What type of variable is required when drawing a time-series plot? Why do we draw time-series plots?
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2. Describing Data with Tables and Graphs
Time-Series Graph
Problem 2.2.18d
Textbook Question
"Age at First Marriage The following time-series plot shows the average age at which individuals first marry by gender for each year of the census since 1890.

d. In which year was the difference in the average age of men and women at which they first married the least?"
Verified step by step guidance1
Identify the two lines on the graph: the blue line represents the average age at first marriage for men, and the red line represents the average age at first marriage for women.
For each year shown on the x-axis, note the corresponding average ages for men and women from the y-axis values.
Calculate the difference in average age between men and women for each year by subtracting the women's average age from the men's average age: \(\text{Difference} = \text{Age}_{men} - \text{Age}_{women}\).
Compare these differences across all years to find the smallest difference value.
Identify the year corresponding to this smallest difference, which is the year when the average ages at first marriage for men and women were closest.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Time-Series Data
Time-series data consists of observations collected sequentially over time. In this question, the average age at first marriage is recorded for men and women across different census years, allowing us to analyze trends and changes over time.
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Difference Between Two Data Series
To find the year with the least difference in average age at first marriage between men and women, we calculate the absolute difference between the two series for each year. The smallest difference indicates the year when the ages were closest.
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Probabilities Between Two Values
Graph Interpretation
Interpreting line graphs involves reading data points accurately and comparing trends. Here, understanding how to read the plotted points for men and women and visually or numerically comparing their values is essential to answer the question.
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