How to Calculate the Mean
Many calculations and operations in mathematics and statistics can be derived by getting the middle value of a given set of numbers. The mean, which is an umbrella term for many mathematical values, is a very useful tool for surveys, business, or even many situations in everyday life. Here are some important equations and steps you have to remember when calculating the mean.
Measures of Central Tendency
Measures of central tendency are also known as “averages,” although the average is just one of the many middle values in statistics and mathematics. Measures of central tendency can provide a researcher, teacher, or student with an idea of the distribution of values in a given set. The values derived from central tendency also act as factors for other equations, which makes them particularly useful for many other statistical and mathematical operations.
Values and Calculations
There are two important measures of central tendency that you should be aware of:
Mean
The “mean value” is often understood as the arithmetic mean or the average, which is the sum of all the elements in the set divided by the total number of the elements in the set (cardinality). Let’s take the values 7,17, 21, 22, 29, 43, 47, and 104. To get the mean of these numbers, follow these steps:
Get the sum of all the numbers (290).
Divide the sum (290) by the number of elements in the array (8).
In the case of the given values, the quotient should be 36.25, which is also the value of the mean.
Median
For skewed distributions and for other statistical operations where outliers are not as significant, the median is a very useful measure of central tendency. The median is simply the middle value of an ordered statistical array. If the cardinality of the set is an odd number, then the middle number of the set is the median. For an ordered array with an even-numbered cardinality, follow the succeeding steps (we will still use the array in the example above):
Look over the array carefully. Note that the two middle values in the array are 22 and 29.
Add up both numbers. You should get a sum of 51.
Divide the sum by 2. The quotient should be 25.5, which is the value of the median.
Calculating the mean is especially useful in education, engineering, research, and business. With these steps, you can calculate the mean of simple statistical arrays very quickly and easily without the aid of a calculator.