A sociologist is studying the relationship between parents’ ages and their parenting practices. The sociologist collects a random sample of 20 married couples, each of whom has an eight-year-old boy.
The sociologist decides to refer to the moms’ ages as X and the dads’ ages as Y. The sum of the moms’ ages in the sociologist’s sample is 764 years (or, written in symbols, ∑X = 764). The sum of the dads’ ages in her sample is 802 years (or, written in symbols, ∑Y = 802).
Since the sociologist is interested in how the difference in the parents’ ages affects their parenting practices, she needs the sum of the differences in their ages, or ∑(Y – X). The sum of the differences in the parents’ ages in the sociologist’s sample is years.
The sociologist decides to look at variables associated with the eight-year-old boys’ births. To do so, she wants to consider the parents’ ages eight years ago at the time of the boys’ births. The sum of the dads’ ages eight years ago, or ∑(Y – 8), is years.
The sociologist decides to convert the current ages to months. The sum of the moms’ ages in months, or ∑12X, is months.