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 samplemeanformula is used to calculate the average value of the given sample data. It is necessary sometimes to calculate the averageof the sample termsrather than expressing them with actual terms. The sample meanformulacan beexpressed as the ratio of the sum of terms to the number of terms. i.e.,
Sample MeanFormula
The sample meanformula 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.
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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 is69.
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 meanheight 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 minutesrespectively. 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 termsin the data set. When calculating the sample mean the following steps can be considered:
- Add the totalsample 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 MeanFormula?
The general sample mean formula for calculating the sample mean is expressed as x̄ = ( Σ xi ) ÷ n. Here, x̄ denotes the average value ofthe 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:
\(∑x_i = (x_1 +x_2 + x_3+⋯+x_n)\).
