Class interval |
Mid value (xi) |
Frequency (fi) |
fiui |
0 - 20 |
10 |
5 |
50 |
20 - 40 |
30 |
f1 |
30f1 |
40 - 60 |
50 |
10 |
500 |
60 - 80 |
70 |
f2 |
70f2 |
80 - 100 |
90 |
7 |
630 |
100 - 120 |
110 |
8 |
880 |
|
|
N = 50 |
\(\sum\)fiui = 30f1 + 70f2 + 2060 |
Given,
Sum of frequency = 50
5+ f1 + 10 + f2 + 7 + 8 = 50
f1 + f2 = 50 – 5 – 10 – 7 – 8
f1 + f2 = 20
3f1 + 3f2 = 60 (i) [Multiply by 3]
And mean = 62.8
\(\frac{\sum f_iu_i}{N}=62.8\)
\(\frac{30f1+70f2+2060}{50}=62.8\)
30f1 + 70f2 = 3140 – 2060
30f1 + 70f2 = 1080
3f1 + 7f2 = 108 (ii) [Divide by 10]
Subtract (i) from (ii), we get
3f1 + 7f2 – 3f1 – 3f2 = 108 – 60
4f2 = 48
f2 = 12
Put value of f2 in (i), we get
3f1 + 3 x 12 = 60
3f1 + 36 = 60
3f1 = 24
f1 = 8
So,
f1 = 8 and f2 = 12