Range and Quartile Deviation

In this class, We discuss Range and Quartile Deviation.

For Complete YouTube Video: Click Here

The reader should have prior knowledge of the measure of dispersion. Click Here.

Range:

Example:

8, 5, 16, 33, 7, 24, 5, 30, 33, 37, 30, 9, 11, 26, 32

Arrange the data in ascending order.

5, 5, 7, 8, 9, 11, 16, 23, 24, 26, 30, 30, 32, 3, 37

Range = maximum value – minimum value

Range = 37 – 5 = 32

The range is one of the ways to find the measure of dispersion.

The range is not used much in the statistics.

Quartile Deviation:

The reader should have prior knowledge of quartile points. Click Here.

Quartile Deviation = (Q3 – Q1)/2

Q3 is upper quartile

Q1 is lower quartile.

We understand the uses of quartile deviation with an example.

Example:

8, 2, 5, 1, 9, 15, 20, 7, 3, 25, 27

Arrange the data in ascending order.

1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27

n = 11

Q1 = ((n+1)/4) = 3

Q3 = (3(n+1)/4) = 20

QD = (20 – 3) / 2

QD = 8.5

1) Quartile deviation helpful if we need the dispersion of middle 50% data values.

2) Not involving extreme terms. last and first 25% data values. So not affected by outliers.

Some times we use quartiles to identify outliers.

Interquartile range:

IQR = Q3 – Q1

Identifying outliers is helpful in data analysis.

The interquartile range is one of the ways to identify outliers.

Example:

1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27

IQR = Q3 – Q1

IQR = 20 – 3

IQR = 17

Outlying points are given as

1) Q1 – 1.5*IQR

Below the value, Q1 – 1.5*IQR is considered an outlier.

3 – 1.5*17 = -22.7

We will discuss why we use the value 1.5 in the equation in our later classes when we discuss normal distribution.

2) An outlying point is above the value Q3 + 1.5 * IQR.

20 + 1.5 * 17 = 45.5

Coefficient of Quartile Deviation:

The coefficient of quartile deviation is the relative measure of quartile deviation.

CQD = (Q3- Q1)/(Q3 + Q1)

We use the coefficient of quartile deviation to measure the dispersion of two different distributions.

Example:

1) 1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27

CQD = (Q3- Q1)/(Q3 + Q1) = (20 – 3) (20 + 3)

CQD = 0.73

2) 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11

CQD = (Q3- Q1)/(Q3 + Q1) = (9 – 3) / (9+3)

CQD = 0.5

The first data is having more data distribution.