The mean of the following distribution is 53 . Find the missing frequency p . Class Interval: 0-20 20-40 40-60 60-80…

CBSE Class 10 Maths PYQ · Statistics · Find Freuency · 5 Marks · March 2026 · Standard

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1255 Marks · March 2026 · Standard

The mean of the following distribution is $53$. Find the missing frequency $p$.
Class Interval: $0-20 \quad 20-40 \quad 40-60 \quad 60-80 \quad 80-100$
Frequency: $12 \quad 15 \quad p \quad 28 \quad 13$
Hence, find mode of the distribution.

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Correct table (2 Marks)
Mean = $53 = \frac{3700 + 50p}{68 + p}$ (1/2 Mark)
$\Rightarrow p = 32$ (1/2 Mark)
Modal class is $40 - 60$ (1/2 Mark)
Mode = $40 + \frac{32-15}{64-15-28} \times 20$ (1 Mark)
= $\frac{1180}{21}$ or $56.1$ (approx.) (1/2 Mark)