Answer:

[tex]Mean = 100[/tex]

[tex]Median = 96[/tex]

Step-by-step explanation:

Given

[tex]C_v = 30\%[/tex] — coefficient of variation

[tex]mode = 88[/tex]

[tex]Skp = 0.4[/tex]

Required

The mean and the median

The coefficient of variation is calculated using:

[tex]C_v = \frac{\sigma}{\mu}[/tex]

Where:

[tex]\mu \to[/tex] mean

So:

[tex]30\% = \frac{\sigma}{\mu}[/tex]

Express percentage as decimal

[tex]0.30 = \frac{\sigma}{\mu}[/tex]

Make [tex]\sigma[/tex] the subject

[tex]\sigma = 0.30\mu[/tex]

The coefficient of skewness is calculated using:

[tex]Skp = \frac{\mu – Mode}{\sigma}[/tex]

This gives:

[tex]0.4 = \frac{\mu – 88}{\sigma}[/tex]

Make [tex]\sigma[/tex] the subject

[tex]\sigma = \frac{\mu – 88}{0.4 }[/tex]

Equate both expressions for [tex]\sigma[/tex]

[tex]0.30\mu = \frac{\mu – 88}{0.4 }[/tex]

Cross multiply

[tex]0.4*0.30\mu = \mu – 88[/tex]

[tex]0.12\mu = \mu – 88[/tex]

Collect like terms

[tex]0.12\mu – \mu = – 88[/tex]

[tex]-0.88\mu = – 88[/tex]

Divide both sides by -0.88

[tex]\mu = 100[/tex]

Hence:

[tex]Mean = 100[/tex]

Calculate [tex]\sigma[/tex]

[tex]\sigma = 0.30\mu[/tex]

[tex]\sigma = 0.30 * 100[/tex]

[tex]\sigma = 30[/tex]

So:

Also, the coefficient of skewness is calculated using:

[tex]Skp = \frac{3 * (Mean – Median)}{\sigma}[/tex]

[tex]0.4= \frac{3 * (100 – Median)}{30}[/tex]

Multiply both sides by 30

[tex]0.4*30= 3 * (100 – Median)[/tex]

Divide both sides by 3

[tex]0.4*10= 100 – Median[/tex]

[tex]4= 100 – Median[/tex]

Collect like terms

[tex]Median = 100 – 4[/tex]

[tex]Median = 96[/tex]

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