Population vs Sample & Parameter vs Statistic & Biased vs Unbiased in Statistics

We will cover Population and Sample, Parameter and Statistic, Population Mean and Sample Mean, Biased and Unbiased

Introduction

In this blog, you will see about these topics in Statistics

• Population & Sample
• Parameter & Statistic
• Population Mean & Sample Mean
• Biased & Unbiased Estimator

Want to learn about Measure of Central Tendency and Measure of Variability. Here is the Blog for you. . .

Statistics: Mean, Median and Mode

Statistics: Range, Variance and Standard Deviation

Let’s get into Action . . . . . . . .

Population & Sample

https://www.omniconvert.com/what-is/sample-size/

Population : The Population is the Entire group that you are taking for analysis or prediction.

Sample : Sample is the Subset of the Population(i.e. Taking random samples from the population). The size of the sample is always less than the total size of the population.

Let’s take a Scenario to describe the Population and Sample to make more clarity.

You are doing a Voting Prediction to analyze/predict which party will get majority of vote and won the Election.

So, your next step is to collect the data from the people that they voted for which party. Let’s consider India, there are above 130 Crore people, you can’t get all the people opinions that they voted.

Due to constraints of resources, time, and accessibility computing data from a population is nearly impossible, hence a sample is used. As an analogy, you can think of your sample as an aquarium and your population as the ocean. Your sample is small portion of a vaster ocean that you are attempting to understand.

Coming back to the Scenario, you randomly select some people and take their opinions then you will do the analysis/prediction.

Note: You have to take the people opinions randomly. Because, If you collect information from one State/district for the Entire Indian People voting, your prediction/analysis goes wrong, because the data would get biased. We will see “Bias & Unbiased” in the below part

While taking the samples from the population, there are different types. . .

Sampling with and Without Replacement: Let’s start with an example, you have one basket contains 5 Red Balls and 4 Blue Balls. In the first event, you are taking a sample of 3 Red Balls and 2 Blue Balls and Calculating their probability.

• If you put the sample of 3 Red Balls and 2 Blue Balls back into the basket is referred as Sampling With Replacement.
• If you didn’t put the sample back into the basket and calculation probability for the next event, this is referred as Sampling Without Replacement.

Parameter & Statistic

Parameters

Calculating Mean, Variance and Standard Deviation on Population Data known to be a Population parameters. The population mean and population standard deviation are represented by the Greek letters µ and σ respectively. A parameter is a characteristic of a population.

Statistic

Calculating Mean(x̅), Variance and Standard Deviation on Sample Data known to be a Sample statistic. A statistic is a characteristic of a sample.

If anyone ask and calculate statistic means, you have to calculate x̅, s2 ( S Square) and S.

Notation of Population and Sample — Image Created by Author

Population Mean & Sample Mean

Population Mean

Mean gives the average of the data. If you calculate mean for population data is known as Population Mean. Population mean is a fixed one. . . it doesn’t vary.

Image Created by Author

Sample Mean

Calculation of mean using Sample data is known as Sample Mean. Sample mean vary as our data size/sample size increases. . .

Image Created by Author

Biased & Unbiased Estimator

Biased

If your Population Parameter and Sample Statistic is not equal, then it is called as Biased. Usually Bias somewhat tilt towards one sided of the data rather than random.

Unbiased

If your Population Parameter and Sample Statistic is equal, then it is called as Unbiased

Conclusion

I hope this article will help you to know about Population, Sample, Parameter and Statistic, Population Mean, Sample Mean, Biased and Unbiased Estimator.

Like . . If you like. . .

Thank you,

Bala Murugan N G

Bala Murugan N G - Associate - Data Scientist | LinkedIn

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