Understanding the Median in Statistics: Definition, Calculation, and Importance

Median

the middle score in a distribution; half the scores are above it and half are below it

The median is a measure of central tendency in statistics. To find the median of a set of data, the data must first be arranged in order from least to greatest. The median is the middle value of the data set if there is an odd number of values, or the average of the two middle values if there is an even number of values.

For example, consider the following data set: 2, 5, 7, 8, 10. The data is already arranged in order from least to greatest, so the median can be found by selecting the middle value, which is 7. Therefore, the median of this data set is 7.

Another example could be the following data set: 2, 5, 7, 8, 10, 12. In this case, there are six values, which is an even number. To find the median, we need to take the average of the two middle values. The middle two values are 7 and 8, so the median can be calculated as follows: (7+8)/2 = 7.5. Therefore, the median of this data set is 7.5.

The median is useful because it is a robust measure of central tendency that is not influenced by extreme values in the data set (i.e. outliers). It is often used in conjunction with other measures, such as the mean and mode, to provide a comprehensive description of the data set.

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