ and its upper quartile is 60, find its first quartile.

Here,
Coefficient of quartile deviation = $\frac 12$
Upper quartile(Q3) = 60
First quartile(Q1) = ?

Now, we know, Coefficient of quartile deviation = $\frac{Q_3 \, - \, Q_1}{Q_3 \, + \, Q_1}$ or, $\frac 12$ = $\frac{60 \, - \, Q_1}{60 \, + \, Q_1}$
or, 60 + Q1 = 120 - 2Q1
or, 3Q1 = 60
∴ Q1 = 20

In a continuous series, the coefficient of quartile deviation is $\frac 37$ and its first quartile is 20, find its upper quartile.

Here,
Coefficient of quartile deviation = $\frac 37$
First quartile(Q1) = 20
Upper quartile(Q3) = ?

Now, we know, Coefficient of quartile deviation = $\frac{Q_3 \, - \, Q_1}{Q_3 \, + \, Q_1}$ or, $\frac 37$ = $\frac{Q_3 \, - \, 20}{Q_3 \, + \, 20}$
or, 3Q3 + 60 = 7Q3 - 140
or, 140 + 60 = 4Q3
∴ Q3 = 50