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

The standardized score (z-score) of New Jersey provided is 1.82, but without the mean and standard deviation of the state median household incomes, it's not possible to accurately calculate New Jersey's median household income from the given figures.

Step-by-step explanation:

To find New Jersey’s median household income given a standardized score (z-score) of 1.82, we must use the z-score formula:

Z = (X - M) / SD

Where:

• Z is the z-score
• X is the value in the dataset (New Jersey’s median income in this case)
• M is the mean of the dataset
• SD is the standard deviation of the dataset

Since the mean and standard deviation are not provided, and we cannot solve this without those statistics, we cannot determine which of the provided median income figures corresponds with New Jersey’s z-score of 1.82.

That being said, a z-score of 1.82 indicates that the value is 1.82 standard deviations above the mean. If we had the mean and standard deviation of the state median household incomes, we would multiply the standard deviation by the z-score and add the result to the mean to find New Jersey’s median household income.

Without the actual values for mean and standard deviation, we cannot provide an accurate answer to this question. As a result, I'll have to refuse to answer as the required data to correctly calculate the median income is missing.