Question

# In government data, a house-hold consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are

Sampling distributions

In government data, a house-hold consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.

$$\text{Number of people}\\ \begin{array}{|l|c|c|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \\ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \\ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}$$

Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family. The standard deviations of the 2 random variables are $$\sigma H=1.421$$ and $$\sigma F=1.249.$$ Explain why this difference makes sense.

2021-06-16

Given:
Household $$\sigma = 1.421$$
Family $$\sigma = 1.249$$
In part (a), we concluded that the spread of the household distribution was greater than the spread of the family distribution, becatise the histogram of the household distribution is wider.
This is confirmed hy the standard deviations, hecausethe standard deviation of household is greater than the standard deviation of family.
Moreover, this also makes sense, becatise a hotischold can contain 1 individual but a family always needs to contain more than 1 individual and thus there are more possible values for the number of individuals in a household (making its standard deviation greater).