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,
= 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}](https://tex.z-dn.net/?f=SK%20%3D%20%5Cdfrac%7BQ_3%20%2B%20Q_1%20-%202%20%5Ctimes%20Q_2%7D%7BQ_3%20-%20Q_1%7D)
Plugging in the values, we have;
![-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}](https://tex.z-dn.net/?f=-0.38%20%3D%20%5Cdfrac%7BQ_3%20%2B%2030.8%20-%202%20%5Ctimes%2048.5%7D%7BQ_3%20-%2030.8%7D)
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.