Assumed Mean Method

In statistics, assumed mean method is used for calculating mean or arithmetic mean of a grouped data. If the given data is large, then this method is recommended rather than a direct method for calculating mean. This method helps in reducing the calculations and results in small numerical values for easy computation. This method depends on estimating the mean and rounding to an easy value to calculate with. Again this value is subtracted from all the sample values. When the samples are converted into equal size ranges or class intervals, a central class is chosen and the count of ranges from that is used in the calculations.

Assumed Mean Method Formula

Let x1, x2, x3,…,xn are mid-ponts or class marks of n class intervals and f1, f2, f3, …, fn are the respective frequencies. The formula of assumed mean method is:

Assumed mean formula

Here,

a = assumed mean

fi = frequency of ith class

di = xi – a = deviation of ith class

Σfi = n = Total number of observations

xi = class mark = (upper class limit + lower class limit)/2

The value for a will be taken one among xi’s with the assumption that the frequency of a class is centred at its mid-point, called its class mark.

Read more:

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Assumed Mean Method Questions

If xi and fi are numerically large, the assumed mean method is preferred. Below are some examples of calculating the mean of a grouped data by this method.

Example 1:

The following table gives the information about the marks obtained by 100 students in an examination.

Class

0-10

10-20

20-30

30-40

40-50

Frequency

12

28

32

25

13

Find the mean marks of the students using assumed mean method.

Solution:

Class (CI)

Frequency (fi)

Class mark (xi)

di = xi – a

fidi

0-10

12

5

5 – 25 = – 20

-240

10-20

28

15

15 – 25 = – 10

-280

20-30

32

25 = a

25-25 = 0

0

30-40

25

35

35-25 = 10

250

40-50

13

45

45-25 = 20

260

Total

Σfi =100

Σfidi = -10

Assumed mean = a = 25

Mean of the data:

Assumed mean formula

= 25 + (-10/ 100)

= 25 – 1/10

= (250-1)/10

= 249/10

=24.9

Hence, the mean marks of the students are 24.9.

Example 2:

The table below gives the information about the percentage distribution of female employees in a company of various branches and number of departments.

Percentage of female employees

Number of departments

5-15

1

15-25

2

25-35

4

35-45

4

45-55

7

55-65

11

65-70

6

Find the mean percentage of female employees by assumed mean method.

Solution:

Percentage of female employees (CI)

Number of departments (fi)

Class mark (xi)

di = xi – a

fidi

5-15

1

10

-30

-30

15-25

2

20

-20

-40

25-35

4

30

-10

-40

35-45

4

40 = a

0

0

45-55

7

50

10

70

55-65

11

60

20

220

65-70

6

70

30

180

Total

Σfi =35

Σfidi = 360

Assumed mean = a = 40

Mean = a+ (Σfidi /Σfi)

=40+ (360/35)

= 40+(72/7)

= 40 + 10.28

=50.28 (approx)

Hence, the mean percentage of female employees is 50.28.

2 Comments

  1. Thank you sir/ma for this, I learnt alot Im grateful. I have a question Is the assumed mean always centrally placed in the class mark?. Thank you.

  2. This website is really good you can even have a with an academic advisor if you are still confused

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