Formula to Calculate Population Mean

It arrives by summing up all the observations in the group and dividing the summation by the number of observations. When one uses the whole data set for computing a statistical parameter, the data set is the population. For example, the returns of all the stocks listed in the NASDAQ stock exchange in the population of that group. So, for this example, the population meansMeansMean refers to the mathematical average calculated for two or more values. There are primarily two ways: arithmetic mean, where all the numbers are added and divided by their weight, and in geometric mean, we multiply the numbers together, take the Nth root and subtract it with one.read more that the return of all the stocks listed in the NASDAQ stock exchange will be the average return of all the stocks listed in that exchange.

To calculate the population mean for a group, we first need to find out the sum of all the observed values. So, if the total number of observed values is denoted by X, then the summation of all the observed values will be ∑X. And let the number of observations in the population be N.

The formula is represented as follows,

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  • µ= Population mean

Examples

Example #1

Let us analyze the return of a stock XYZ for the last twelve years. And the returns for the stock in the last twelve years are 12%, 25%, 16%, 14%, 40%, 15%, 13%, 17%, 23%, 13%, 17%, and 19%. To calculate the mean for the whole population, we must first find out the summation of all the observed values. So in this example, the ∑X is 224%, and the number of observed values for the population is 12 as it comprises the return for the stock for 12 years period.

With these two variables, we can calculate the population mean for the stock return with the formula’s help.

The following is the given data:

Therefore, using the above information mean can be calculated as,

  • µ= 224%/12

The example shows that the mean or average return for the observed value is 19%. 

Example #2

Let us analyze the return of a thematic mutual fund for the last eight years. And the returns for the stock in the last twelve years are 25%, 16%, 14%, 15%, 13%, 23%, 33%, and 27%. To calculate the mean for the whole population, we must first find the summation of all the observed values. So in this example, the ∑X is 166%, and the number of observed values for the population is 8 as it comprises the return of the mutual fund for 8 years.

Below is given data for the calculation:

Therefore, the mean can be calculated as,

  • µ= 166%/8

The example shows that the mean or average return for the observed value is 21%. 

Example #3

Let us find out the population mean of the weight of 15 students in a class. The weight of each student in the class of 15 students in kg is as follows 35, 36, 42, 40, 44, 45, 38, 42, 39, 42, 44, 45, 48, 42, and 40. To calculate the mean for the whole population, we must first find out the summation of all the observed values. So in this example, the ∑X is 622 Kg, and the number of observed values for the population is 15 as it comprises the weight of 15 students.

The following are the given data for the calculation:

Therefore, using the above information population average can be calculated as,

  • µ= 622/15

 The example shows that the mean or average return for the observed value is 41.47

Relevance and Use

The population means is a very important statistical parameter. It helps in knowing the average of the population’s parameters. The mean is important as one can use it to calculate several other statistical parameters like the variance, standard deviations, and others. One may calculate it using the concept of the arithmetic mean formulaArithmetic Mean FormulaArithmetic mean denotes the average of all the observations of a data series. It is the aggregate of all the values in a data set divided by the total count of the observations.read more. It represents the average or means based on which one can infer whether an observation is high or low in the whole population of observations.

This article has been a guide to Population Mean Formula. Here, we discuss calculating the population means along with the practical examples and downloadable Excel template. You can learn more about financing from the following articles: –

  • Geometric and Arithmetic MeanGeometric And Arithmetic MeanGeometric mean is the calculation of mean or average of a series of product values that takes into account the effect of compounding and is used to determine investment performance, whereas arithmetic mean is the calculation of mean by sum of total of values divided by number of values.read moreMean ExamplesMean ExamplesMean examples comprise various situations where we can apply arithmetic, weighted, geometric and harmonic means to measure the central tendency. Moreover, we use the arithmetic mean in our daily lives to find the percentage scored by a student in academics or cost per person for a party.read moreMean vs MedianMean Vs MedianMean is an average of given numbers. It sums up the numbers and divides them with the count of numbers which provides us with the mean. On the other hand, the median returns the middle number from the whole data set.read moreFormula of Sampling DistributionFormula Of Sampling DistributionA sampling distribution is the probability-based distribution of detailed statistics. It helps calculate means, range, standard deviation, and variance for the undertaken sample. For a sample size of more than 30, the formula is: µ͞x =µ and σ͞x =σ / √n
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