# Sample Mean Formula

Sample mean represents the measure of the center of the data. Any population's mean is estimated using the sample mean. In many of the situations and cases, we are required to estimate what the whole population is doing, or what all are the factors going throughout the population, without surveying everyone in the population. In such cases sample mean is useful. An average value found in a sample is termed the sample mean. the sample mean so calculated is used to find the variance and thereby the standard deviation. Let us see the sample mean formula and its applications in the upcoming sections.

## What Is Sample Mean Formula?

The sample mean formula is used to calculate the average value of the given sample data. It is necessary sometimes to calculate the average of the sample terms rather than expressing them with actual terms. The sample mean formula can be expressed as the ratio of the sum of terms to the number of terms. i.e.,

### Sample Mean Formula

The sample mean formula is written as

**Sample Mean = (Sum of terms) ÷ (Number of Terms) **=\(\dfrac{∑x_i}{n}\) =\(\dfrac{(x_1 + x_2 + x_3+⋯+x_n)}{n}\)

Where,

- \(∑x_i\) = sum of terms
- n = number of terms

Let us see the applications of the sample mean formula in the section below.

## Examples on Sample Mean Formula

**Example 1:** Find the sample mean of 60, 57, 109, 50.

**Solution:**

To find: Sample mean

Sum of terms = 60 + 57 + 109 + 50 = 276

Number of terms = 4

Using sample mean formula,

mean = (sum of terms)/(number of terms)

mean = 276/4 = 69

**Answer: **The sample mean of 60, 57, 109, 50 is 69.

**Example 2:** Five friends having heights of 110 units, 115 units, 109 units, 112 units, and 114 units respectively. Find their sample mean height.

**Solution: **

To find: Sample mean height

Sum of all heights = 110 + 115 + 109 + 112 + 114 = 560

Number of person = 5

Using sample mean formula,

mean = (sum of terms)/(number of terms)

mean =560/5

= 112 units

**Answer: **The sample mean height of five friends is 112 units.

**Example 3:** Five children having different time slots of finishing their homework 30 minutes, 60 minutes, 45 minutes, 40 minutes, and 90 minutes respectively. Find their sample mean time.

**Solution: **

To find: Sample mean time

Sum of all time slots= 30 + 40 + 45 + 60 + 90 = 265

Number of children = 5

Using sample mean formula,

mean = (sum of terms)/(number of terms)

mean =265/5

= 53 minutes

**Answer: **The sample mean time of five children is 53 minutes.

## FAQs on Sample Mean Formula

### How to Calculate the Sample Mean Using Sample Mean Formula?

The general formula for calculating the sample mean is given by x̄ = ( Σ xi ) / n. Here, x̄ represents the sample mean, xi refers all X sample values and n stands for the number of sample terms in the data set. When calculating the sample mean the following steps can be considered:

- Add the total sample items
- Divide the total of sample items by the number of samples.
- The obtained result is the sample mean.

### What Does n Represent in the Sample Mean Formula?

The general sample mean formula for calculating the sample mean is expressed as x̄ = ( Σ xi ) ÷ n. Here, x̄ denotes the average value of the samples or sample mean, xi refers all X sample values and 'n' stands for the number of sample terms in the given data.

### How To Add Up the Sample Items Using the Sample Mean Formula?

To add up the sample items or to get the sum up value of all the sample items we follow the following pattern:

\(∑x_i = (x_1 + x_2 + x_3+⋯+x_n)\).

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