Mathematics: 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?

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In the distribution, the first quartile,median

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28.01.2022

The third quartile is 56.45

Step-by-step 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;

$SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}$

Plugging in the values, we have;

$-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}$

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.

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