"Household size" is defined as the number of people living in a household. In a sample of 1200 households in California in 2010, the average household size was 2.9 people. Which of the following conclusions can be drawn from this information? Select all that are correct.
a) There must have been an error in the calculation, because no household can have 2.9 people.
b) The typical household in the sample consisted of 2.9 people.
c) There were 3480 people living in the sampled households.
d) In the sample, 600 households had fewer than 2.9 people.
To answer this question, let's analyze the given information and the options:
The information provided states that in a sample of 1200 households in California in 2010, the average household size was 2.9 people.
Now, let's go through each option and determine if it can be drawn from this information:
a) There must have been an error in the calculation, because no household can have 2.9 people.
This conclusion is incorrect. While it is true that a household cannot have a fractional number of people, the average household size can be a decimal value. It is calculated by dividing the total number of people in all households by the total number of households.
b) The typical household in the sample consisted of 2.9 people.
This conclusion is correct. The average household size of 2.9 people indicates that, on average, the households in the sample had 2.9 people.
c) There were 3480 people living in the sampled households.
This conclusion is incorrect. To calculate the total number of people living in the sampled households, we need to multiply the average household size by the total number of households. Therefore, 2.9 people/household * 1200 households equals 3480 people.
d) In the sample, 600 households had fewer than 2.9 people.
To draw this conclusion, we would need additional information. The provided information only gives the average household size, not the specific number of households that fall below or exceed this average.
Based on the analysis, the correct conclusions that can be drawn from the given information are:
- The typical household in the sample consisted of 2.9 people.
- There were 3480 people living in the sampled households.
Therefore, the correct options are b) and c).