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What is mean method formula?

  • Last Updated : 29 Nov, 2021

Statistics is a mathematical branch that is carried out by the collection and summarization of data. It is concerned with collecting, analyzing, interpreting, presenting a set of data. Statistics has its role in the field of data collection especially data used by the government like a population census, mortality rate, etc. Qualitative and quantitative stats are also part of the economy, geology, psychology, and other fields.

Mean

Mean is an average of a set of data which is calculated by dividing the sum of all the data by the number of counts. In simple words, the mean is the total average which can be calculated by adding all the numbers and then, dividing by the count of numbers present. The mean value is a derived average that falls between maximum and minimum values in the set of data.

The mathematical formula of mean is given by,

\bar X=\sum x/n

Mean method formula

The mean formula for a grouped set of data can be derived by three different methods based on the size of data given,

  • Direct method

In, direct method mean is calculated by

\bar X=\frac{\sum fx}{\sum f}

where, 

f = frequency

x = number of observation

For the direct method, let us suppose x be the number of observations with respect to frequency f, which means x occurs f times in the set. This method of mean calculation is used for a small set of data.

  • Assumed mean method

In the assumed mean method mean is calculated by

\bar X=A+\frac{\sum fd}{\sum f}

where,

A = assumed mean

d = x – A = deviation

f = frequency

For the assumed mean method, The data is given in frequency distribution table form. Generally assumed a value from the data as the mean value for calculation. On the basis of this assumed mean deviation is calculated by the formula (d = x – A).

  • Step-deviation method

In the step-deviation method mean is calculated by,

\bar X= A+\frac{\sum fd}{\sum f} x c

where,

A = assumed mean

d = x – A/c = deviation

c = common factor

f = frequency

The step deviation method of mean calculation is used when the provided data is large in size.

Sample Problems

Question 1: Find the mean value of given data.

10, 20, 30, 40, 50, 60, 70

Solution:

Number of observation(n) = 7

sum of observation(x) = 10 + 20 + 30 + 40 + 50 + 60 + 70 = 280

Now,

X=∑x/n

X = 280/7

X = 40

Question 2: Find the mean value by the assumed mean method.

Class interval0 – 1010 – 2020 – 3030 – 4040 – 50
Frequency1228322513

Solution:

Class intervalFrequency(f)Midpoint(x)d=x-Afd
0 – 10125-20-240
10 – 202815-10-280
20 – 30322500
30 – 40 25 = A3510250
40 – 50134520260
    ∑fd = -10

Now,

X=A+∑fd/∑f

=>X=25+(-10/110)

=>X=275-1/11

=>X=24.9

Question 3: Find the mean value by the step deviation method.

Items0 – 1010 – 2020 – 3030 – 40
frequency410104

Solution:

ItemsMidpoint (x)Frequency(f)d/c=x-Ad=x-A/cfdx
0 – 1054-10-1-4
10 – 2015 = A10000
20 – 30251010110
30 – 403542028
     ∑fdx = 14

X = A + ∑fd/∑f x c

X = 15 + 14/28 × 10

X = 15 + 5

X = 20

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