How To Find The Population Mean
The concept of Population Mean falls under the domain of statistics, which involves the collection, analysis, interpretation, and presentation of organized data. The Population Mean Formula represents the average of all the values in a given data set or population.
Understanding Population Mean
The population mean, denoted by the symbol μ, can be calculated by summing all the values in the given data set or population and then dividing the sum by the total number of values in the population. The sum of numbers is represented as a single term, Summation.
Population Mean Formula
If X is the variable holding the data, then the formula for Population Mean (μ) is given by:
Population Mean (μ) = ∑X / N
Where, ∑X is the summation of data in X and N is the count of data in X.
Steps to Calculate Population Mean
The following steps can be followed to calculate the Population Mean:
- Find the total sum of data in a given population.
- Divide the resultant summation by the total count of the population.
Examples
Let’s consider a few examples to gain a better understanding of how to calculate the Population Mean.
Example 1
Question: 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 the given population
∑X = 50 + 60 + 70 + 100 + 80 + 55 + 60 + 65 = 540
Step-2: Find Population mean
μ = ∑X / N
Here, the size of the population (N) = 8
Population Mean = 540 / 8 = 67.5
So, the population mean for the given population is 67.5
Example 2
Question: 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 the given population
∑X = 10 + 20 + 30 + 40 + 50 + 55 + 45 + 35 + 25 + 15 = 325
Step-2: Find Population mean
μ = ∑X / N
Here, the size of the population (N) = 10
Population Mean = 325 / 10 = 32.5
So, the population mean for the given population is 32.5
Example 3
Question: Find the population mean for the given population 20, 25, 20, 25, 22.
Solution:
Step-1: Find the summation of the given population
∑X = 20 + 25 + 20 + 25 + 22 = 112
Step-2: Find Population mean
μ = ∑X / N
Here, the size of the population (N) = 5
Population Mean = 112 / 5 = 22.4
So, the population mean for the given population is 22.4
Example 4
Question: 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 the 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, the size of the population (N) = 6
Population Mean = ∑X / N
= 94.5 / 6 = 15.75
So, the population mean for the given population is 15.75
Example 5
Question: Find the population mean for the given population 100, 200, 300, 400, 500, 600.
Solution:
Step-1: Find the summation of the given data i.e., total of all values
∑X = 100 + 200 + 300 + 400 + 500 + 600 = 2100
Step-2: Find Population mean
Here, the size of the population (N) = 6
Population Mean = ∑X / N
= 2100 / 6 = 350
So, the population mean for the given population is 350
Conclusion
Calculating the population mean is essential in statistics as it provides a measure of the central tendency of the data. By following the simple steps and using the population mean formula, one can easily determine the average value of a given population.
FAQs
Q: What is the significance of calculating the population mean?
A: Calculating the population mean helps in understanding the central value around which the data is distributed, providing valuable insights for decision-making and analysis.
Q: Can the population mean be used to make predictions?
A: Yes, the population mean can be used to make predictions and draw inferences about the entire population from which the data is derived.
Q: How is the population mean different from the sample mean?
A: The population mean represents the average of all values in the entire population, while the sample mean is the average of a subset of the population (a sample).
Q: What are the limitations of using the population mean?
A: One limitation is that extreme values in the population can significantly affect the population mean, leading to potential distortion of the central tendency measure.
Q: In what real-world scenarios is the population mean commonly used?
A: The population mean is frequently used in fields such as economics, demographics, and quality control to analyze and understand various parameters and make informed decisions.
Q: How can one ensure the accuracy of the calculated population mean?
A: To ensure accuracy, it is important to verify the data inputs, perform thorough calculations, and cross-verify the results using statistical software or tools.