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Interpreting and comparing data distributions
Description
Exercise Name: Interpreting and comparing data distributions
Math Missions: High school statistics and probability Math Mission
Types of Problems: 3

The Interpreting and comparing data distributions exercise appears under the High school statistics and probability Math Mission. This exercise practices interpreting the effect of distributions on the common measurements of center and spread.

## Types of Problems

There are three types of problems in this exercise:

1. Compare populations: This problem describes three populations and there are several statements below that have drop-down menus to uses ${<}$, ${>}$, and ${=}$ to compare some summary statistics about them. The student selects the correct symbol to fill in the statements and make them true.
2. Select the truths: This problem describes multiple populations and has some statements comparing some of their summary statistics. The student is asked to select all the statements that are true.
3. Interpret graphs: This problem has visual displays of a couple data sets. The student is asked to select the correct comparison symbol to make true statements.

## Strategies

This exercise is easy to get accuracy badges, especially if students sit and draw some examples or use numbers to make it more concrete. The speed badges are hard because the problems do take a fair amount of time to analyze for each statement, and even with that there are multiple statements.

1. In normal distributions the mean is close to the median. Measurements of spread are moderate.
2. If data is split into two equal sized groups, the mean and median will be the same and in the middle of the two groups. The measurements of spread will be high.
3. If data is almost split into two equal sized groups, the median will be on the end with more actual people. The spread will still be high.
4. If data is uniform (equally distributed) mean will be same as medium, spread will be moderate, but higher than in the normal case.
5. If all data is identical the mean and median are the same and the spread is very small (in fact, zero if all data points are literally identical).

## Real-life Applications

1. Statisticians frequently assume that data follow a normal distribution when developing statistical methods and performing practical data analysis.
2. Data and statistics appear in news reports and in the media every day.
3. Many of the problems in this exercise could be viewed as real-life applications.
4. Statistics can be seen more frequently than calculus in every day life.