The Median: A Useful Measure Of Central Tendency For Skewed And Outlier-Prone Data.

Median

Is a median, altitude, angle bisector, or perpendicular bisector shown?

The median is a measure of central tendency in statistics that represents the value separating the higher and lower halves of a dataset. It is the middle value of a sorted dataset, such that half of the data falls above and half falls below the median.

To find the median of a dataset, we first need to sort the values in ascending or descending order. Once the values are sorted, we can identify the middle value. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the middle two values.

The median is often used to characterize the typical value of a dataset and is particularly useful when dealing with skewed data or values that have outliers. In such cases, the median often provides a more robust measure of central tendency than the mean, which can be heavily influenced by extreme values.

For example, imagine we have the following dataset of 10 values: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. To find the median, we first sort the values: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. The middle value is 12, so the median is 12.

Now imagine we add an outlier to the dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 1000. The mean of this dataset would be greatly influenced by the outlier (mean = 116), but the median would not change and would still be 12.

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