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.

What does it mean in this situation if the average rate of change is negative?
a.
It means that the median age of a man at the time of his first marriage is increasing.
b.
It means that the median age of a man at the time of his first marriage is decreasing.
c.
It means that the median age of a man at the time of his first marriage has a constant rate of change.
d.
There is no way to determine the average rate of change in this situation.

The Answer is D

Answer 1

D

Explanation:

took the test

Answer 2

If the average rate of change in the data is negative, based on the variables analyzed;

b. It means that the median age of a man at the time of his first marriage is decreasing

Explanation:

The given data is presented as follows;

Year;
`{}` 1910, 1920, 1930, 1940, 1950, 960, 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

The date points are plotted on a graph using Microsoft Excel

`The \ average \ rate \ of \ change = (The \ change \ in \ the \ median \ age)/(The \ corresponding \ change \ in \ years \ (always \ +ve))`The corresponding change in years, Δx, is positive because, we have;

Δx = x₂ - x₁ = Higher year - Previous year

Therefore, for a negative average rate of change, we have;

`The \ average \ rate \ of \ change = -ve = (The \ change \ in \ the \ median \ age)/(+ve)`

∴ The change in the median age, Δy = +ve × (-ve) = -ve (negative)

Δy = -ve

∴ Δy = Median age for higher year - Median age for previous year = -ve

Median age for higher year = -(y) + Median age for previous year

Where 'y' is positive

∴ Median age for subsequent year < Median age for previous year

Therefore, if the average rate of change is negative, the median age of a man's first marriage is decreasing