How To Calculate Median

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Calculating the median can be a helpful tool for understanding the distribution of a data set. The median is the middle value of a data set and is used to measure the central tendency or the average of a data set. Calculating the median is a simple process, whether done by hand using pencil and paper or using a calculator.

If done by hand, the process starts by ordering numbers from the smallest to the largest number. After the numbers are aligned in an ordered list, count the numbers in the set. To determine the median, find it’s position in the series. If the data set has an even number, the median is determined by taking the average of the two next to the middle. If the list has an odd numbers, the median is the number in the middle.

For example, in a list of five numbers, 8, 5, 7, 6, and 2, the median is 6. This is calculated by ordering the numbers from smallest to largest; 2, 5, 6, 7 and 8. Since there are an odd amount of numbers, the middle position is at the third place and the number 6 is the median.

For the same list, if one of the numbers (let’s say 6) was removed, the data set would contain 4 numbers and the median would be determined by taking the average of the two numbers closest to the middle. The numbers would be ordered in a list; 2, 5, 7 and 8 and the median is calculated by taking the average of the two numbers at the midpoint. In this case it is (7 + 5) / 2 = 6.

After the median is found, it can be compared to the average of the same data set to get a better understanding of the overall data set. The median will usually be the same or close to the mean, but there can be cases when the median is far from the mean. For example, if there are extreme numbers or outliers in the data set, the calculation of the median would take out the effect of the outliers and will be closer to the midpoint of the complete set.

In summary, calculating the median of a data set is simple and can provide a better understanding of the data set. To calculate the median by hand, list the numbers in an ordered set and then determine the middle position. If the list is even, take the average of the two numbers at the midpoint. If it’s odd, the median will be the number in the middle. As a comparison, analyzing the median against the mean can help to determine the overall spread of the data set.