Mean Formula (Table of Contents)
Mean Formula
Mean is a point in a data set that is the average of all the data points we have in a set. It is an arithmetic average of the data set and can be calculated by taking a sum of all the data points and then dividing it by the number of data points we have in the data set. In statistics, the mean is the most common method to measure the center of a data set. It’s a fundamental yet important part of the statistical analysis of data. If we calculate the average value of the population set, then it is called the population mean. But sometimes, what happens is that population data is huge, and we cannot perform analysis on that data set. So, in that case, we take a sample out of it and take an average. That sample represents the population set, and the mean is called a sample mean. Mean value is the average value that will fall between the maximum and minimum values in the data set but will not be the number in the data set.
A formula for Mean is given by:
There is another way of calculating mean, which is not very commonly used. It is called the Assumed mean method. In that method, a random value is selected from the data set and assumed to be the mean. Then the deviation of the data points from this value is calculated. So mean is given by:
Examples of Mean Formula (With Excel Template)
Let’s take an example to understand the calculation of Mean formula in a better manner.
You can download this Mean Template here – Mean Template
Mean Formula – Example #1
Let’s say you have a data set with 10 data points, and we want to calculate the mean for that.
Data set : {4,6,8,9,22,83,98,45,87,10}
Solution:
Mean is calculated using the formula given below
Mean = Sum of All Data Points / Number of Data Points
- Mean = (4+6+8+9+22+83+98+45+87+10) / 10
- Mean = 372 / 10
- Mean = 37.2
Let’s use Assumed Mean method to find mean in the same example.
Let’s assume that the mean for the given data set is 40. So Deviations will be calculated as:
For 1st data point, 4 – 40 = -36
The result will be as given below.
Similarly, We have to calculate deviation for all the data points.
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Mean is calculated using the formula given below
Mean = Assumed Mean + (Sum of All Deviations / Number of Data Points)
- Mean = 40 + (-36 -34-32-31-18+43+58+5+47-30) / 10
- Mean = 40 + (-28) / 10
- Mean = 40 + (-2.8)
- Mean = 37.2
Mean Formula – Example #2
Let us take IBM stock and we will take its historical prices from the last 10 months and will calculate the annual return for 10 months.
Source Link: https://in.finance.yahoo.com/quote/IBM/
Solution:
Mean is calculated using the formula given below
Mean = Sum of All Data Points / Number of Data Points
- Mean = (3.74% + 1.07% +4.34% + (-23.66)% + 7.66% + (-7.36)% + 18.25% + 2.76% + 1.48% + 0.00%) / 10
- Mean = 8.28% / 10
- Mean = 0.83%
So if you see here, in the last 10 months, IBM return has fluctuated very much.
Overall, in the last 10 months, the average return is only 0.83%.
Explanation
Mean is a simple average of the data points in a data set and helps us understand the average point. But there are certain limitations to using mean. Mean value is easily distorted by extreme values/outliers. These extreme values can be very small or very large, which can distort the mean. For example: Let’s say we have returns of stock for the last 5 years given by 5%, 2%, 1%, 5%, -30%. Mean for these values is -3.4% ((5+2+1+5-30)/5). So although the stock has provided a positive return for the first 4 years, we have a negative mean of 3.4% on average. Similarly, if we have a project for which we are analyzing the cash flow for the next 5 years. Let say the cash flows are: -100, -100, -100, -100, +1000.
Mean is 600 / 5 = 120. Although we have a positive mean, we are only getting money in the last year of the project, and it can happen that if we incorporate the time value of money, this project will not look as lucrative as it is now.
Relevance and Uses of Mean Formula
Mean is very simple yet one of the crucial elements of statistics. It is the basic foundation of statistical analysis of data. It is very easy to calculate and easy to understand also. If we have data set with data points scattered all over the place, the mean helps us see that data point’s average. For example : If a stock X has returns from last 5 years as 20%, -10%, 3%, -7%, 30%. If you see, all the years have different returns. Mean for this is 7.2% ((20-10+3-7+30)/5). So we can now simply say that, on average, the stock has given us a yearly return of 7.2%.
But if we see mean in a silo, it has relatively less significance because of the flaws discussed above and is more of a theoretical number. So we should use the mean value very carefully and not analyze the data based only on the mean.
Mean Formula Calculator
You can use the following Mean Calculator
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