Calculate the mean deviation about median age for the age distribution of 100 persons given below

Age Number
16-20 5
21-25 6
26-30 12
31-35 14
36-40 26
41-45 12
46-50 16
51-55 9

Asked by Abhisek | 1 year ago |  110

1 Answer

Solution :-

The class interval containing Nth/2 or 50th item is 35.5 – 40.5

So, 35.5 – 40.5 is the median class.

Then,

Median = \( l +\dfrac{\dfrac{N}{2}-C}{f}× h\)

Where, l = 35.5, c = 37, f = 26, h = 5 and N = 100

Median = \( 35.5+\dfrac{50-37}{26}× 5\)

= 35.5 + 2.5

= 38

Thus, mean deviation about the median is given by

\(MD(M) = \dfrac{1}{N} \displaystyle\sum_{i=1}^{8} f_i |X_i-M|\)

\( \dfrac{1}{100}\times 735\)

= 7.35

Answered by Pragya Singh | 1 year ago

Related Questions

Find the mean deviation from the mean and from a median of the following distribution:

Marks 0-10 10-20 20-30 30-40 40-50
No. of students 5 8 15 16 6

 

Class 11 Maths Statistics View Answer

The age distribution of 100 life-insurance policy holders is as follows

Age (on nearest birthday) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5
No. of persons 5 16 12 26 14 12 6 5

 

Class 11 Maths Statistics View Answer

Compute mean deviation from mean of the following distribution:

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of students 8 10 15 25 20 18 9 5

 

Class 11 Maths Statistics View Answer

Find the mean deviation from the mean for the following data:

Classes 95-105 105-115 115-125 125-135 135-145 145-155
Frequencies 9 13 16 26 30 12

 

Class 11 Maths Statistics View Answer

Find the mean deviation from the mean for the following data:

Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
Frequencies 4 8 9 10 7 5 4 3

 

Class 11 Maths Statistics View Answer