Question

If the mean of the following frequency distribution is 91, and sum of frequencies is 150, find the missi
frequency x and y:
120 - 150
Classes
60 - 90
30 - 60
0 - 30
150 - 180
90 - 120
Frequency
12
21
x
52
y
26.
11​

Answer 1

Answer:

x = 34

y = 20

Step-by-step explanation:

Let's workout the midpoint for each class.

Midpoint =(lower limit + upper limit)/2

Let's call the midpoint M.

Working out M for each class we have:

Class                               M                                      M × Frequency

0 - 30                               15                                       180

30 - 60                             45                                      945

60 - 90                             75                                       75x

90 - 120                            105                                     5460

120 - 150                           135                                      135y

150 - 180                            165                                     1815

x + y = 150 - (12 + 21 + 52 + 11) = 54

Mean = ∑f.M/∑f

∑f.M = 180 + 945 + 75x + 5460 + 135y + 1815 = 8400 + 75x + 135y

91 = (8400 + 75x + 135y)/ 150

91 × 150 = 8400 + 75x + 135y

13650 = 8400 + 75x + 135y

75x + 135y = 5250

We have two simultaneous equations:

x + y = 54.............................. i)

75x + 135y = 5250 ..............................ii)

Multiply i by 75 and get the difference between the two equations.

75x + 75y = 4050 .........................iii)

75x + 135y = 5250............................iv)

60y = 1200

y = 20

20 + x = 54

x = 54 - 20 = 34