Mean Median Mode: You Need To Know The Difference

Mean, median, and mode are all measures for averages or central tendencies. While some people use them interchangeably in conversation, they are distinct statistical vehicles that summarize data differently. The mean is the arithmetic average, calculated by summing all the values in a dataset and dividing by the number of values. Very sensitive to outliers. The median is the middle value when the dataset is arranged in an ascending or descending order. Robust to outliers and used where data is skewed. The mode is the value that occurs most frequently in a dataset. It’s useful to identify what is mots common.

Let’s see them in practice to drill in the difference. There are 25 people in a room. 13 of them make 75,000 per year. 11 are c-suite executives who make 700,000 annually. And then there’s the janitor. The mean salary in this room is over 40 million. Whereas the median is 75,000, and so is the mode — because it is the most frequent value, and the value in the middle of the dataset. Spoiler: the janitor is secretly a billionaire. This is why you have to be careful when observing what is presented to you. If you, by virtue of ignorance or lack of knowledge, mix the mean and median, you can start believing things that are entirely false.

The mean is used in everyday situations to understand typical values. If you want to know the average income of people in a city, you would calculate the mean. Median is in household income data, and provides a better representation of the typical income rather than the mean where there are extreme values. Or janitors. Mode represents the most frequently occurring value in a dataset. It can be used in manufacturing, for instance, to identify the most common defect in a production line. These are basics anyone who wants to evaluate statistical values must understand. They each provide a different perspective of what “typical” looks like.

Real-life applications of each:

• Mean: it fits best where data is distributed normally. In a large class where exam scores follow a bell curve, the mean is a reliable indication of overall performance. It works since extreme values are rare, so every score contributes proportionately. It typically works for businesses tracking monthly revenue to smooth out fluctuations and understand average income per period, and for temperature readings since measurement errors cancel out.

• Median: it fits best in skewed distributions. Household incomes, for instance. In many economies, incomes are skewed by a tiny fraction of very high earners. Thus you use the median, since it is not affected by extreme values, and provides a realistic measure of central tendency or “typical”. Real estate pricing within a city would benefit from a median as well, and so would survey responses, as it minimizes the influence of extremes.

• Mode: it fits best in categorical data. Favorite ice cream flavors surveys are going to be most accurately assessed when the mode is put into play. Consumer behaviors and product preferences in retail fall under the same umbrella, revealing the most frequently bought item. There is no numerical average. It helps businesses focus on demand, and highlights the most common behavior, even if the data isn’t normally distributed (doesn’t follow a bell curve).

How to use the mean, median, and mode as mental models: (1) identify the pattern — pick between mean (best for a comprehensive summary that incorporates all of the data, such as in time-series data like monthly sales), median (best for where outliers skew the data to get an accurate middle value, like income across regions), and mode (best to determine the most frequent occurrence in categorical data or behavior); (2) analyze the data — using the correct measure that best represents the “typical” value for your context, and do your calculations; (3) make a choice — integrate these measures in your analyses for financial, marketing, or management decisions, as they help summarize data into actionable insights; (4) communicate your findings — tailor your presentation to your audience, explaining why you picked a particular measure and what it means.