If X and Y are related as 3X – 4Y = 20 and the quartile deviation of X is 12,then the quartile deviation of Y is :(a) 14(b) 15(c) 16(d) 9

The quartile deviation, also known as the semi-interquartile range, is a measure of statistical dispersion. It is half the difference between the upper and lower quartiles.

Given the relationship between X and Y as 3X – 4Y = 20, we can express Y in terms of X as follows:

4Y = 3X - 20 Y = (3/4)X - 5

The quartile deviation of Y will be affected by the coefficient of X in this equation. The constant term (-5) does not affect the quartile deviation because it simply shifts the data without changing its spread.

Therefore, the quartile deviation of Y is (3/4) times the quartile deviation of X.

Given that the quartile deviation of X is 12, the quartile deviation of Y is (3/4)*12 = 9.

So, the answer is (d) 9.