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Q.

State true or false.


The mean of the following data using step-deviation method is 544.


Class

Frequency

500-520

14

520-540

9

540-560

5

560-580

4

580-600

3

600-620

5


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a

True

b

False 

answer is A.

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Detailed Solution

Given,

Class

Frequency

500-520

14

520-540

9

540-560

5

560-580

4

580-600

3

600-620

5

Mean using step deviation method:
 Mean =A+ h× f i u i f i  where,  u i = x i A h   , A is the assumed mean, f   is the frequency and h is the size of the class of the given data.
We have to find the arithmetic mean of each of the following frequency distributions using step-deviation method class.

Class

Frequency, fi

Mid-value, xi

ui=xi-Ah=xi-55020

fiui

500-520

14

510

-2

-28

520-540

9

530

-1

-9

540-560

5

550=A

0

0

560-580

4

570

1

4

580-600

3

590

2

6

600-620

5

610

3

15

 

Σfi=40

 

 

Σfiui=-12

To find the arithmetic mean of each of the frequency distributions, we will substitute the values from the above table: A=550,h=20, f i =40, and  f i u i =12  
Applying formula:
 Mean  =550+ 20× 12 40 =5506 =544  
Thus, the mean of the frequency distribution is 544.
Hence, the given statement is true so the correct option is 1.
 
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