Q. 29 - Elementary Statistics

Question

29. Reshaping the Labor Force. The following graph is based on one that appeared in an Arizona Republic newspaper article entitled "Hand That Rocked Cradle Turns to Work as Women Reshape U.S. Labor Force." The graph depicts the labor force participation rates for the years 1960,1980 , and 2000 .

a. Cover the numbers on the vertical axis of the graph with a piece of paper.
b. Look at the 1960 and 2000 graphs for women, focusing on the 35 to 44-year-old age group. What impression does the graph convey regarding the ratio of the percentages of women in the labor force for 1960 and 2000 ?
c. Now remove the piece of paper from the graph. Use the vertical scale to find the actual ratio of the percentages of 35 - to 44-yearold women in the labor force for 1960 and 2000.
d. Why is the graph potentially misleading?
e. What can be done to make the graph less potentially misleading?

Step-by-Step Solution

Answer

(a) Ignore the vertical axis scaling.

(b) Within $40$ years, the female population tripled.
(c) Women make up roughly $70\%$of the population in $2000$, compared to $40\%$ in $1996$.

(d) The frequency and relative frequency is given below:

(e) The graph less potentially misleading as:

Part (a) Step 1: Given information

To cover the numbers on the vertical axis of the graph with a piece of paper.

Part (a) Step 2: Explanation

The number of data values that fall into a class is known as frequency.
When answering the question, ignore the vertical axis scaling.

Part (b) Step 1: Given information

To find the impression does the graph convey regarding the ratio of the percentages of women in the labor force for $1960$and $2000$.

Part (b) Step 2: Explanation

Each category is represented as a slice in a pie chart.
In $2000$, the percentage of women has more than tripled compared to $1960$.
As a result, within $40$ years, the female population tripled.

Part (c) Step 1: Given information

To use the vertical scale to find the actual ratio of the percentages of $35$ - to $44$ -year old women in the labor force for $1960$ and $2000$.

Part (c) Step 2: Explanation

The number of data values that fall into a class is known as frequency.
Women make up roughly $70\%$ of the population in $2000$, compared to $40\%$ in $1996$.

As a result, the percentage of women in $2000$ is about $70\%$ but in $1996$ it was about $40\%$.

Part (d) Step 1: Given information

To determine whether the graph potentially misleading.

Part (d) Step 2: Explanation

The number of data values that fall into a class is known as frequency. The frequency and relative frequency is given below:

Part (e) Step 1: Given information

To determine and make the graph less potentially misleading.

Part (e) Step 2:Explanation

Each category is represented as a slice in a pie chart. The graph less potentially misleading as: