In a certain year , the ages of 130 cardiac patients,admitted in a hospital,are given in the following distribution Age - Maths - Statistics

Question

In a certain year , the ages of 130 cardiac patients,admitted in
a hospital,are given in the following distribution
Age in years
20-24
24-28
28-32
32-36
36-40
40-44
44-48
48-52
52-56
56-60
Numbers of patients
3
5
9
12
15
2
X
22
14
y
If mode of the above data is 47 find the missing frequencies x
and y

Manbar Singh · Accepted Answer

CLASS INTERVAL
FREQUENCY

20 - 24
3

24 - 28
5

28 - 32
9

32 - 36
12

36 - 40
15

40 - 44
2

44 - 48
x

48 - 52
22

52 - 56
14

56 - 60
y

TOTAL
82 + x + y

We have, mode =  47So, modal class = 44 - 48lower limit of modal class, l = 44frequency of modal class, f1 = xfrequency of class preceeding modal class, f0 = 2frequency of class succeeding modal class, f2 = 22class size, h = 4Mode = l + f1 - f02f1 - f0 - f2 × h⇒ 47 = 44 + x - 22x - 2 - 22 × 4⇒ 3 = x - 22x - 24 × 4⇒ 3 = x - 2x - 12 × 2⇒ 3x - 36 =2x - 4⇒ x = -4 + 36⇒ x = 32 Now,  Total patients = 130⇒ 82 + x + y = 130⇒ 82 + 32 + y = 130⇒ y = 130 - 114 ⇒ y = 16

CLASS INTERVAL	FREQUENCY
20 - 24	3
24 - 28	5
28 - 32	9
32 - 36	12
36 - 40	15
40 - 44	2
44 - 48	x
48 - 52	22
52 - 56	14
56 - 60	y
TOTAL	82 + x + y