Class interval
2-4
4-6
6-8
8-10
10-12
frequency
2
4
6
10
5
What is the mode for the grouped data?

10.5

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12.5

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13.7

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9.1

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Solution

The correct option is B $9.1$
Here frequency of class interval $8 - 10$ is maximum.
So, it is the modal class
Now, $l =$ lower limit of modal class $= 8$
$f_{1}$ $=$ frequency of modal class $= 10$
$f_{0}$ $=$ frequency of class preceding the modal class $= 6$
$f_{2}$ $=$ frequency of class succeeding the modal class $= 5$
$h =$ class interval width $= 2$
So, Mode $=$ $l + (\frac{f_{1} - f_{2}}{2 f_{1} - f_{0} - f_{2}} \times h)$
$=$ $8 + (\frac{10 - 5}{2 \times 10 - 6 - 5} \times 2)$
$= 8 + 1.1111$
Mode $= 9.1$

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Class	$33$	$44$	$55$	$66$	$77$	$88$	$99$
Frequency	$12$	$3$	$90$	$100$	$100$	$10$	$6$

63 - 72

(72

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30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, 102, 110, 88, 74, 112, 14, 34, 44

Find median

Class interval 0-2. 2-4 4-6 6-8 8-10 10-12 12-14

Plants. 1. 2. 1. 5. 6. 2. 3

Class interval	$22 - 33$	$33 - 44$	$44 - 55$	$55 - 66$	$66 - 77$	$77 - 88$	$88 - 99$
Frequency	$23$	$45$	$67$	$89$	$100$	$123$	$20$

class interval	0-4	4-8	8-12	12-16
frequency	4	8	5	6

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