Mean is an important measure of central tendency in statistics. There are various kinds of mean in various branches of statistics, especially statistics. The arithmetic mean of a data set is the central value of a range of values or quantities, computed by dividing the total of all values by the number of values. So if you want to clear your basic statistical concepts you need to understand how to find the mean of data. Finding the arithmetic mean of different data set of numbers is taught to students at school so it is a very important part of mathematics and statistics which they would find useful later in their life too.
The statistical data can be classified into two parts – grouped and ungrouped. There are different formulas to calculate the mean for both the categories of data. So through this article, we shall help you understand how you can calculate the mean of grouped and ungrouped data and also understand the various concepts of mean.
How To Find (Calculate) the Mean
There are different types of mean in mathematics, but today we shall discuss Arithmetic Mean (or A.M.). The other types of the mean are Geometric Mean (G.M.) and Harmonic Mean (H.M.). The mean is the simplest and commonly used average we use for any data set.
The formula for the arithmetic mean is :
Here, x₁, x₂, x₃, etc. are the values of the sample. N is the total number of observations in the data. Hence to calculate the Arithmetic Mean of any data, you need to divide the sum of observations by the number of observations.
For example, consider you have the following data set: 8,9,6,12,19.
So the mean of the data would be (8+9+6+12+19)/2 = 54/2 = 27.
How To Find the Mean of Ungrouped Data
As you know, an ungrouped data is a set of raw data which is not categorized or divided into class-intervals. The formula for calculation for mean is slightly different from grouped data.
The formula for calculating mean for ungrouped data is :
How To Find the Mean Deviation
Mean deviation is the numerical value of the difference of the observations from the mean value of the data. So it is the measure of the dispersion of the observations around the central observation or mean of the data. There are various methods to calculate the measures of dispersion of the observations from the central tendencies.
The mean deviation states how close or scattered are the data points from the mean value of the observations. For calculating mean deviation, you first need to calculate the mean value of the data. So you can use the formula we have provided above to calculate the mean of the data. Then you need to subtract each observation individually from the mean value.
The formula for calculating the mean deviation is as given below
Here we shall provide you with an example on how to calculate the mean deviation for any data :
For example let us suppose
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