If mode of the following frequency distribution is 55, then find the value of $x$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Since mode = 55 lies in class 45–60, this is the modal class.
Here, $l = 45$, $h = 15$, $f_1 = 15$, $f_0 = x$, $f_2 = 10$
Using Mode formula:
$$55 = 45 + \left(\frac{15 - x}{2(15) - x - 10}\right) \times 15$$
$$10 = \frac{(15 - x) \times 15}{20 - x}$$
$$10(20 - x) = 15(15 - x)$$
$$200 - 10x = 225 - 15x$$
$$5x = 25$$
$$\boxed{x = 5}$$
Source: Chapter 13, Section 13.3 – Mode of Grouped Data
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Explanation
- Since mode = 55 falls in 45–60, that is the modal class. The class before it (30–45) has frequency $x$, so $f_0 = x$.
- Substitute directly into the mode formula and solve the linear equation.
- Examiners award 1 mark for correct identification of modal class/formula setup and 1 mark for the correct value of $x = 5$.