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

Question

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.

Accepted Answer

Step 1: Mode $= 75$, Modal class $= 65$-$80$
$l = 65$, $f_0 = 6$, $f_2 = 8$
Mode $= l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} 	imes h$
Step 2: $75 = 65 + \frac{f_1 - 6}{2f_1 - 6 - 8} 	imes 15$
Step 3: $4f_1 - 28 = 3f_1 - 18 \Rightarrow f_1 = 10$
$	herefore$ Frequency of modal class is 10.

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