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Statistics
NCERT Exemplar
CBSE
Grade 10

Question:

Find the mode of the following frequency distribution:
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 5, 8, 12, 7, 4

Step-by-Step Solution

Key Concept: Modal class is $20-30$ ($f_1 = 12, f_0 = 8, f_2 = 7, l = 20, h = 10$). Mode $= l + \left(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h$.
Modal class $= 20-30$. Here $l=20, f_1=12, f_0=8, f_2=7, h=10$. [0.5 Mark]
$\text{Mode} = 20 + \left(\dfrac{12 - 8}{2(12) - 8 - 7}\right) \times 10 = 20 + \left(\dfrac{4}{24 - 15}\right) \times 10 = 20 + \dfrac{40}{9} = 20 + 4.44 = 24.44$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Identifying modal class $20-30$ and values $l=20, f_1=12, f_0=8, f_2=7$: 0.5 Mark
Evaluating mode formula to get $24.44$: 1.5 Marks

Correct Answer:
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