Everyone has studied statistics in our mathematics class and we have done mean, median, and modes. These are statistical terms in the world of mathematics and I am sure that not everybody personally liked 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.

Now, under mean, there are two types where you will find sample mean and population mean. I am sure that most of you know the difference between the two and they have quite simple meanings in statistics. The sample mean is nothing but is used as a tool to calculate the central tendency or it is the average set of a particular data.

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

**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 mean can be almost similar but they are denoted by different sign as sample mean is denoted by the symbol or letter x with a bar at the top whereas population mean comes from the Greek word mu.

**Comparison Table Between Sample Mean and Population Mean**

Parameters of Comparison | Sample Mean | Population Mean |

Meaning | Sample mean means the mean of a sample data that is also the average of a set of data. | The population mean, on the other hand, means the arithmetic or the statistical mean of the total population altogether. |

Accuracy | Sample mean consists of a lower accuracy as compared to population mean. | Population mean, on the other hand, has got a higher accuracy. |

Set | It is a sub-division of the whole population. | It is a complete set. |

Containing specific group | Sample mean is a sub-division representing the whole population. | It contains all the objects of a designated group. |

Calculation | Easy to calculate | Difficult to calculate. |

**What is Sample Mean?**

As stated above that the sample mean is a small sample data that is actually 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.

The sample mean is considered as the efficient and it is an unbiased estimator for the calculation of the population means. This means that the value which is the most expected for the sample statistic is actually the population statistic.

When comparing with the population mean there are certain differences but 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 are how they are presented. The denoting sign is different for both cases. The sample mean is shown by the letter x with a bar drawn at the top of the letter x and is pronounced as x bar.

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

**What is Population Mean?**

Population mean, on the other hand, is the mean of the values of the entire population. This is the other type of mean in the statistical world or in the arithmetical world. Most people find it difficult to calculate the population mean because they are difficult because there are many elements to calculate, unlike sample mean.

The population mean is called the average of all the elements of a population. The population can be referred to as anything such as any group of objects or even a group of people. The population is large and this is why the accuracy is also high in the case of the population mean.

Since the population is large and is unknown then the population mean will be unknown constant. The population mean is denoted by a Greek sign called as mu. As said earlier that it is difficult to calculate population mean because population mean has got lot of elements and therefore they are time consuming.

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

**Main Differences Between Sample Mean and Population Mean**

- The mean that is drawn out from a population is called as the sample mean whereas a population mean is the aggregate of the entire population.
- The sample mean is represented by the letter x with a bar at the top of the x and is called as x bar whereas the population mean is represented by the Greek named sign mu.
- The calculation of sample mean is quite easy because it contains less elements whereas calculating population mean is difficult because they contain more elements that become time-consuming.
- The accuracy of sample mean is lower than that of the population mean.
- The letter ‘N’ is used for presenting the elements of the population whereas the letter ‘n’ is used for referring the size of sample.

**Conclusion**

In the end, it is important to know how to calculate the sample mean and as well as the population mean because both can be handy when you are doing arithmetic. But, when you are calculating sample mean and population mean then there might be no difference but while presenting them then there will be a huge difference.

**References**

- https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1969.tb00794.x
- http://isas.org.in/jsp/volume/vol58/issue2/hpsingh_1.pdf

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