How do you find the range of a data set? What's the relationship to the mean and median?
- Let's take a look at these two small data sets. Notice both have the same average, both have the same median values. Still, it's obvious that the data sets are vastly different. These data sets are small so we can quickly view all of the data and see the differences. What happens when the data sets are enormous? How can we measure the differences in data sets that might have very similar medians and means? Better yet, how can we get a better idea of what kind of data makes up this data set? When we measured mean and median, we were looking for the middle.
Let's now measure how far out from the means and averages the farthest data points lie. The simplest measure of variability is the range. Finding the range is easy. You just take the largest number in the data set and the smallest number in the data set. The difference between these two numbers is the range. When you look at this data set, our range is 50.
Here, our range is 150. Now, when you are provided with these numbers, mean 60, median 58, range 70, we begin to understand that while the center of the data is near 60, the difference between values in the data set can be very large. What's a possible pit fall here? I think the most common mental error is thinking that since 60 is our theoretical middle and the range is 70 that the biggest numbers in the data set are likely 35 units bigger than 60, and the smallest numbers in the data set are 35 units smaller than 60.
Don't just assume that a mean of 60 with a range of 70 means that the highest score was about 95 and the lowest score was 25. Suppose these are exam scores. It's possible one student didn't study at all and got a 15%, 45% less than the average, and the highest grade might've been 85%. Again, I would recommend using a histogram to help you better understand the makeup of your mean, median, and range.
Here, we can see that one student really opened up the range. Perhaps the range isn't as helpful as we thought. Then again, if the data set looks like this, mean 60, median 58, range 10, we know that this data would seem to be fairly centralized. Not only are the mean and median similar, the difference between the biggest and smallest values is only 10 units. Range is a nice, simple tool for our statistics toolbox, but we need to remember that it's not always indicative of the overall data set.
It only takes one rogue data point to exaggerate the size of your data set's range.
Professor Eddie Davila covers statistics basics, like calculating averages, medians, modes, and standard deviations. He shows how to use probability and distribution curves to inform decisions, and how to detect false positives and misleading data. Each concept is covered in simple language, with detailed examples that show how statistics are used in real-world scenarios from the worlds of business, sports, education, entertainment, and more. These techniques will help you understand your data, prove theories, and save time, money, and other valuable resources—all by understanding the numbers.
- Calculate mean and median for specific data sets.
- Explain how the mode is used to assess a data set.
- Identify situations in which standard deviation can be used to investigate individual data points.
- Use mean and standard deviation to find the Z-score for a data point.
- List the three different categories of probability.
- Analyze data to determine if two events are dependent or independent.
- Predict possible outcomes for a situation using basic permutation calculations.
- Give examples of binomial random variables.