All three measures of central tendency explained clearly, with a full worked example using the same data set and a guide to when each one actually matters.
The average. Add all the values, divide by how many there are.
The middle value when data is arranged in order. Half the values are above it, half below.
The value that appears most often. A data set can have one mode, multiple modes, or no mode.
Add all values together to get the sum.
Divide the sum by the total number of values. That's your mean.
Arrange the data in order from least to greatest. This step is non-negotiable — skip it and you'll get the wrong median every time.
If there's an odd number of values: the median is the exact middle value.
If there's an even number of values: the median is the average (mean) of the two middle values. Add them and divide by 2.
Find the value(s) that appear most frequently. If every value appears the same number of times, there is no mode. If two values tie for most frequent, both are modes (bimodal).
The data has no extreme outliers and is roughly symmetric. Most common in everyday contexts ("class average").
The data has outliers or is skewed. Home prices and salaries use the median because a few very high values would distort the mean.
You're working with categorical data or want to know the most common value (most popular shoe size, most frequently ordered item).
Finding the median without sorting first. The most common error by far. You must arrange the data from least to greatest before finding the middle. Finding the middle of an unsorted list gives you a meaningless number.
Forgetting to average the two middle values for even-count data sets. With an even number of values, there's no single middle — you average the two that are closest to the middle.
Assuming there's always exactly one mode. A data set can have no mode, one mode, or multiple modes. "No mode" is a valid answer when every value appears the same number of times.
Confusing mode with median. Mode = most frequent. Median = middle value when sorted. They sound similar but measure completely different things.
Mean, median, and mode are just the beginning. Book a free consultation and we'll cover whatever your class is working on right now.
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