Population Mean Formula

Population Mean is the most important concept of Statistics, which is the study of collecting, analyzing, interpreting, and presenting data in an organized way. The population mean gives a quick snapshot of what the "typical" value of the population look like. Whether you are analyzing your exam score or the height of a student, the mean simplifies a large set of data.

The 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. The 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 Formula

Let X be the variable that holds data then,

Population Mean (μ) = ∑X / Na

where,

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

Application of the Population Mean Formula

• Academic Grading - Calculate the average score to assess class performance.
• Quality Control - Monitors product consistency using average measurement.
• Healthcare- Track patient data like average BMI or blood pressure.
• Economic Analysis - Studies income, inflation, and Stock prices.

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: The population

Let's look at a few examples to get a better understanding.

Solved Examples on Population Mean Formula

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.