91Ó°ÊÓ

The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household (http://www.census.gov, March 20, 2006). The following data show the age at the time of first marriage for a sample of men and a sample of women. \\[ \begin{array}{lcccccccc} \text { Men } & 26 & 23 & 28 & 25 & 27 & 30 & 26 & 35 & 28 \\ & 21 & 24 & 27 & 29 & 30 & 27 & 32 & 27 & 25 \\ \text { Women } & 20 & 28 & 23 & 30 & 24 & 29 & 26 & 25 & \\ & 22 & 22 & 25 & 23 & 27 & 26 & 19 & & \end{array} \\] a. Determine the median age at the time of first marriage for men and women. b. Compute the first and third quartiles for both men and women. c. Twenty-five years ago the median age at the time of first marriage was 25 for men and 22 for women. What insight does this information provide about the decision of when to marry among young people today?

Step by step solution

01

Organize the Data

First, we need to organize the ages for both men and women in ascending order for easier calculations in subsequent steps. - **Men:** 21, 23, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 30, 30, 32, 35 - **Women:** 19, 20, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 29, 30

02

Find the Median for Men

To find the median, locate the middle value in the sorted data set for men. Since there are 17 values: - The median is the 9th value. - **Median for Men:** The 9th value is 27.

03

Find the Median for Women

Similarly, find the median for the women's data set. There are 15 values: - The median is the 8th value. - **Median for Women:** The 8th value is 25.

04

Find the First and Third Quartiles for Men

For men, the first quartile (Q1) is the median of the first half of the data (values 1 to 8) and the third quartile (Q3) is the median of the second half (values 10 to 17). - **Q1 for Men:** Median of 21, 23, 24, 25, 25, 26, 26, 27 is 25. - **Q3 for Men:** Median of 28, 28, 29, 30, 30, 32, 35 is 30.

05

Find the First and Third Quartiles for Women

For women, calculate the first quartile (Q1) using the middle of values 1 to 7 and the third quartile (Q3) using values 9 to 15. - **Q1 for Women:** Median of 19, 20, 22, 22, 23, 23, 24 is 22. - **Q3 for Women:** Median of 26, 26, 27, 28, 29, 30 is 28.

06

Analyze Historical Comparison

Compare today's median to those from 25 years ago. The median age for men at the first marriage has increased from 25 to 27. For women, it has increased from 22 to 25, suggesting young people today are marrying later than they did 25 years ago.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Median Calculation

To calculate the median, you first have to sort your data in ascending order. The median is the middle value in a data set, providing a measure of the center. It effectively divides your data into two equal halves. If there is an odd number of data points, the median is the value right in the middle. If it's even, then the median will be the average of the two middle numbers.

For the men's dataset, the sorted ages are: 21, 23, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 30, 30, 32, 35. With 17 numbers, the median is the 9th value, which is 27.

For women's ages (19, 20, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 29, 30), the median is the 8th value out of 15, which is 25. This step is critical to understanding where most people in the dataset fall regarding age.

Quartile Calculation

Quartiles divide your data into four parts. The first quartile (Q1) is the median of the first half, excluding the median, and the third quartile (Q3) is the median of the second half.

For men, Q1 is found using values from 21 to 27. The sorted sequence is: 21, 23, 24, 25, 25, 26, 26, 27. Here, the median or Q1 is 25. Q3 is determined from values 28 to 35, which are: 28, 28, 29, 30, 30, 32, 35. The Q3 or median here is 30.

For women, Q1 is computed from the following set: 19, 20, 22, 22, 23, 23, 24. The median value or Q1 is 22. Q3 uses values: 26, 26, 27, 28, 29, 30, where the median or Q3 is 28. These quartiles offer an insight into how the ages vary across the data.

Historical Comparison

By comparing current statistics with historical data, we gain insight into trends over time. Twenty-five years ago, the median ages for first marriages were 25 for men and 22 for women.

Today's medians—27 for men and 25 for women—indicate a change. This historical comparison reflects a societal shift towards marrying at an older age. This trend may be due to various factors such as education, career planning, and changes in societal norms.

U.S. Census Bureau Data

The U.S. Census Bureau provides comprehensive data, which is crucial for statistical analysis. By using such reliable data, researchers and statisticians can track and analyze changes in societal behaviors and demographics over time.

This data allows insights into family dynamics, marriage patterns, and household compositions. It’s important because it supports policies and understanding of societal changes on a broader scale.

The data showing marriage ages is gathered from a large sample, ensuring that it accurately reflects the population's behavior.

Statistical Analysis of Marriage Age

Statistical analysis helps us interpret and make predictions based on data. It involves summarizing data, finding trends, and making comparisons. In this case, analyzing marriage age helps to understand patterns and behaviors among young adults.

By calculating medians and quartiles, we see both central tendency and data spread. This statistical examination of marriage age not only reflects individual life choices but also deeper societal change, providing valuable insight for sociologists and demographers.

Such analysis is fundamental for making informed decisions in policy-making and societal planning.