Find the mode of the following distribution:
Height(in cm) 30-40 40-50 50-60 60-70 70-80 80-90
No. of plants 4 3 8 11 6 2

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Solution

Height No. of parents
$30 - 40$ $4$
$40 - 50$ $3$
$50 - 60$ $8$
$60 - 70$ $11$ $\to$ Modal class as it has highest frequency
$70 - 80$ $6$
$80 - 90$ $2$
$l_{1} = 60$
$f_{o} = 8$
$f_{1} = 11$
$f_{2} = 6$
$c = 10$
Mode $= l_{1} + (\frac{f_{1} - f_{o}}{2 f_{1} - f_{o} - f_{2}} \times c)$
$= 60 + \frac{30}{3}$
$= 63.7$ .

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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

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	7	14	13	12	20	11	15	8

Height(in cm)	30-40	40-50	50-60	60-70	70-80	80-90
No. of plants	4	3	8	11	6	2

Marks	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No. of students	4	6	10	25	7	5	2

Class	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency	9	11	15	24	19	9	8	5