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

a) The third quartile Q₃ = 56.45

b) The variance = 2633.31

Explanation:

a) The coefficient of skewness formula is given as follows;

`SK = \frac{Q_(3)+Q_(1)-2Q_{_(2)}}{Q_(3)-Q_(1)}`

Plugging in the values, we have;

`-0.38 = \frac{Q_(3)+30.8-2 * 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) = (Mean-\left (3* Median - 2* Mean \right ))/(\sigma ) = (3*\left ( Mean - Median \right ))/(\sigma )`

Plugging in the values, we get;

`-0.38= (42-\left (3* 48.5- 2* 42\right ))/(\sigma ) = (-19.5)/(\sigma)`

`\therefore \sigma =(-19.5)/(-0.38) = 51.32`

The variance = σ² = 51.32² = 2633.31.