Sample Mean vs Population Mean: Difference and Comparison

Everyone has studied statistics in our mathematics class, and we have done mean, median, and mode. These are statistical terms in mathematics, and I am sure that not everybody likes the subject.

Now, the mean in statistical language will show the average of a particular data. To find out the mean of a set of numbers, you have to sum up all the numbers and then divide by the number of values, and it is then you will get the mean value.

Under mean, there are two types where you will find the sample mean and population means. I am sure that most of you know the difference between the two, and they have quite simple meanings in statistics.

On the other hand, the population mean is denoted as the entire pool, and the population in statistics may refer to a group of people, objects, and other kinds of stuff. Population mean means the aggregate observation that is grouped by a common feature.

Key Takeaways

  1. The sample mean is the average value of a subset of data from a population, whereas the population mean is the average value of the entire population.
  2. The sample mean is used to estimate the population mean, while the population mean measures the central tendency of the entire population.
  3. As the sample size increases, the sample mean becomes more representative of the population mean, and the difference between the two becomes smaller.

Sample Mean vs. Population Mean

The difference between sample and population mean is that sample mean is the sample values accumulated or collected, and population means, on the other hand, means the mean of the population. Though calculating both sample mean and population means can be almost similar, they are denoted by a different sign, as the sample mean denoted by the symbol or letter x with a bar at the top. In contrast, population means comes from the Greek word mu.

Sample Mean vs Population Mean

Comparison Table

Parameters of ComparisonSample MeanPopulation Mean
MeaningSample mean means the mean of sample data and the average of a data set.On the other hand, the population means the arithmetic or the statistical mean of the total population.
AccuracyThe sample mean has a lower accuracy than the population means.Population means, on the other hand, has got a higher accuracy.
SetIt is a sub-division of the whole population.It is a complete set.
Containing specific groupThe sample mean is a sub-division representing the whole population.It contains all the objects of a designated group.
CalculationEasy to calculateDifficult to calculate.

What is Sample Mean?

As stated above, the sample mean is a small sample of data drawn from a population. In other words, the sample mean is the mean that can be calculated from a group of random data or variables.

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The sample mean is considered efficient, and an unbiased estimator for calculating the population means. This means that the most expected value for the sample statistic is the population statistic.

When comparing with the population means, there are certain differences. Still, they are calculated almost in the same way, that is, by summing all the observations divided by the number of the observations.

The only difference that these two make is how they are presented. The denoting sign is different for both cases.

Many people say that calculating the sample mean of a particular variable is very easy because the elements to calculate the sample mean are very few and therefore take less time to calculate. This is not the case for calculating the population mean because they are difficult to calculate.

What is Population Mean?

Population means, on the other hand, the mean of the values of the entire population. This is the other type of mean in the statistical or arithmetical world.

The population mean is called the average of all the elements of a population. The population can be anything, such as any group of objects or people.

Since the population is large and unknown, the population means will be unknown constant. The population mean is denoted by a Greek sign called mu.

The elements of the population mean they can be denoted as the capital letter ‘N.’ When the population mean is used in a particular standard deviation calculation, they are represented by the sigma sign.

Main Differences Between Sample Mean and Population Mean

  1. The mean drawn out from a population is called the sample mean, whereas population means are the aggregate of the entire population.
  2. The sample mean is represented by the letter x with a bar at the top of the x and is called the x bar, whereas the Greek named sign mu represents the population means.
  3. Calculating the sample mean is relatively easy because it contains fewer elements, whereas calculating the population mean is difficult. After all, they contain more elements that become time-consuming.
  4. The accuracy of the sample mean is lower than that of the population mean.
  5. The letter ‘N’ is used for presenting the elements of the population, whereas the letter ‘n’ refers to the sample size.
References
  1. https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1969.tb00794.x
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Last Updated : 11 June, 2023

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24 thoughts on “Sample Mean vs Population Mean: Difference and Comparison”

  1. The author does a commendable job explaining the intricacies of sample mean and population mean. It’s a thought-provoking piece.

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  3. The article might be a bit too technical and challenging for those new to statistics. It could benefit from more accessible language.

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  6. This article does a great job explaining the differences between sample mean and population mean. It’s very informative and useful to those studying statistics.

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