# Population Mean Formula

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

### Population Mean

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population. We can call the sum of numbers as a single term Summation.

The population mean is denoted by the symbol μ.

Let X be the variable that holds data then,

Population Mean (μ) = ∑X / NWhere, ∑X is the summation of data in X

And, N is the count of data in X.

**Steps to calculate Population mean**

- Find the total sum of data in a given population.
- Divide the resultant summation by the total count of the population.

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

### Sample Problems

**Question 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 meanμ = ∑X / N

Here size of population (N) = 8

= 540 / 8

= 67.5

So population mean for given population is 67.5

**Question 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 meanμ = ∑X / N

Here size of population (N) = 10

= 325 / 10

= 32.5

So population mean for given population is 32.5

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

**Solution:**

Step-1:Find the summation of given populationSummation(Population) ∑X = 20 + 25 + 20 + 25 + 22

= 112

Step-2:Find Population meanμ = ∑X / N

Here size of population (N) = 5

= 112 / 5

= 22.4

So population mean for given population is 22.4

**Question 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 meanHere size of population (N) = 6

Population Mean (μ) = ∑X / N

= 94.5 / 6

= 15.75

So population mean for given population is 15.75

**Question 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 meanHere size of population (N) = 6

Population Mean (μ) = ∑X / N

= 2100 / 6

= 350

So population mean for given population is 350.