Question

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Median age 25.1 24.6 24.3 24.3 22.8 22.8 23.2 24.7 26.1 26.8 What does it mean in this situation if the average rate of change is negative?

1) It means that the median age of a man at the time of his first marriage is increasing.
2) It means that the median age of a man at the time of his first marriage is decreasing.
3) It means that the median age of a man at the time of his first marriage has a constant rate of change.
4) There is no way to determine the average rate of change in this situation.

Answer 1

The negative average rate of change in the median marrying age for American men implies that this age is decreasing. However, the provided data from 1910 to 2000 show that the median age has actually increased from 25.1 to 26.8 years.

Step-by-step explanation:

When statisticians calculate the median age of first marriage for American men, they are observing the central trend over time. From the data provided by the U.S. Census Bureau, we can calculate the average rate of change in the median marrying age over various decades. If this rate of change is negative, it means that the median age of a man at the time of his first marriage is decreasing. Conversely, a positive rate of change would indicate an increasing trend in the marrying age.

Looking at the sequence of the median age provided (25.1, 24.6, 24.3, 24.3, 22.8, 22.8, 23.2, 24.7, 26.1, 26.8), we notice fluctuations over the decades. However, the median age in 1910 was 25.1 years and increased to 26.8 years by 2000. Therefore, over the 90-year span, the median age has increased.

Answering the student question directly, if the average rate of change is negative, the correct interpretation is option 2: "It means that the median age of a man at the time of his first marriage is decreasing." In this case, though, the trend from 1910 to 2000 reflects an overall increase, not decrease, in the median age of men's first marriage.