Find the mode of following distribution
C.I. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Freq. 5 8 7 12 28 20 10 10

4.67

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67.46

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46.67

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6.6

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Solution

The correct option is C $46.67$
The frequency table of the given observations are:
$x_{i}$ $f_{i}$
$0 - 10$ $5$
$10 - 20$ $8$
$20 - 30$ $7$
$30 - 40$ $12$
$40 - 50$ $28$
$50 - 60$ $20$
$60 - 70$ $10$
$70 - 80$ $10$
$l = 40, f_{o} = 12, f_{1} = 28, f_{2} = 20$
Mode $= l + (\frac{f_{1} - f_{o}}{2 f_{1} + f_{o} - f_{2}}) \times h$
Mode $= 40 + (\frac{28 - 12}{56 - 12 - 20}) \times 10$
Mode $= 40 + \frac{160}{24} = 40 + 6.67$
Mode $= 46.67$

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C.I.	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Freq.	5	8	7	12	28	20	10	10