Answer:
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, [tex]\bar x[/tex] = 42.0
Coefficient of skewness = -0.38
The Bowley's coefficient of skewness (SK) is given as follows;
[tex]SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}[/tex]
Plugging in the values, we have;
[tex]-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}[/tex]
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.
