# What is mean method formula?

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,

### 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

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

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,

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 interval | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |

Frequency | 12 | 28 | 32 | 25 | 13 |

**Solution:**

Class interval Frequency(f) Midpoint(x) d=x-A fd 0 – 10 12 5 -20 -240 10 – 20 28 15 -10 -280 20 – 30 32 25 0 0 30 – 40 25 = A 35 10 250 40 – 50 13 45 20 260 ∑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.**

Items | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 |

frequency | 4 | 10 | 10 | 4 |

Solution:

Items Midpoint (x) Frequency(f) d/c=x-A d=x-A/c fdx 0 – 10 5 4 -10 -1 -4 10 – 20 15 = A 10 0 0 0 20 – 30 25 10 10 1 10 30 – 40 35 4 20 2 8 ∑fdx = 14 X = A + ∑fd/∑f x c

X = 15 + 14/28 × 10

X = 15 + 5

X = 20

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