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What is the middle in a list of numbers called?

Published in Statistical Measures 3 mins read

The middle in a list of numbers, especially when the list is sorted, is called the median.

Understanding the Median

The median represents the central value in a dataset. It is literally the middle number in a sorted list of numbers. Unlike the average (or mean), the median provides a truer sense of the center, particularly in data sets that might be unevenly distributed or contain unusually high or low values.

For instance, the median can be more descriptive of a data set than the average. This is because the median is sometimes used rather than the mean when there are outliers in the sequence that might significantly skew the average of the values. Outliers are extreme values that are very different from the other values in the dataset.

How to Find the Median

Finding the median involves a simple, two-step process:

  1. Order the Data: Arrange all the numbers in your list from the smallest to the largest (or largest to smallest).
  2. Locate the Middle Value:
    • If the list has an odd number of data points: The median is the single number directly in the middle.
      • Example: In the list [3, 1, 7, 4, 2], first sort it: [1, 2, 3, 4, 7]. The middle number is 3.
    • If the list has an even number of data points: There will be two middle numbers. The median is the average of these two middle numbers.
      • Example: In the list [10, 5, 8, 2], first sort it: [2, 5, 8, 10]. The two middle numbers are 5 and 8. The median is (5 + 8) / 2 = 13 / 2 = 6.5.

Why the Median is Important

The median is a crucial measure of central tendency, particularly useful in scenarios where data can be heavily skewed:

  • Robustness to Outliers: As mentioned, the median is not affected by extreme values. For example, if you're looking at house prices in a neighborhood, a few extremely expensive mansions won't dramatically inflate the median price as they would the mean price, giving a more realistic picture of typical housing costs.
  • Income and Wealth Distribution: The median income often provides a better reflection of a typical household's earnings than the average income, which can be skewed upwards by a small number of very high earners.
  • Understanding Typical Values: In many real-world applications, knowing the typical value (represented by the median) is more insightful than knowing the arithmetic average.

For a deeper dive into the median and its calculation, you can refer to resources like Investopedia's explanation on the topic: Median: What It Is and How to Calculate It.