Q.

The mean of the following data, using the assumed-mean method is ____.


Class

0-10

10-20

20-30

30-40

40-50

Frequency

7

10

15

8

10


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Detailed Solution

The mean of the following data, using the assumed-mean method is 25.8.
Given:

Class

0-10

10-20

20-30

30-40

40-50

Frequency

7

10

15

8

10

Formula:
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.
The frequency distribution table:

Class Interval

Frequency, fi

Mid-value, xi

ui=xi-Ah=xi-2510

fiui

0-10

7

5

-2

-14

10-20

10

15

-1

-10

20-30

15

25=A

0

0

30-40

8

35

1

8

40-50

10

45

2

20

 

Σfi=50

 

 

Σfiui=4

We have to find mean.
Observing from the above table: A=25,h=10, f i =50, and  f i u i =4  
 Substitute in formula:
Mean=25+ 10× 4 50 Mean=25+(10×0.08) Mean=25+0.8 Mean=25.8  
The mean of the given data is 25.8.
 
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The mean of the following data, using the assumed-mean method is ____.Class0-1010-2020-3030-4040-50Frequency71015810