Mean, Median, Mode, & Range

Ever wondered how to make sense of a bunch of numbers? These four measures can help! Let's break them down using the example data set: {1, 2, 2, 3, 4, 4, 4, 5, 5, 5}.

The mean is the average of all values. Simply add up all numbers and divide by how many there are. For our example: $1+2+2+3+4+4+4+5+5+5$/10 = 3.5. Remember that the mean can be affected by outliers (extremely high or low values).

The median is the middle value when all numbers are arranged in order. With our sorted data {1, 2, 2, 3, 4, 4, 4, 5, 5, 5}, we have 10 numbers (even), so we average the two middle values: $4+4$/2 = 4. The median is great when your data has outliers since it's not easily influenced by extreme values.

The mode is the value that appears most frequently. In our example, both 4 and 5 appear three times each, so we have two modes: 4 and 5. This makes our data "bimodal." If every value appears the same number of times, there's no mode at all!

Pro Tip: When deciding which measure to use, think about your data. Mean works for most situations, median is better when you have outliers, and mode helps identify the most common value (especially useful for non-numerical data).

The range shows how spread out the data is by finding the difference between the highest and lowest values. In our example: 5 - 1 = 4. While simple to calculate, remember that range only considers two values and can be distorted by outliers.