Question

You survey 171 males and 180 females at Grand Central Station in New York City. Of those, 132 males and 151 females wash their hands after using the public rest rooms. Organize these results in a two-way table. Then find and interpret the marginal frequencies. (See Example 1.)

Short answer

As per the survey, 132 males and 151 females washed hands whereas 39 males and 29 females didn't. The marginal frequencies show that a majority of both genders do wash their hands after using the public restroom with 283 people doing so and 68 not. Women showed slightly better hand-washing habits than men.

Step-by-step solution

Organization of the data.

A two-way table needs to be set up with columns for male and female, and rows for 'washed hands' and 'didn't wash hands'. Another row and column should be added to facilitate the calculation of the marginal frequencies.

Filling out the table

The data given should be inputted into the appropriate cells. Out of 171 males surveyed, 132 washed their hands and so, 171-132 = 39 males didn't. Similarly, out of 180 females, 151 washed their hands, which means 180 - 151 = 29 didn't.

Calculation of the marginal frequencies

The total survey count for each gender and hand washing behaviour is calculated and filled in the last row and column of the table. This is done by adding across the rows and down the columns.

Interpretation of the marginal frequencies

The numbers obtained represent the total counts for each category. It shows the hygiene practices of the surveyed individuals separated by gender, as well as the overall cleanliness of all surveyed people.

Key concepts

Marginal Frequencies

Marginal frequencies refer to the totals in a two-way table, either for the rows or columns. They are called "marginal" because they appear at the "margins" – the outer rows and columns of the table. These totals give us important insights about the surveyed groups overall.
In the example of the survey conducted at Grand Central Station, marginal frequencies help us understand the total number of people for each gender and each handwashing habit. By summing rows, you find the total number of males and females; by summing columns, you find the number who washed their hands versus those who didn't.
These frequencies summarize the key findings of the survey, showing the overall behaviors of each gender in terms of hygiene. It is crucial to always check these totals for completeness and any apparent errors as they help verify the accuracy of the two-way table.

Data Organization

Data organization is essential to making sense of collected data, especially from surveys. A well-organized two-way table is a fundamental tool for this purpose. It helps in assessing complex relationships and trends within your data. For the Grand Central Station survey, a two-way table is organized to systematically display data about males and females against their handwashing behaviors.
Creating such a table involves:

• Listing all categories (like gender and behavior) clearly as rows or columns.
• Ensuring all raw data is accurately and carefully entered into the correct cells.
• Adding an additional row and column to capture totals, which are the marginal frequencies.

Clear data organization ensures that the subsequent analysis is meaningful, maximizes insights, and minimizes errors.

Survey Analysis

Survey analysis is the process of interpreting data to gain insights and answer specific research questions. For the Grand Central Station survey, analysis involves examining the relationship between gender and handwashing habits. By arranging data into two-way tables, you can easily identify patterns and compare them.
Some steps in survey analysis include:

• Calculating the proportions or percentages for various groups—such as the percentage of males and females who washed their hands.
• Comparing these proportions to assess patterns, like the difference in hygiene practices between genders.
• Looking for correlations or unexpected findings that might prompt further investigation.

Survey analysis helps in visualizing the effectiveness of a survey and the representation of different behaviors among groups. It's an important step to finalize decisions or recommendations based on empirical data.