Math Problem Statement

Develop a cross-tabulation for the data, with x as the row variable and y as the column variable. For x, use classes of 10-29, 30-49, and so on; for y, use classes of 40-59, 60-79, and so on.

Solution

To solve this task, we need to develop a cross-tabulation of the given data. We are asked to divide the xx values into classes of 102910-29, 304930-49, and so on, while dividing the yy values into classes of 405940-59, 607960-79, and so on.

Step-by-Step Process

  1. Identify Classes for xx:

    • 10-29
    • 30-49
    • 50-69
    • 70-89
  2. Identify Classes for yy:

    • 40-59
    • 60-79
    • 80-99
  3. Count Observations in Each Class Combination:

xx \\backslash yy40-5960-7980-99Total
10-293148
30-491315
50-691214
70-890123
Total57820

Explanation:

  • For x=1029x = 10-29, count how many corresponding yy values fall into each of the yy ranges.
    • y=72,99,58,34,60,22,77,85,45,47,98,71,32,81,64,68,67,39,28y = 72, 99, 58, 34, 60, 22, 77, 85, 45, 47, 98, 71, 32, 81, 64, 68, 67, 39, 28
  • We repeat this process for the other xx-classes and fill in the table.

Would you like more details on any of these steps or have questions? Here are five related questions to expand on this:

  1. How do you calculate marginal totals in a cross-tabulation?
  2. Can cross-tabulation help in identifying correlations between variables?
  3. What is the importance of choosing appropriate class intervals in cross-tabulation?
  4. How could you visualize this cross-tabulation using a heatmap?
  5. What other data analysis techniques could be applied to this dataset?

Tip: Cross-tabulation is especially useful for categorical data analysis and identifying relationships between two variables at different levels.

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Math Problem Analysis

Mathematical Concepts

Cross-tabulation
Classification
Bivariate Data Analysis

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12