In frequency distribution, the coefficient of skewness based on the quartiles is given to be 0.4. If the sum of the upper and lower quartile is 100 and the median is 38, find the values of the upper and lower quartiles

Answer 1

Let Q1 be the lower quartile, Q3 be the upper quartile, and M be the median.

The coefficient of skewness is given by (Q3 - 2M + Q1) / (Q3 - Q1).

We are given that Q1 + Q3 = 100 and M = 38.

Substituting the given values, we have (Q3 - 2(38) + Q1) / (Q3 - Q1) = 0.4.

Simplifying the equation, we get (Q3 - 76 + Q1) / (Q3 - Q1) = 0.4.

Multiplying both sides by (Q3 - Q1), we have Q3 - 76 + Q1 = 0.4(Q3 - Q1).

Expanding and simplifying further, we get Q3 - 76 + Q1 = 0.4Q3 - 0.4Q1.

Combining like terms, we obtain 0.6Q3 - 0.6Q1 = 76.

Since we know that Q1 + Q3 = 100, we can rewrite the equation as 0.6Q3 - 0.6(100 - Q3) = 76.

Simplifying, we get 0.6Q3 - 60 + 0.6Q3 = 76.

Combining like terms, we have 1.2Q3 - 60 = 76.

Adding 60 to both sides, we get 1.2Q3 = 136.

Dividing both sides by 1.2, we obtain Q3 = 113.33.

Since Q1 + Q3 = 100, we can solve for Q1 by subtracting Q3 from both sides, giving Q1 = 100 - 113.33.

Simplifying, we have Q1 = -13.33.

Therefore, the lower quartile is -13.33 and the upper quartile is 113.33.