Question

The cumulative relative frequency graph describes the distribution of median household incomes in the 50 states in a recent year. Given are summary statistics for the state median household incomes. New Jersey had a standardized score of 1.82.

Find New Jersey’s median household income for that year.

$51,740.62
$51,742.44
$66,685.80
$64,952.36
$36,799.08

Answer 1

New Jersey’s median household income for that year was approximately $66,685.80.

New Jersey's standardized score = 1.82

The mean median household income = $51,742.44

The standard deviation = $8,210.64

The standardized score, also known as the z-score, measures how many standard deviations an element is from the mean.

New Jersey’s median household income's z-score = 1.82. Therefore, New Jersey's median household income is 1.82 standard deviations above the mean.

New Jersey’s median household income using the formula:

Median household income = Mean + Z-score x Standard Deviation

Substituting:

Median household income = 51742.44 +1.82 x 8210.64 ≈ 66,685.80

Thus, we can conclude that New Jersey’s median household income for that year was approximately $66,685.80.