3. The data below is a small sample of household income brackets, taken from the

Question

3. The data below is a small sample of household income brackets, taken from the 2010 US census. Income House n House- Income House- class ($k) holds! class (%) holds! class (Sk) holds .176 70-75 5,055 75-80 7,061 80-85 7,260 85-90 6,93790-95 6,730 95-100 6,148 100-105 2,498170-175 5,907 105-110 ,778175-180 3,769 140-145 3,118 145-150 3,143 150-155 2,680 155-160 2,516 160-165 2,110 165-170 974 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 983 671 636 541 472 464 335 358 290 4,627 110-115 1,782 180-185 1,480 185-190 4,933 115-120 5,088 120-125 ,470 190-195 4,203 125-130 24195-200 ,412 130-135 ,236 >200 3,579 135-140 1,058 65-70 The total numer of households in the sample is 118,683. The sample mean is S67,530, and the sample median is $49,445. (a) Because we don't have the actual sample data (i.e, for each distinct house- hold in the sample), assume that all households in a given income bracket (i.e., class) have incomes in the middle of the bracket. So in other words, assume ll households in the $65-70k bracket have an income of $67.5k. Given this assumption, find the average (i.e, menincome for all house- holds making under $200k. (b) Given that the mean income for the entire sample is $S67,530, find the mean income for all households making over $200k. Does the answer seem

Explanation / Answer

For solving this problem we will use MS-EXCEL

a) 1) input all ranges of income in two distinct collumns in spreadsheet.

2) compute average of these two collumns in another collumn. This gives the assumption of income of households

3) compute some of these averages.

4) we want to calculate average income for all households under 200k.

Therefore, sample size = total sample size - sample size over 200k income

i.e. sample size= 118683-4627

= 114056

5) average income of average f all households under 200k = some of averages/ sample size

= 4000/114056

= $0.03507k= $35.07049

b) we want to calculate average income for all households over 200k

1) total income will be, average income* total population

Total income= $8014662990

Income of households over 200k is

Total income- income under 200k

= $8010662990

Average income over 200k will be

= Income of households over 200k/ toatl nu of households over 200k

= 8010662990/4627

= $1731286.58

a) average income of all households under 200k= $35.07049

b) average income of all households over 200k = $1731286.58

  

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