In a frequency distribution,the coefficient of skewness based upon the quartile is 0.6 . if the sum of the upper and lower Quartile is 100 and median is 38 ,find the value of quartiles hence compute ?

To find the value of the quartiles, we need to use the formula for the coefficient of skewness based on the quartiles:

Coefficient of skewness = (Q3 + Q1 - 2 * Median) / (Q3 - Q1)

Given that the coefficient of skewness is 0.6 and the median is 38, we can substitute these values into the formula:

0.6 = (Q3 + Q1 - 2 * 38) / (Q3 - Q1)

We also know that the sum of the upper and lower quartiles is 100, so we can write another equation:

Q3 + Q1 = 100

Now we have a system of two equations with two unknowns (Q3 and Q1). We can solve this system to find the values of the quartiles.

First, let's solve the second equation for Q3:

Q3 = 100 - Q1

Substituting this into the first equation, we get:

0.6 = (100 - Q1 + Q1 - 2 * 38) / (100 - Q1 - Q1)

0.6 = (100 - 2 * 38) / (100 - 2 * Q1)

0.6 = (100 - 76) / (100 - 2 * Q1)

0.6 = 24 / (100 - 2 * Q1)

Multiplying both sides by (100 - 2 * Q1), we get:

0.6 * (100 - 2 * Q1) = 24

60 - 1.2 * Q1 = 24

Subtracting 60 from both sides, we get:

-1.2 * Q1 = -36

Dividing both sides by -1.2, we get:

Q1 = 30

Substituting this value back into the equation Q3 + Q1 = 100, we get:

Q3 + 30 = 100

Subtracting 30 from both sides, we get:

Q3 = 70

Therefore, the value of the lower quartile (Q1) is 30 and the value of the upper quartile (Q3) is 70.