Population Mean Formula

Population Mean concept comes under parent topic statistics. In brief statistics deals with the topics of collecting data, analyzing, interpreting, and presenting organized data. Population Mean Formula is the average of all the values in the given data/population.

Population mean, denoted by the Greek symbol ‘μ’, is the average of all the values in a population. It is a measure of central tendency that provides a single value representing the centre of the distribution of the population data. Population mean can be calculated by the sum of all values in the given data/population divided by the total number of values in the given data/population. We can call the sum of numbers a single-term Summation.

Population mean is denoted by the symbol μ.

Let X be the variable that holds data then,

Population Mean (μ) = ∑X / N

where,

• ∑X is Summation of X
• N is Number of X

Steps to Calculate Population Mean

To calculate the population mean follow the steps added below:

Step 1: Find the total sum of data in a given population.

Step 2: Divide the resultant summation by the total count of the population.

Let’s look at a few examples to get more understanding.

Example 1: What is the population mean for the given weights of persons- {50, 60, 70, 100, 80, 55, 60, 65}

Solution:

Step-1: Find the summation of given population

∑X = 50 + 60 + 70 + 100 + 80 + 55 + 60 + 65

= 540

Step-2: Find Population mean

μ = ∑X / N

Here size of population (N) = 8

= 540 / 8

= 67.5

So population mean for given population is 67.5

Example 2: Find the population mean for the given population 10, 20, 30, 40, 50, 55, 45, 35, 25, 15.

Solution:

Step-1: Find the summation of given population

∑X = 10 + 20 + 30 + 40 + 50 + 55 + 45 + 35 + 25 + 15

= 325

Step-2: Find Population mean

μ = ∑X / N

Here size of population (N) = 10

= 325 / 10

= 32.5

So population mean for given population is 32.5

Example 3: Find the population mean for the given population 20, 25, 20, 25, 22.

Solution:

Step-1: Find the summation of given population

Summation(Population) ∑X = 20 + 25 + 20 + 25 + 22

= 112

Step-2: Find Population mean

μ = ∑X / N

Here size of population (N) = 5

= 112 / 5

= 22.4

So population mean for given population is 22.4

Example 4: Find the population mean for the given data 10.5, 12.5, 20.5, 15.5, 20.5, 15

Solution:

Step-1: Find the summation of given data i.e., total of all values

∑X = 10.5 + 12.5 + 20.5 + 15.5 + 20.5 + 15

= 94.5

Step-2: Find Population mean

Here size of population (N) = 6

Population Mean (μ) = ∑X / N

= 94.5 / 6

= 15.75

So population mean for given population is 15.75

Example 5: Find population mean for the population 100, 200, 300, 400, 500, 600.

Solution:

Step-1: Find the summation of given data i.e., total of all values

∑X = 100 + 200 + 300 + 400 + 500 + 600

= 2100

Step-2: Find Population mean

Here size of population (N) = 6

Population Mean (μ) = ∑X / N

= 2100 / 6

= 350

So population mean for given population is 350.

What is the meaning definition of population?

Whole number of people or inhabitants in a country or region are defined as population of that region.

How to calculate for population mean?

Population mean is calculated by taking the sum of all values in the given data/population divided by a total number of values in the given data/population.

What is population mean vs sample mean?

• Population mean is the average of all observations in a specific population.
• Sample mean is the average of a subset (sample) of observations taken from a larger population. The

What is meant by population in statistics?

Population is the entire set of items from which you draw data for a statistical study.