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When it comes to the means meaning, in statistics, it is simply referred to as an average of the given data set. It is the value of the mean that represents the equal distribution of values in the given data set. One of the most used tools for measures of central tendency, there are three different types of means and these include arithmetic mean, geometric mean, and harmonic mean. 

Calculating the Mean

For calculating the value of the mean, first, the sum of all the observations in the given set of data is computed and then the estimated value of the sum is divided by the total number of observations present in the same data set. 

Mean for ungrouped data

The following mentioned is the formula that is used to calculate the mean for the ungrouped data:

Mean = Sum of all observations in a data set / Total number of observations in the data set

The Mean formula can be represented symbolically as:

x̄ = ∑x/n

where, 

x̄ represents the calculated mean;

∑ represents the observations that are to be added;

x represents all observations in the given data set; and 

n represents the total number of values in the given data set.

The following mentioned example will help an individual better understand how the value of the mean can be found:

Example: 

In a class, there are 8 students and have secured a percentage of 74, 86, 81, 75, 94, 85, 73, and 84.

Calculate the value of the mean percentage secured by the entire class.

Solution:

Mean = Sum of percentage secured by 8 students in the class / total number of students in the class

= (74 + 86 + 81 + 75 + 94 + 85 + 73 + 84) / 8

= 652 / 8

= 81.5

Hence, the value of the mean percentage secured by each student in the class is 81.5%

Mean for grouped data

When it comes to calculating the mean for the ungrouped data, the below-mentioned three methods can be used:

  • Direct method: The direct method uses the following mentioned Mean formula:

Mean = ∑xifi / ∑fi

  • Assumed Mean method: According to the assumed mean method, the following mentioned formula is used to calculate the mean:

Mean = A +∑fidi / ∑fi

Step-deviation method: According to the step-deviation method, the following mentioned formula is used to calculate the mean

mn

Different types of mean and their calculation

The mean, in statistics, is further classified into three types. The Types of Mean are listed below:

  • Arithmetic Mean: When it comes to the Arithmetic mean, it is calculated by dividing the sum of all observations given in the data set by the total number of observations in the same data set. The below-mentioned formula is used to compute the arithmetic mean:

Arithmetic Mean = ∑x/n

For example, to compute the arithmetic mean of 7, 5, 8, 9, 1, first all the given numbers in this particular data set are added (7 + 5 + 8 + 9 + 1 = 30) and then the computed sum is divided by total numbers (5).

Here, 

sum of all observations (∑x)  = 30

total observations (n) = 5

Hence, the arithmetic mean is equal to 6 (30 / 5).

  • Geometric Mean: Geometric mean is one of the Types of Mean which is calculated by multiplying all the given observations in the data set and then square rooting the computed multiplied value. The below-mentioned formula is used to compute the geometric mean:
mn1

For example, to compute the geometric mean of 2, 4, 7, and 5, first the given numbers are multiplied (3 × 5 × 6 × 4 = 360), then the square root of the computed multiplied value (280) is calculated.

Geometric Mean = 280 = 16.73

  • Harmonic Mean = The harmonic mean, one of the types of mean is basically used to average ratios. It can be computed by dividing the total number of observations in the given data set by the computed sum of the reciprocals of each observation given in the same data set. The below-mentioned formula is used to compute the harmonic mean:
mn2

Conclusion

Mean is one of the most used measures of central tendency in both statistics and mathematics. This particular value represents the average of the given set of observations. When it comes to the calculation of the mean, it is the simplest and easiest average to compute. If you are considering learning the basics of meaning including meaning, its types, formulas, and merits, then it is recommended to go through the above-mentioned article.Â