A set of data presented in the form of a frequency distribution table with class intervals and their respective frequencies had a mode of $48.5$. The lower boundary of the modal class was $46.5$; the frequency of the modal class was $34$; the frequency of the class interval just preceding the modal class was $32$ and the frequency of the class interval just succeeding the modal class was $25$. What was the width of the modal class?

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**Solution:**
**Given data:**
- Mode = 48.5 - Lower boundary of modal class, $l$ = 46.5 - Frequency of modal class, $f_m$ = 34 - Frequency of preceding class, $f_1$ = 32 - Frequency of succeeding class, $f_2$ = 25
**Formula for mode in grouped data:**
$$	ext{Mode} = l + \frac{f_m - f_1}{2f_m - f_1 - f_2} 	imes h$$
where $h$ is the class width.
**Substituting the known values:**
$$48.5 = 46.5 + \frac{34 - 32}{2 	imes 34 - 32 - 25} 	imes h$$
**Simplifying the fraction:**
$$48.5 = 46.5 + \frac{2}{11} 	imes h$$
**Rearranging:**
$$2 = \frac{2}{11} 	imes h$$
**Solving for h:**
$$h = \frac{2 	imes 11}{2} = 11$$
**The width of the modal class is 11.**

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