How to Calculate the Median of a Number of Figures

A median is the middle value in a list of numbers.

A median is a type of average studied in both basic math and higher levels, such as statistics. It represents the middle number in a set of figures, dividing the data into lower and upper values. When a data set has an even amount of figures, you can obtain the median by averaging the 2 middle numbers. Although the concepts of "mean" and "median" are often used interchangeably, the latter differs significantly from a precise average when there are widely ranging values in a data set.

Things You'll Need

• Paper
• Pen or pencil
• Calculator (optional)

Instructions

1. Identify the set of figures you want to use and arrange them in numerical order. For example, the numbers 73, 12, 61, 90, 44, 28, 36 and 42 should be re-arranged to the following order: 12, 28, 36, 42, 44, 61, 73 and 90.

2. Locate the median number using the following formula: (n+1) ÷ 2. Count the amount of numbers in the data set and insert this value in place of the variable "n" in the formula. For example, if there are 15 numbers in the set, the equation would be (15 + 1) ÷ 2 = 8. This means that the eighth number in the set is the median.

3. Locate the 2 middle numbers in the data set if the value you calculated in the previous step was not a whole number. In a data set containing 16 numbers, the equation would yield a solution of 8.5, or the average of the sequential positions of the 2 middle numbers. This means that the 8th and 9th numbers in the set are the middle values.

4. Add the 2 middle numbers together. Divide the resultant value by 2 to calculate the average. This value is also the median of the data set.

References

• Math Goodies: The Median of a Set of Data
• Mathwords: Median of a Set of Numbers
• Statistics Canada: Calculating the Median