Question

2) The graph below represents household income for the US population in the year 2005. The average (mean) income was $63,344 and the median income was $46,326. population standard deviation of $27,435. Assume a 112,363,000 households below $250,000 150000 Total 114,384,000 households 94 705 1250,000 a. Explain why the Empirical rule cannot be used for this data. Why would Chebyshev's rule be a good alternative? According to Chebyshev's rule, what income range would have at least the middle 75% of the population? b. A household income of $120,000 is more than 2 standard deviations higher than the mean for US household incomes in 2005. Would an income of $120,000 be considered unusual? Justify your answer. c.

Answer 1

a) Since the distribution histogram appears to be extremly skewed towards right hence we cannot use emperical rule which is only applied to a normal distribution which is symmetric in appearance. So for Non normal distribution we use chebychev's Theorem.

b) According to chebychev's 75 % middle of population lies within 2 standard devaition , hence, dara within 2 standard deviaion

where SD=$27425 and Mean=$63344

63344-2*27425=$8494 to 63344+2*27425=$118194

c) SInce the distribution is not symmetric and is right skewed then it follows chebychev's rule by which we calculated above that 2 standard deviation the value is 118194 and the value 120000 is more than 2 standard deviayon which is unusual here .