## Formula to Calculate Population Mean

The population mean is the mean or average of all values in the given population and is calculated by the sum of all values in population denoted by the summation of X divided by the number of values in population which is denoted by N.

It is arrived at by summing up all the observations in the group and dividing the summation by the number of observations. When the whole set of data is taken for computing a statistical parameter, the set of data is the population. For example the returns of all the stocks listed in the NASDAQ stock exchange in the population of that group. For this example, the population mean for the return of all the stocks listed in the NASDAQ stock exchange will be the average of the return all the stocks listed in that exchange.

In order to calculate the population mean for a group we first need to find out the sum of all the observed values. So, if the total number of observed values is denoted by X then the summation of all the observed values will be ∑X. And let the number of observations in the population is N.

The formula is represented as follows,

**µ= ∑X/N**

- µ= Population mean

### Examples

#### Example #1

**Let us try to analyze the return of a stock XYZ for the last twelve years. And the returns for the stock in the last twelve years are 12%, 25%, 16%, 14%, 40%, 15%, 13%, 17%, 23%, 13%, 17%, and 19%. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. So in this example, the ∑X is 224% and the number of observed values for the population is 12 as it comprises the return for the stock for 12 years period. **

With these two variables, we can calculate the population mean for the return of stock with the help of the formula.

Following are the given data

Therefore, using the above information mean can be calculated as,

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- µ= 224%/12

The example shows that the mean or average return for the observed value is 19%.** **

#### Example #2

**Let us try to analyze the return of a thematic mutual fund for the last eight years. And the returns for the stock in the last twelve years are 25%, 16%, 14%, 15%, 13%, 23%, 33%, and 27%. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. So in this example, the ∑X is 166% and the number of observed values for the population is 8 as it comprises the return of the mutual fund for 8 years period. **

With these two variables, we can calculate the population mean for the return of stock with the help of the formula.

Below is given data for calculation

Therefore, the mean can be calculated as,

- µ= 166%/8

The example shows that the mean or average return for the observed value is 21%.** **

#### Example #3

**Let us find out the population mean of the weight of 15 students in a class. The weight of each student in the class of 15 students in kg is as follows 35, 36, 42, 40, 44, 45, 38, 42, 39, 42, 44, 45, 48, 42, and 40. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. So in this example, the ∑X is 622 Kg and the number of observed values for the population is 15 as it comprises the weight for 15 students.**

With these two variables, we can calculate the population mean for the return of stock with the help of the formula.

Following are the given data for the calculation

Therefore, using the above information population average can be calculated as,

- µ= 622/15

** **The example shows that the mean or average return for the observed value is 41.47

### Relevance and Use

The population mean is a very important statistical parameter. It helps in knowing the average of the population’s parameters. The mean is important as it is used in the calculation of several other statistical parameters like the variance, standard deviations, and other. It is calculated using the concept of the arithmetic mean formula and represents the average or mean on the basis of which one can make an inference of whether an observation is high or low in the whole population of observations.

### Recommended Articles

This has been a guide to Population Mean Formula. Here we discuss how to calculate the population mean along with the practical examples and downloadable excel template. You can learn more about financing from the following articles –

- Geometric and Arithmetic Mean
- Mean Examples
- Mean vs Median
- Formula of Sampling Distribution
- Annuity vs Lump Sum

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