Question : If the mode of the following distribution is 55, then find the value of x.
| Class | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 | 75-90 |
| Frequency | 10 | 7 | x | 15 | 10 | 12 |
Doubt by CBSE 2022
Solution :
| Class Intervals (C.I.) | Frequency (fi) |
| 0-15 | 10 |
| 15-30 | 7 |
| 30-45 | x |
| 45-60 | 15 |
| 60-75 | 10 |
| 75-90 | 12 |
Mode = 55 (Given)
Modal Class = 45-60
Lower limit of the modal class (l) = 45
Class Size (h) = 60-45 = 15
f1=15
fo=x
f2=10
Mode = l+[(f1-fo)/(2f1-fo-f2)]×h
55 = 45+[(15-x)/(2×15-x-10)]×15
55-45 = [(15-x)/(30-x-10)]×15
10 = [(15-x)/(20-x)]×15
10/15 = [(15-x)/(20-x)]
2/3 = (15-x)/(20-x)
2(20-x) = 3(15-x)
40-2x = 45-3x
3x-2x=45-40
x = 5
Hence, the required value of x is 5.