Find the mode from the following table: Class-interval 0–10 10–20 2...

Question

Find the mode from the following table: Class-interval 0–10 10–20 20–30 30–40 40–50 Frequency 6 11 18 21 15

Accepted Answer

Step 1 — Identify the modal class. The highest frequency is 21, belonging to the class 30–40. Step 2 — Read off the values: Symbol Meaning Value $l$ lower limit of the modal class 30 $f_1$ frequency of the modal class 21 $f_0$ frequency of the class before 18 $f_2$ frequency of the class after 15 $h$ class size 10 Step 3 — Write the formula: $$	ext{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}ight) 	imes h$$ Step 4 — Substitute: $$= 30 + \left(\frac{21 - 18}{42 - 18 - 15}ight) 	imes 10$$ Step 5 — Simplify the bracket: $$= 30 + \left(\frac{3}{9}ight) 	imes 10$$ $$= 30 + \frac{10}{3}$$ Step 6 — Calculate: $$= 30 + 3.33$$ $$\boxed{	ext{Mode} = 33.33 	ext{ (approximately)}}$$ Sense check: The mode lies inside the modal class 30–40 ✔

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Symbol	Meaning	Value
$l$	lower limit of the modal class	30
$f_1$	frequency of the modal class	21
$f_0$	frequency of the class before	18
$f_2$	frequency of the class after	15
$h$	class size	10

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