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

Question

Calculate the mean deviation about median age for the age distribution of 100 persons given below :AgeNumber16-20521-25626-301231-351436-402641-451246-501651-559

Filo · Accepted Answer

Clearly, we can see that given data is not continuous. So, to convert into continuous frequency distribution, we need to subtract

0.5

from the lower limit and add

0.5

to the upper limit of each class interval

Class	$f_{i}$	Cumulative frequency	$x_{i}$	$∣ x_{i} - M ∣$	$f_{i} ∣ x_{i} - M ∣$
15.5-20.5	5	5	18	20	100
20.5-25.5	6	11	23	15	90
25.5-30.5	12	23	28	10	120
30.5-35.5	14	37	33	5	70
35.5-40.5	26	63	38	0	0
40.5-45.5	12	75	43	5	60
45.5-50.5	16	91	48	10	160
50.5-55.5	9	100	53	15	135
Total	100				735

Here,

N = 100

\frac{N}{2} = \frac{100}{2} = 50

which occurs in the cumulative frequency

63

.

Hence, the median class is

35.5 - 40.5

.

Median

M = l + \frac{\frac{N}{2} - C _{f_{- 1}}}{f _{m}} \times h

= 35.5 + \frac{50 - 37}{26} \times 5

= 35.5 + \frac{13}{26} \times 5

\Rightarrow M = 35.5 + 2.5 = 38

Mean deviation about the median is

M . D . (M) = \frac{1}{N} i = 1 \sum 8 f_{i} ∣ x_{i} - M ∣

= \frac{1}{100} \times 735 = 7.35

Question Text	Calculate the mean deviation about median age for the age distribution of $100$ persons given below :
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

Practice questions from similar books

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