Calculating Mean Using Assumed Mean Method


 
 
Concept Explanation
 

Calculating Mean Using Assumed Mean Method

Calculating Mean Using the Assumed Mean Method :

If a is taken as assumed mean for a data and d_{1}=x_{1}-a denotes the deviation of x_{1} from a, then arithmetic mean bar{x} is given by

                              bar{x}=a+frac{1}{n}sum_{i=1}^{n}f_{i}d_{i}

Here   a = assumed mean 

f_{i} = frequency of i^{th} class

d_{i}=x_{i}-a = deviation of i^{th} class

sum f_{i} = n = total ;no.; of; observations

x_{i}=Class:mark= frac{upper:class:limit + lower:class:limit}{2} 

Illustration:  Calculate the mean of the data given below.

Range of wages (in Rs) 235-245 245-255 255-265 265-275 275-285 285-295 295-305
Numbers of workers 15 25 32 47 15 12 4

Solution.  To calculate the mean using assumed mean method, we will first find the class mark for each class and will then assume a value as the mean.

Range of wages

wages

large x_{i}

Frequency

large f_{i}    

Deviation

d_{i}=x_{i}-270

large f_{i}d_{i}

235-245

245-255

255-265

265-275

275-285

285-295

295-305

240

250

260

270=a

280

290

300

15

25

32

47

15

12

4

-30

-20

-10

0

10

20

30

-450

-500

-320

0

150

240

120

  Total 150  

-760

By the assumed-mean method

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Sample Questions
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Question : 1

In the method to calculate mean using assumed mean method, find the value of f_id_i for the class 20 - 40 is _______________ .

Marks No. of students
0 - 20 11
20 - 40 18
40 - 60 24
60 - 80 17
80 - 100 11

 

Right Option : C
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Explanation
Question : 2

To find out the concentration of NO_2  in air, the data given below was collected for 30 localities in a certain city .Identify the class which contains assumed mean. 

Concentration of NO_2  in (ppm) Frequency
0.00 - 0.05 4
0.05 - 0.10 9
0.10 - .0.15 9
0.15 - 0.25 2
0.20 - 0.25 6

 

Right Option : C
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Explanation
Question : 3

In the method to calculate mean using assumed mean method, The value of assumed mean for the following data  is_______________ .

Marks No. of students
0 - 20 11
20 - 40 18
40 - 60 24
60 - 80 17
80 - 100 11

 

Right Option : B
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Explanation
 
 


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