Mean Definition

In Mathematics, a mean is simply defined as the average of the given set of numbers. The mean is also considered as one of the measures of central tendencies in Statistics. It gives the central value of the set of values. The other two measures of central tendency are median and mode. Many students get confused with these three terms. In this article, let us discuss the definition of mean, formula with an example.

Definition of Mean

Mean is also said to be arithmetic mean. The meaning of mean is to evaluate the average. It is defined as the average of the given numbers. Mean is the sum of all the given data values divided by the total number of data values given in the set. It is given by:

Mean = Sum of Observations/Total number of observations

In the case of median and mode, median refers to the middle value of the data set, whereas mode refers to the repeated numbers in the data set.

How to Find Mean

To calculate the mean value of the given data, it includes two steps. They are:

  1. Add all the values in the data set
  2. After adding, divide that value by the total number of data given

Mean Formula

According to the definition of mean, the formula to calculate the mean is given by,

Mean = Sum of Given Data / Total Number of Data

In terms of Sigma (∑) notation, the mean formula is:

\(\bar{X}= \frac{\sum_{i=1}^{n} X_{i}}{N}\)

Where

N = Total number of given data

∑ Xi= Sum of given data values

Types of Mean

The three different types of mean are:

  • Arithmetic Mean (AM)
  • Harmonic Mean (HM)
  • Geometric Mean (GM)

Mean Example

Question:

Find the mean for the given data set: 2, 6, 4, 5, 8

Solution:

Given data set = 2, 6, 4, 5, 8

Total number of data value = 5

Therefore, the formula to find the mean is given by:

Mean = Sum of given data / Total number of the data

= (2 + 6 + 4 + 5 + 8) / 5

= 25/5

= 5

Hence, the mean value of the given data is 5.

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