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The Trends in categorical data exercise appears under the High school statistics and probability Math Mission. This exercise analyzes trends and uses them to predict answers in contingency tables of categorical data.

Types of Problems

There are four types of problems in this exercise:

  1. Find row, column and table percentages: This problem gives some raw data from a study in a contingency chart or words. The student uses this information to make predictive guesses on percentages of situations.
    Compcat1

    Find row, column and table percentages

  2. Use chart to make conclusions: This problem has a contingency table filled with percentages. The student is asked to select all options that are reasonable based on the given chart of information.
    Compcat2

    Use chart to make conclusions

  3. Connect charts: This problem gives a contingency percentage chart and it's corresponding raw data table. The student is asked to fill missing numbers in the raw data table and find percentages in the percentage chart by using common information between the displays.
    Compcat3

    Connect charts

  4. Find ideal: This problem provides a situation where there is supposedly no bias. The students is asked to find the distribution of numbers that will cause a conclusion of no association between variables to be reached.
    Compcat4

    Find ideal

Strategies

This exercise is medium to get accuracy badges because it takes some concentration to adjust to working in contingency tables. Once done the speed badges are okay, but should be considered medium because they still take some intense analysis to ensure correctness.

  1. On Find row, column and table percentages it seems like one of the people will be a "row" person, one will be a "column" and one will be irrelevant to row and column and thus a "total" person.
  2. On connect charts it is recommended to aim at the most top left corner that users can. After that, the others can be filled in by looking and marginal totals.
  3. To fill in Find ideal the top left corner will be row total divided by total total times column total. Or, row total times column total divide by total total.

Real-life Applications

  1. Data and statistics appear in news reports and in the media every day.
  2. Many of the problems in this exercise could be viewed as real-life applications.
  3. Statistics can be seen more frequently than calculus in every day life.
  4. Categorical data analysis is a specialized field of statistics used mostly for the social sciences and business research.
  5. A boxplot is useful for dividing data into manageable quarters.

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