In a distribution, Q.D= 15 and co-efficient of Q.D=0.3 75% of the observation are less than?
a)67
b)65
c)78
d)75
To determine the value for which 75% of the observations are less than, we need to use the formula for the quartile deviation (Q.D) and its coefficient.
The formula for quartile deviation (Q.D) is:
Q.D = (Q3 - Q1) / 2
Where Q1 represents the first quartile and Q3 represents the third quartile.
The coefficient of quartile deviation is defined as the ratio of the quartile deviation to the average (or mean) of the data.
Coefficient of Q.D = (Q.D / Average) * 100
Given that Q.D = 15 and the coefficient of Q.D = 0.3, we can rearrange the formula for the coefficient to find the average (or mean):
Average = (Q.D / (coefficient of Q.D / 100))
Therefore, the average (or mean) is:
Average = (15 / (0.3 / 100)) = 500
To find the value for which 75% of the observations are less than, we need to calculate Q3 using the formula:
Q3 = average + (Q.D * 0.75)
Q3 = 500 + (15 * 0.75) = 500 + 11.25 = 511.25
Hence, 75% of the observations are less than 511.25.
Since none of the given answer options match this value, there seems to be a mistake in the provided options.