Question

2071 Old Q.No.5 Person's coefficient of skewness for a distribution is 0.4 and its coefficient of variation is 30%. If mode is 88, find mean and median.​

Answer 1

Answer:

$Mean = 100$

$Median = 96$

Step-by-step explanation:

Given

$C_v = 30\%$ --- coefficient of variation

$mode = 88$

$Skp = 0.4$

Required

The mean and the median

The coefficient of variation is calculated using:

$C_v = \frac{\sigma}{\mu}$

Where:

$\mu \to$ mean

So:

$30\% = \frac{\sigma}{\mu}$

Express percentage as decimal

$0.30 = \frac{\sigma}{\mu}$

Make $\sigma$ the subject

$\sigma = 0.30\mu$

The coefficient of skewness is calculated using:

$Skp = \frac{\mu - Mode}{\sigma}$

This gives:

$0.4 = \frac{\mu - 88}{\sigma}$

Make $\sigma$ the subject

$\sigma = \frac{\mu - 88}{0.4 }$

Equate both expressions for $\sigma$

$0.30\mu = \frac{\mu - 88}{0.4 }$

Cross multiply

$0.4*0.30\mu = \mu - 88$

$0.12\mu = \mu - 88$

Collect like terms

$0.12\mu - \mu = - 88$

$-0.88\mu = - 88$

Divide both sides by -0.88

$\mu = 100$

Hence:

$Mean = 100$

Calculate $\sigma$

$\sigma = 0.30\mu$

$\sigma = 0.30 * 100$

$\sigma = 30$

So:

Also, the coefficient of skewness is calculated using:

$Skp = \frac{3 * (Mean - Median)}{\sigma}$

$0.4= \frac{3 * (100 - Median)}{30}$

Multiply both sides by 30

$0.4*30= 3 * (100 - Median)$

Divide both sides by 3

$0.4*10= 100 - Median$

$4= 100 - Median$

Collect like terms

$Median = 100 - 4$

$Median = 96$