What is calculated by summing the values of the observations in the sample and then dividing the sum by the number of observations in the sample?

Formula to Calculate Population Mean

The population mean is the mean or average of all values in the given population and is calculated by the sum of all values in population denoted by the summation of X divided by the number of values in population which is denoted by N.

Inhaltsverzeichnis Show

• Formula to Calculate Population Mean
• Relevance and Use
• Recommended Articles
• What is the sum of observations divided by the number of observation is known as?
• Is defined as the sum of the values of the variables divided by the number of observations?
• Is the total of the sum of all values in a collection of numbers divided by the number of items in a collection?
• What is the sum of the deviations taken from the mean of each of its observations for any information?

It is arrived at by summing up all the observations in the group and dividing the summation by the number of observations. When the whole set of data is taken for computing a statistical parameter, the set of data is the population. For example, the returns of all the stocks listed in the NASDAQ stock exchange in the population of that group. For this example, the population meansMean 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 for the return of all the stocks listed in the NASDAQ stock exchange will be the average of the return all the stocks listed in that exchange.

In order 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 is N.

The formula is represented as follows,

µ= ∑X/N

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For eg:
Source: Population Mean Formula (wallstreetmojo.com)

• µ= Population mean

Examples

Example #1

Let us try to 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%. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. 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 return of stock with the help of the formula.

The following are 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 try to 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%. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. 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 period.

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

Below is given data for 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. In order to calculate the mean for the whole population, we need to find out the summation of all the observed values first. 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 for 15 students.

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

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 a very important statistical parameter. It helps in knowing the average of the population’s parameters. The mean is important as it is used in the calculation of several other statistical parameters like the variance, standard deviations, and other. It is calculated using the concept of the arithmetic 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 and represents the average or mean on the basis of which one can make an inference of whether an observation is high or low in the whole population of observations.

Recommended Articles

This has been a guide to Population Mean Formula. Here we discuss how to calculate the population mean along with the practical examples and downloadable excel template. You can learn more about financing from the following articles –

• Geometric 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 more
• Mean 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 more
• Mean 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 more
• Formula 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 read more
• Annuity vs Lump SumAnnuity refers to the series of frequent payments made at regular intervals over a certain period. Whereas lump sum means the disbursement of the due amount all at once, i.e., settling the total sum in a single payment.read more