The following table shows the age distribution of patients of malaria in a village during a particular month:

Age (in years)
No. of cases
5-14
6
15-24
11
25-34
21
35-44
23
45-54
14
55-64
5

The average age of the patients is ____ years.

Question

The following table shows the age distribution of patients of malaria in a village during a particular month:

Age (in years)
No. of cases
5-14
6
15-24
11
25-34
21
35-44
23
45-54
14
55-64
5

The average age of the patients is ____ years.

Accepted Answer

The average age of the patients is 34.87 years.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.Given:Age (in years)No. of cases5-14615-241125-342135-442345-541455-645We have to find the average age of the patients.The given table is inclusive. Hence, we will convert the given series into exclusive series:Class IntervalFrequency, fiMid-value, xiui=xi-Ah=xi-29.510fiui4.5-14.569.5-2-1214.5-24.51119.5-1-1124.5-34.52129.5=A0034.5-44.52339.512344.5-54.51449.522854.5-64.5559.5315 Σfi=80  Σfiui=80To calculate the mean, observe from the above table:

A=29.5,h=10,
    ∑ 
     
      f
      i

=80, and 
    ∑ 
     
      f
      i

u
    i
   
   =43
   Applying formula:

Mean

=29.5+
        
         10×
          
           43
          
           80

=29.5+5.37

=34.87 years

The mean of the frequency distribution is

34.87 years.

The following table shows the age distribution of patients of malaria in a village during a particular month:

Age (in years)
No. of cases
5-14
6
15-24
11
25-34
21
35-44
23
45-54
14
55-64
5

The average age of the patients is ____ years.

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Age (in years)	No. of cases
5-14	6
15-24	11
25-34	21
35-44	23
45-54	14
55-64	5

Class Interval	Frequency, $f_{i}$	Mid-value, $x_{i}$	$u_{i}$ = $\frac{x_{i} - A}{h}$ = $\frac{x_{i} - 29.5}{10}$	$f_{i} u_{i}$
4.5-14.5	6	9.5	-2	-12
14.5-24.5	11	19.5	-1	-11
24.5-34.5	21	29.5=A	0	0
34.5-44.5	23	39.5	1	23
44.5-54.5	14	49.5	2	28
54.5-64.5	5	59.5	3	15
	Σ $f_{i}$ =80			Σ $f_{i} u_{i}$ =80

The following table shows the age distribution of patients of malaria in a village during a particular month:Age (in years)No. of cases5-14615-241125-342135-442345-541455-645The average age of the patients is ____ years.

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Detailed Solution

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The following table shows the age distribution of patients of malaria in a village during a particular month:

Age (in years)
No. of cases
5-14
6
15-24
11
25-34
21
35-44
23
45-54
14
55-64
5

The average age of the patients is ____ years.