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Q.

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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Detailed Solution

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 cases

5-14

6

15-24

11

25-34

21

35-44

23

45-54

14

55-64

5

We 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 Interval

Frequency, fi

Mid-value, xi

ui=xi-Ah=xi-29.510

fiui

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

 

Σfi=80

 

 

Σfiui=80

To 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  
 
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