Point measure discrete3/18/2023 ![]() Outliers and skewed data have a smaller effect on the mean vs median as measures of central tendency. ![]() Consequently, 28 is the median of this dataset. When there is an even number of values, you count in to the two innermost values and then take the average. Therefore, 12 is the median of this dataset. In the dataset with the odd number of observations, notice how the number 12 has six values above it and six below it. In the examples below, I use whole numbers for simplicity, but you can have decimal places. I’ll show you how to find the median for both cases. The method for locating the median varies slightly depending on whether your dataset has an even or odd number of values. To find the median, order your data from smallest to largest, and then find the data point that has an equal number of values above it and below it. It is the value that splits the dataset in half, making it a natural measure of central tendency. Related posts: Using Histograms to Understand Your Data and What is the Mean? Median When to use the mean: Symmetric distribution, Continuous data Read my post about the geometric mean to learn when it is a better measure. However, there are other types of means, such as the geometric mean. In statistics, we generally use the arithmetic mean, which is the type I discuss in this post. More about this issue when we look at the mean vs median! Consequently, it’s best to use the mean as a measure of the central tendency when you have a symmetric distribution. As the distribution becomes more skewed, the mean is drawn further away from the center. Extreme values in an extended tail pull the mean away from the center. This problem occurs because outliers have a substantial impact on the mean as a measure of central tendency. In the histogram above, it is starting to fall outside the central area. However, in a skewed distribution, the mean can miss the mark. In a symmetric distribution, the mean locates the center accurately. It is crucial to understand that the central tendency summarizes only one aspect of a distribution and that it provides an incomplete picture by itself. The panel on the left displays a distribution that is tightly clustered around the mean, while the distribution on the right is more spread out. The graph below shows how distributions with the same central tendency (mean = 100) can actually be quite different. While measures of variability is the topic of a different article (link below), this property describes how far away the data points tend to fall from the center. Another aspect is the variability around that central value. Whether you’re using the mean, median, or mode, the central tendency is only one characteristic of a distribution. Related posts: Guide to Data Types and How to Graph Them Consequently, you need to know the type of data you have, and graph it, before choosing between the mean, median, and mode! Coming up, you’ll learn that as the distribution and kind of data changes, so does the best measure of central tendency. Measures of central tendency represent this idea with a value. As the graphs highlight, you can see where most values tend to occur. ![]()
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