Sample Mean and Population Mean - Statistics
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6 months ago
Published on Apr 22, 2024
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Table of Contents
How to Calculate Sample Mean and Population Mean in Statistics
1. Understand the Difference Between Sample and Population:
- Population: Refers to the entire group being studied. For example, the population of city XYZ with a hundred thousand people.
- Sample: Represents a smaller portion of the population that is used to make inferences about the entire population. For instance, measuring the weight of 1000 people to estimate the average weight of all citizens in the city.
2. Calculate Sample Mean:
- Sample Mean (x̄): Calculated by summing up all the data values in the sample and dividing by the number of individuals in the sample (n).
- Formula: x̄ = Σx / n
3. Calculate Population Mean:
- Population Mean (μ): Represents the average of all individuals in the entire population.
- Formula: μ = Σx / N, where N is the total number of individuals in the population.
4. Aim for Accuracy:
- Ideally, the sample mean should closely approximate the population mean. Increasing the sample size (n) towards the population size (N) improves the accuracy of the estimate.
5. Understand Terminology:
- Statistic: Refers to measures calculated from a sample, such as the sample mean, median, or mode.
- Parameter: Denotes characteristics of a population, like the population mean.
6. Formulas for Mean Calculation:
- Sample Mean Formula: x̄ = (x₁ + x₂ + ... + xn) / n
- Population Mean Formula: μ = (x₁ + x₂ + ... + xn) / N
7. Sigma Notation:
- The formulas can also be represented using sigma notation, where Σ denotes the sum of all data values from the first to the last item in the sample or population.
8. Apply the Formulas:
- Calculate the sample mean and population mean by substituting the data values and respective sample or population sizes into the formulas.
By following these steps, you can effectively calculate the sample mean and population mean in statistics to draw meaningful insights from your data.