Erica found the mean of the yearly incomes of a sample of households in her hometown as shown in the chart below. In a report, she stated, “The typical income in my neighborhood is about $81,500 per year.” How is this misleading?

Question

Erica found the mean of the yearly incomes of a sample of households in her hometown as shown in the chart below. In a report, she stated, “The typical income in my neighborhood is about $81,500 per year.” How is this misleading?

$35,000 $25,000 $28,000 $30,000 $35,000
$225,000 $18,000 $12,000 $25,000 $26,000
$390,500 $16,250 $320,325 $22,000 $29,500
$32,300 $22,200 $18,500 $30,500 $290,000
A. The mean of the data is not about $81,500.
B. Erica’s statement is not misleading.
C. The mean is not a good measure of the incomes because a few higher incomes pull the mean higher than most of the household incomes.
D. The mean is not a good measure of the incomes because the lower incomes pull the mean lower than most household incomes.

Answer 1

C. The mean is not a good measure of the incomes because a few higher incomes pull the mean higher than most of the household incomes.

Answer 2

Game wardens use experiments to help determine the number of deer in the state of North Carolina. Suppose 120 deer are caught, tagged, and released back into the wild. A month later, 800 deer are caught with 16 found to have tags. Using this information, estimate the number of deer in North Carolina.

A. 800
B. 1,200
C. 1,920
D. 6,000

Answer 3

C. 1,920

To estimate the number of deer in North Carolina, we can use the formula:

(Number of deer caught and tagged in first sample x Total number of deer in second sample) / Number of tagged deer in second sample = Estimated total number of deer

Plugging in the given values, we get:

(120 x 800) / 16 = 6,000

Therefore, the estimated total number of deer in North Carolina is 6,000.

Answer 4

The correct answer is C. The mean is not a good measure of the incomes because a few higher incomes pull the mean higher than most of the household incomes.

This is misleading because the mean is influenced by extreme values, such as the very high incomes in the data set. These high incomes significantly increase the mean and make it appear higher than what most households actually earn. Therefore, the mean is not representative of the typical income in the neighborhood.