91Ó°ÊÓ

The given information is:

The highest bars in the histograms are to the left, while a tail of lower bars is to the right, both distributions are skewed to the right.

The largest bar in both histograms is centered at 2, the most common number of people in a family and a household is both 2.

The histogram of families is narrower than the histogram of households, the spread of the number of people in a household is bigger than the spread of the number of people in a family.

There are no outliers in either distribution since there are no gaps in the histogram.

Mean of Household:

$$\begin{gathered} \mathrm{μ}=∑xP\left(X=x\right) \\ =1×0.25+2×0.32+3×0.17+4×0.15+5×0.07+6×0.03+7×0.01 \\ =2.6 \end{gathered}$$

Mean of Family:

$$\begin{gathered} \mathrm{μ}=∑xP\left(X=x\right) \\ =1×0+2×0.42+3×0.23+4×0.21+5×0.09+6×0.03+7×0.02 \\ =3.14 \end{gathered}$$

We can see that the Family has a greater expected value than the household which means all household has a minimum of one person and all families have a minimum of 2 persons.

The histogram of the household distribution is bigger, we inferred in part (a) that the spread of the home distribution was greater than the spread of the family distribution.

This is supported by standard deviations, which show that the household standard deviation is higher than the family standard deviation.

Furthermore, this makes sense because a household can only have one person, whereas a family must always have more than one person, and so there are more possible values for such a number of people in a household (leading to a higher standard deviation).