Statistics
NCERT Exemplar
CBSE
Grade 10
Question:
Find the mode of the following distribution:
Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
No. of students: 4, 6, 10, 12, 5, 3
Step-by-Step Solution
Key Concept: Modal class is $30-40$ ($l=30, f_1=12, f_0=10, f_2=5, h=10$). Mode $= l + \left(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h$.
Modal class is $30-40$. $l=30, f_1=12, f_0=10, f_2=5, h=10$. [1.0 Mark]
$\text{Mode} = 30 + \left(\dfrac{12 - 10}{2(12) - 10 - 5}\right) \times 10 = 30 + \left(\dfrac{2}{24 - 15}\right) \times 10 = 30 + \dfrac{20}{9} = 30 + 2.22 = 32.22$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Identifying modal class $30-40$ and parameters: 1.0 Mark
Evaluating mode formula to get $32.22$: 2.0 Marks
Correct Answer:
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