Question

In the distribution, the first quartile,median and mean are 30.8,48.5 and 42.0 respectively. If the co efficient skewness is -0.38, find the third quartile?

Answer 1

The third quartile is 56.45

Explanation:

The given parameters are;

The first quartile, Q₁ = 30.8

The median or second quartile, Q₂ = 48.5

The mean,
`\bar x` = 42.0

Coefficient of skewness = -0.38

The Bowley's coefficient of skewness (SK) is given as follows;

`SK = (Q_3 + Q_1 - 2 * Q_2)/(Q_3 - Q_1)`

Plugging in the values, we have;

`-0.38 = (Q_3 + 30.8 - 2 * 48.5)/(Q_3 - 30.8)`

Which gives;

-0.38×(Q₃ - 30.8) = Q₃ + 30.8 - 2 × 48.5

11.704 - 0.38·Q₃ = Q₃ - 66.2

1.38·Q₃ = 11.704 + 66.2 = 77.904

Q₃ = 56.45

The third quartile = 56.45.