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प्रश्न
The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.
उत्तर
Given, Mode = 75
Modal class = 65 – 80
Frequency of the class preceding the modal class, f0 = 6
Frequency of class succeeding the modal class, f2 = 8
Here, the lower limit of modal class, l = 65 and class size = 15
Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`
⇒ 75 = `65 + ((f_1 - 6)/(2f_1 - 6 - 8)) xx 15`
⇒ 10 = `(f_1 - 6)/(2f_1 - 14) xx 15`
⇒ `20f_1 - 140 = 15f_1 - 90`
⇒ `5f_1` = 50
⇒ `f_1` = 10
Hence, the frequency of modal class `(f_1)` is 10.
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