The Differences Between the Mean and Median
In statistics, sometimes you need to calculate the central tendency of a data set to have a greater understanding of the information. The sample mean and median are both statistical methods of finding the middle amount. Sometimes the sample mean and median can be the same amount, but there are differences between these two methods of deriving an "average."
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What is the sample mean?
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The sample mean of a data set is what is commonly referred to as the "average," though the median is also an average. The sample mean is calculated by adding all the data points in the data set and dividing by the number of data points. For example, if there are children whose ages are 3, 4, 5, 7 and 11, the sample mean is 6 years old. The sample mean is not necessarily a whole number.
What is the median?
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The median of a data set is the number in the middle of the set, so that half the data points are less than the median and half the data points are greater than the median. Using the previous example, with the ages of the children as 3, 4, 5, 7 and 11, the median is 5 years old -- the middle number after the numbers are listed from lowest to highest.
The median calculation for the median does not change if there are duplicate numbers, so if the children are 3, 3, and 7 years old, the median is still 3, because it is the middle number. If there are an even number of data points, the median is derived by finding the mean of the two numbers in the middle.
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When to use the sample mean
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The sample mean is the most common method of calculating the central tendency, because it is useful in most circumstances. It is best used with a large data set with random data points. The sample mean uses all of the data to draw a conclusion about the entire set, whereas the median uses one data point to comment on the entire data set.
When to use the median
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The median is most useful when there are outliers in the data set. That is, there are data points that are much greater or lesser than the bulk of the numbers. Outliers significantly alter the sample mean but have no impact on the median. For instance, if test scores for the class were 48, 47, 45, 44, 44, 42, 20 and 10, the sample mean is 32, but the median is 44. The much lower numbers "pull" the sample mean to a lower number, but the median remains unaffected.
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References
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