Understanding the Median: A Statistical Measure of Central Tendency for Skewed Data and Outliers

Median

The median is a statistical measure that represents the middle value in a dataset

The median is a statistical measure that represents the middle value in a dataset. It is often used as a measure of central tendency when the data is skewed or contains outliers.

To find the median, you need to follow these steps:

1. Arrange the data in ascending order (from smallest to largest). If there is an even number of data points, you may need to use additional steps which we will explain later.

2. If the number of data points is odd, the median is the middle value. For example, consider the dataset: {5, 2, 7, 4, 9}. After arranging it in ascending order, it becomes: {2, 4, 5, 7, 9}. As there are 5 data points, the middle value is the third one, which is 5. Hence, 5 is the median.

3. If the number of data points is even, the median is the average of the two middle values. Let’s take an example: {3, 6, 1, 9, 8, 2}. After arranging it in ascending order, it becomes: {1, 2, 3, 6, 8, 9}. As there are 6 data points, the two middle values are 3 and 6. To find the average, you add them and then divide by 2: (3 + 6) / 2 = 9 / 2 = 4.5. Hence, 4.5 is the median for this dataset.

It is important to note that the median is not affected by extreme values, unlike the mean which can be heavily influenced by outliers. This makes the median a more robust measure of central tendency in certain cases.

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