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.