Quartile Deviation and Coefficient of Quartile Deviation

Quartile deviation is a measure of dispersion that indicates the spread of data around the median. It is calculated by finding the difference between the upper quartile (Q3) and the lower quartile (Q1), and then dividing it by 2. The formula for quartile deviation is:

Quartile Deviation (QD) = (Q3 - Q1) / 2

Step 1: Arrange the data in ascending order:
4, 7, 8, 10, 11, 12, 14, 15, 16, 18

Step 2: Find the quartiles:
To find the quartiles, we need to determine the median of the data set. Since the total number of observations is 10, the median will be the average of the 5th and 6th values.

Median (Q2) = (11 + 12) / 2 = 11.5

To find the lower quartile (Q1), we take the median of the lower half of the data set. Since the lower half consists of the first 5 values, the median will be the average of the 2nd and 3rd values.

Q1 = (7 + 8) / 2 = 7.5

To find the upper quartile (Q3), we take the median of the upper half of the data set. Since the upper half consists of the last 5 values, the median will be the average of the 2nd and 3rd values.

Q3 = (15 + 16) / 2 = 15.5

Step 3: Calculate the quartile deviation:
QD = (Q3 - Q1) / 2
= (15.5 - 7.5) / 2
= 8 / 2
= 4

The quartile deviation for the given data set is 4.

Step 4: Calculate the coefficient of quartile deviation:
The coefficient of quartile deviation is calculated by dividing the quartile deviation by the median and multiplying it by 100.

Coefficient of Quartile Deviation = (QD / Median) * 100
= (4 / 11.5) * 100
= 34.78

The coefficient of quartile deviation for the given data set is 34.78.