The mode of the following frequency distribution is 55 . Find the missing frequencies 'a' and 'b'. Class Interval 0-15…

CBSE Class 10 Maths PYQ · Statistics · Find Freuency · 5 Marks · March 2023 · Standard

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675 Marks · March 2023 · Standard

The mode of the following frequency distribution is $55$. Find the missing frequencies 'a' and 'b'.
Class Interval $0-15$ $15-30$ $30-45$ $45-60$ $60-75$ $75-90$ Total
Frequency $6$ $7$ $a$ $15$ $10$ $b$ $51$

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Modal Class: $45 - 60$ ($\frac{1}{2}$)
Mode $= 55$
$55 = 45 + \frac{15 - a}{2 \times 15 - (a + 10)} \times 15$ (2)
$\Rightarrow a = 5$ (1)
$6+7+a+15 + 10 + b = 51$
$\Rightarrow a+b=13$ (1)
$\Rightarrow b=13-5=8$ ($\frac{1}{2}$)