Relative Dispersion of Family Incomes in Two Neighborhoods | CFA Level 1 Exam Answer

Relative Dispersion of Family Incomes

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Question

Mr. and Mrs. Jones live in a neighborhood where the mean family income is $45,000 with a standard deviation of $9,000. Mr. and Mrs. Smith live in a neighborhood where the mean is $100,000 and the standard deviation is $30,000. What is the relative dispersion of the family incomes in the two neighborhoods?

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A. B. C. D. E.

A

The coefficient of variation = (s*100)/mean. Jones: 9000*100/45,000 = 20%. Smith: 30,000*100/100,000 = 30%.

To calculate the relative dispersion of family incomes in the two neighborhoods, we need to compare the standard deviations of the incomes relative to their respective means.

For Mr. and Mrs. Jones' neighborhood: Mean income = $45,000 Standard deviation = $9,000

For Mr. and Mrs. Smith's neighborhood: Mean income = $100,000 Standard deviation = $30,000

The relative dispersion is calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage.

Relative dispersion for Mr. and Mrs. Jones' neighborhood: Jones' relative dispersion = (Standard deviation / Mean income) * 100 = ($9,000 / $45,000) * 100 = 20%

Relative dispersion for Mr. and Mrs. Smith's neighborhood: Smith's relative dispersion = (Standard deviation / Mean income) * 100 = ($30,000 / $100,000) * 100 = 30%

Therefore, the relative dispersion of family incomes in the two neighborhoods is: Jones 20%, Smith 30%.

Hence, the correct answer is option A: Jones 20%, Smith 30%.

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