It is estimated that 46% of people live in households with 1 or 2​ people, 10% live in households with 3 or 4​ people, and 3% live in households with 5 or more people. Using 1.5 for the expected number of people in households with 1 or 2​ people, 3.5 for households with 3 or 4​ people, and 6 for households with 5 or more​ people, find the expected number of people in a regular household. How is this related to the mean household​ size?

For households with 1 or 2 people: 46% of households have 1 or 2 people, and we’re using 1.5 as the expected number of people in these households. So, the contribution to the total from these households is 0.46 * 1.5 = 0.69. For households with 3 or 4 people: 10% of households have 3 or 4 people, and we’re using 3.5 as the expected number of people in these households. So, the contribution to the total from these households is 0.10 * 3.5 = 0.35. For households with 5 or more people: 3% of households have 5 or more people, and we’re using 6 as the expected number of people in these households. So, the contribution to the total from these households is 0.03 * 6 = 0.18. Adding these up gives us 0.69 + 0.35 + 0.18 = 1.22. So, the expected number of people in a regular household is 1.22 This expected number is essentially a weighted average, and it represents the mean household size. The weights are given by the percentages of households in each category (1 or 2 people, 3 or 4 people, and 5 or more people). The mean household size is a measure of central tendency that gives us an idea of what a “typical” household might look like in terms of its size.