When our data aligns to the characteristics of normal distribution, it maintains specific properties that help us interpret results and make decisions.
Respond to the following in a minimum of 175 words:
- Discuss a situation where you can collect data, and the data the Empirical Rule applies, meaning that the data representing this situation follows a normal distribution. You are encouraged to conduct research using the internet to discover a situation that fits this criteria.
- Citing your source, discuss what specifically leads you to believe this situation follows the Empirical Rule. What statistical analysis benefits exist because the situation has data that is distributed normally?
Introduction
The Empirical Rule is a mathematical tool that can be used to determine if your data follows a normal distribution. When you collect data on something, it is possible that this will follow a normal distribution. In this article I will explain how the Empirical Rule works and give examples of when it applies in different situations.
A company is interested in predicting the number of customers they will have on a certain weekend. To collect the data they make a note of the number of customers who come through the door each Saturday and Sunday for a year. They plot the data, find that it is normal, and use the Empirical Rule to determine how many customers they should expect in future years.
The Empirical Rule is a statistical tool that can be used to determine how many data points will fall within a given range. This means that if you collect data, plot it and find that your results follow a normal distribution (or bell curve), then we can use this information to predict future outcomes.
In our example above, we had some data on the number of customers who came through the door each Saturday and Sunday for one year. If we were interested in predicting how many customers would come through during future weekends, we could look at our plot and see that it follows a normal distribution—in other words: most people come during weekends but not all days are busy; some days are busier than others; etcetera…
A professor is interested in determining where students score within their class on tests. The professor records every student’s test score as a percentage (70%, 80%, 90% etc.) and finds that these scores are normally distributed.
A professor is interested in determining where students score within their class on tests. The professor records every student’s test score as a percentage (70%, 80%, 90% etc.) and finds that these scores are normally distributed.
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In this situation, we can use the Empirical Rule because it applies when we have data coming from a normal distribution.
A fitness instructor is interested in determining at what level students finish her fitness classes. She records whether each student finishes (barely, with effort, or strongly) and finds that these three levels are normal when looked at as a proportion of the total class.
The instructor records the level each student finishes. She finds that these three levels are normal when looked at as a proportion of the total class.
The instructor uses this data to predict how many students will finish the class in future, and determines what level each student should finish.
The Empirical Rule can be applied when data comes from a normal distribution.
The Empirical Rule can be applied when data comes from a normal distribution.
The Empirical Rule states that, if you collect data and then use it to calculate the mean, variance and standard deviation of your sample, you will get an estimate of what those values are for other samples. This is true because each sample has its own mean, variance and standard deviation that would have been obtained by randomly shuffling the numbers in our original sample (which always contains all possible combinations of observations). If we now look at any other group of people’s samples—even if they don’t match our original one—we should expect their means and variances to match those calculated by using this method with our own sample.
Conclusion
The Empirical Rule can be applied when data comes from a normal distribution. It allows us to make predictions about how many customers we should expect in future years, how well students perform on tests and where they will finish in classes.