Question

Household incomes Rich and poor households differ in ways that go beyond income. Here are histograms that compare the distributions of household size (number of people) for low-income and high-income households. 50 Low-income households had annual incomes less than \(15,000, and high-income households had annual incomes of at least \)100,000

Part (a). About what percent of each group of households consisted of four or more people?

Part (b). Describe the similarities and differences in these two distributions of household size.

Short answer

Part (a)

Low income 11%

High income 39%

Part (b)

Similarities

We see that household sizes range from 1 to 7 for both low and high income groups.

Outliers exist in neither distribution.

Both distributions lean to the right.

Differences

The distribution of low income is skewed more than the distribution of high income.

The low income distribution's center is at 1, while the high income distribution's center is at 2.

Step-by-step solution

Part (a) Step 1. Given information

Low-income households had annual incomes less than $15,000, and high-income households had annual incomes of at least $100,000.

Part (a) Step 2. percent of each household group had four or more people

Low income households

Let us first calculate the percentage of each bar in the histogram, which is given by the bar's height.

Household size	Percent
1	58
2	20
3	11
4	5
5	3
6	2
7	1
Total	58+20+11+5+3+2+1 = 100

We then note that 5% +3% +2% +1% = 11% of the 100% households consist of four or more people.

High income households

Let us first calculate the percentage of each bar in the histogram, which is given by the bar's height.

Household size	Percent
1	7
2	33
3	21
4	23
5	11
6	3
7	2
Total	7+33+21+23+11+3+7 = 100

We then note that 23% +11% +3% +2% = 39% of the 100% households consist of four or more people.

As a result

Low income 11%

High income 39%

Part (b) Step 1. The similarities and differences between these two household size distributions

Similarity:

We observe that household sizes range from 1 to 7 for both low and high income groups (as the bars in the histogram have vales 1 to 7 on the horizontal axis).

Because there are no gaps in either histogram, neither disution contains outliers.

Because the highest bar in the histogram is to the left, with a tail of smaller bars to the right, both distributions are skewed to the right.

Difference:

The low-income distribution is skewed to the right because the highest bar in the histogram is to the left, with a tail of smaller bars to the right. The distribution of high income, on the other hand, is less skewed to the right.

because the highest bar in the histogram is slightly more to the right (although the histogram still shows an overall right skewed distribution).

Because the highest bar in the histogram is at 1 on the horizontal axis, the center of the low income distribution is at 1. The center of the high income distribution, on the other hand, is at 2, because the highest bar in the histogram is at 2 on the horizontal axis.

As a result:

Similarities:

We see that household sizes range from 1 to 7 for both low and high income groups.

Outliers exist in neither distribution.

Both distributions lean to the right.

Differences:

The distribution of low income is skewed more than the distribution of high income.

The low income distribution's centre is at 1, while the high income distribution's centre is at 2.