Discuss one situation where you can collect data and where the empirical rule applies, meaning that the data representing this situation follows a normal distribution. You are encouraged to conduct online research to discover a situation that fits these criteria.
Answer (2)
Heights of adult male students in a high school can be collected and are often normally distributed. This allows schools to apply the Empirical Rule, which describes the distribution of data in terms of standard deviations from the mean. The practical application aids in various educational and health-related assessments.
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One common situation where you can collect data that follows a normal distribution and where the empirical rule applies is human heights within a specific age group and gender.
Who: In this case, consider collecting data on the heights of adult men living in a particular city.
What: The specific data to be collected is the height of each individual in your sample group, measured in centimeters or inches.
When: The data collection can occur at any time, but to ensure consistency, it is best to measure heights at the same time of day to avoid variations due to factors such as posture changes.
Where: This can be done in a local community center, clinic, or any venue where a group of individuals can be gathered for measurement.
Why: Understanding the distribution of heights can help in various fields such as health planning, clothing manufacturing, or ergonomic design. The normal distribution allows statisticians to make inferences about the general population based on the sample data.
How: First, decide the number of individuals needed for your sample to have enough data points for meaningful analysis. Measure each individual's height accurately and record the data. Once you have your data set, calculate the mean (average) and standard deviation.
Assuming the data follows a normal distribution, the empirical rule (or 68-95-99.7 rule) applies. This rule states:
Approximately 68% of the data lies within one standard deviation of the mean.
About 95% falls within two standard deviations.
Nearly 99.7% lies within three standard deviations.
By using this rule, you can make predictions and draw conclusions about the larger population, which is particularly useful in understanding variations in height and addressing related needs.
