Question

In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38
a) What is the approximate value of the third quartile (Q3 ), correct to 2 decimal places.
b)What is the approximate value of the variance, correct to the nearest whole number

Answer 1

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;

$SK = \dfrac{Q_{3}+Q_{1}-2Q_{_{2}}}{Q_{3}-Q_{1}}$

Plugging in the values, we have;

$-0.38 = \dfrac{Q_{3}+30.8-2 \times 48.5_{_{}}}{Q_{3}-30.8}$

Solving gives Q₃ = 56.45

b) To determine the variance, we use the skewness formula as follows;

$SK_{p} = \dfrac{Mean-\left (3\times Median - 2\times Mean \right )}{\sigma } = \dfrac{3\times\left ( Mean - Median \right )}{\sigma }$

Plugging in the values, we get;

$-0.38= \dfrac{42-\left (3\times 48.5- 2\times 42\right )}{\sigma } = \dfrac{-19.5}{\sigma}$

$\therefore \sigma =\dfrac{-19.5}{-0.38} = 51.32$

The variance = σ² = 51.32² = 2633.31.