Answer :
Answer:
a) The third quartile Q₃ = 56.45
b) The variance = 2633.31
Step-by-step explanation:
a) The coefficient of skewness formula is given as follows;
[tex]SK = \dfrac{Q_{3}+Q_{1}-2Q_{_{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]
Solving gives Q₃ = 56.45
b) To determine the variance, we use the skewness formula as follows;
[tex]SK_{p} = \dfrac{Mean-\left (3\times Median - 2\times Mean \right )}{\sigma } = \dfrac{3\times\left ( Mean - Median \right )}{\sigma }[/tex]
Plugging in the values, we get;
[tex]-0.38= \dfrac{42-\left (3\times 48.5- 2\times 42\right )}{\sigma } = \dfrac{-19.5}{\sigma}[/tex]
[tex]\therefore \sigma =\dfrac{-19.5}{-0.38} = 51.32[/tex]
The variance = σ² = 51.32² = 2633.31.