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Question
If mode of the following frequency 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 |
Solution
Given: Mode of frequency distribution = 55
So, modal class is 45 – 60
Lower limit (l) = 45
Class interval (h) = 15
Also, `f_0` = 15, `f_1` = x and `f_2` = 10
Mode = `l + ((f_0 - f_1)/(2f_0 - f_1 - f_2)) xx h`
⇒ 55 = `45 + ((15 - x)/(30 - x - 10)) xx 15`
⇒ 55 – 45 = `(15(15 - x))/(30 - x - 10)`
⇒ 10(30 – x – 10) = 225 – 15x
⇒ 300 –10x – 100 = 225 – 15x
⇒ 5x = 25
⇒ x = 5
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