Median Meaning in Math

What is Median?

In mathematics, the median represents the middle point of a sorted list of numbers. In a way, it shows the average of a given set of numbers. For example, for a random set {12, 13, 18, 10, 5, 2, 9, 6, 15, 14, 3}, the median will be the number ’10’. In order to find the median in the above set, it is necessary to sort the list first. The sorted list, in this case would be {2, 3, 5, 6, 9, 10, 12, 13, 14, 15, 18}.

From the sorted list given above, the median would represent its middle point. Since there are a total of 11 numbers in the list, the median would be the 6th element of the list. In the sorted list, the 6th element is the number ’10’. Therefore, it is the median of that particular given set of numbers. As mentioned, however, the list must be sorted first.

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The above set of numbers contains an odd number of elements. Therefore, the median for the list is only a single number. The number, in that case, ’10’, represents the central point of the sorted listed that has an equal number of elements above and below it. However, when a list contains an even number of elements, the median will be the average of the pair of numbers that fall in the middle.

Along with mean and mode, the median is a critical concept used to derive the average of a given set of data points. While the median represents the midpoint of the set, the mean and mode calculate the average differently. Another name used for the median is positional average, which gives an accurate description of what it is.

What are the uses of Median?

There are several uses of the median. Most commonly it can be used as a measure of location in cases where the extreme values of a given set of elements have low importance, usually due to a skewed distribution. Similarly, it helps when the extreme values of a set are unknown or when the anomalies or outliers are untrustworthy.

For example, in the set {5, 20, 22, 22, 23, 23, 43}, the mode is 22, which is a better representative of the positional average of the set. In the case of the given set, both the extreme ends (5 and 43) may represent extreme values that are untrustworthy due to how different they are from the average.

Similarly, the median is simple to understand and easy to calculate. However, that does not take away from its usefulness and application in mathematics and other fields. It is one of the most well-known summary statistics in descriptive statistics while also being a robust approximation to the mean.

Can Median help in finance and investing?

In finance and investing, the median can also have an application, especially during comparable analysis. When comparing between stocks of different nature, investors may want to neglect the extreme values that they consider untrustworthy or are significantly different from the average of the given data. In that case, using other ways to calculate the average may not produce a representative result.

However, by using the median, investors can easily avoid the problem and get a representative element that is will give them an idea of the positional average of the given set of data. While the process of determining a median for a large amount of data may be a tedious task, with the use of tools such as Excel, the process becomes simpler. Therefore, any investor can calculate a median for their data if they understand what it represents.

Conclusion

Median, in mathematics, shows a positional average or middle point for a set of sorted numbers. For oddly numbered elements in a sorted set, the median is the number above and below which there are a similar number of items. For evenly numbered elements in a sorted set, the median is the average of the pair of numbers that fall in the middle.

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