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.
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
Given: Mode = 75, modal class = 65–80, $f_0$ = 6, $f_2$ = 8, $l$ = 65, $h$ = 15.
Using the formula:
$$\text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$$
$$75 = 65 + \left(\frac{f_1 - 6}{2f_1 - 6 - 8}\right) \times 15$$
$$10 = \frac{15(f_1 - 6)}{2f_1 - 14}$$
$$10(2f_1 - 14) = 15(f_1 - 6)$$
$$20f_1 - 140 = 15f_1 - 90$$
$$5f_1 = 50 \implies f_1 = 10$$
The frequency of the modal class is 10.
Source: Chapter 13, Section 13.3 Mode of Grouped Data
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Explanation
- Examiners expect you to write the mode formula, substitute all known values clearly, and solve the linear equation step by step.
- Key variables: $l$ = lower limit of modal class, $h$ = class width, $f_1$ = modal class frequency (unknown), $f_0$ = preceding frequency, $f_2$ = succeeding frequency.
- Don't forget: $h = 80 - 65 = 15$.
- Both marks are awarded for correct substitution and correct final answer; show working to secure full credit.