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Class - Intervals

When the raw data are presented in a frequency distribution with equal or unequal, inclusive or exclusive class-intervals,we assume that, all the values falling into a particular class-interval are considered to be located at the mid point (called class-mark) of a class interval. The mid-points of the class interval is obtained by calculating the mean of the lower and the upper limits of the intervals.

Mid-point (mid-value) = 

(or)
Mid-value = lower limit + [size of the class-interval]
 

Example

Calculate the mean of the following frequency distribution.

Class Interval

Frequency

0 - 8 6
8 - 16 7
16 - 24 10
24 - 32 8
32 - 40 9
 

 

Solution

Mid-value= 

Class- Interval Mid-Value xi Frequency fi Product of 
xi and fi    
fixi
0 - 8 4 6 24
8 - 16 12 7 84
16 - 24 20 10 200
24 - 32 28 8 224
32 - 40 36 9 324
Total   N = Σfi = 40 Σfix= 856


Here Σfi =40 and Σfixi = 856

Mean = 21.4.


 

Example

  Calculate the mean of the following frequency distribution.

Marks No. of students Marks No. of students
10 - 20 6 50 - 60 3
20 - 30 8 60 - 70 2
30 - 40 13 70 - 80 1
40 - 50 7    

 

Solution
Marks Mid-value 
xi
No. of students 
fi
fi xi
10 - 20 15 6 90
20 - 30 25 8 200
30 - 40 35 13 455
40 - 50 45 7 315
50 - 60 55 3 165
60 - 70 65 2 130
70 - 80 75 1 75
Total   N = Σfi = 40 Σfix= 1430


 = 35.75

Mean = 35.75.

 

 

Example

The expenditure (in Rs.) on water consumption of 52 houses in a locality is given in the table.

Expenditure in Rs. 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 550 - 55
No. of    Houses 12 10 8 9 6 5 2

Find the average expenditure per house.

Solution

Arranging the distribution

Expenditure in Rs. Class-Mark 
 xi
No. of houses 
fi
fxi
20 - 25 22.5 12 270
25 - 30 27.5 10 275
30 - 35 32.5 8 260
35 - 40 37.5 9 337.5
40 - 45 42.5 6 255
45 - 50 47.5 5 237.5
50 - 55 52.5 2 105
Total   N = Σfi = 52 Σfix= 1740

Average expenditure per house on water =  = Rs.  = Rs. 33.46.


 

Example

 Find the mean of the following frequency distribution.

Class Interval 63 - 65 66 - 68 69 - 71 72 - 74 75 - 77
Frequency 4 3 7 8 3
 
Solution

Class- Interval 

Mid-Value 
xi 

Frequency
fi 

 xi fi

63 - 65 64 4 256
66 - 68 67 3 201
69 - 71 70 7 490
72 - 74 73 8 584
75 - 77 76 3 228
Total   N = Σfi = 25 Σfix= 1759

 Mean  =  = 70.36.





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