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9, 12, 8, 14,...

Question

9, 12, 8, 14, 12, 8, 12, 4, 17, 2, 13, 2, 14, 8, 14, 13, 14, 14, 4, 9, 8, 4.
Find the frequency of 14 in the above data.

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Solution

Lets arrange the given data in ascending order and draw the frequency distribution table
2, 2, 4, 8, 8, 9, 12, 12, 12, 13, 14, 17

Observations Frequency

2 2

4 3

8 4

9 2

12 3

13 2

14 5

17 1

Frequency is the number of times a data value occurs, so frequency of 14 in the given data is 5.
$[1 m a r k]$

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Q. Mark whether true or false.
(a) 8 (7 + 3) = 8 × 7 + 8 × 3 ____
(b) 12 (16 + 4) = 12 × 16 + 12 × 4 ____
(c) 14 (5 + 2) = 14 × 5 + 14 × 2 ____
(d) 9 (8 − 3) = 9 × 8 − 9 × 3 ____

Q. The ages of students of 10^th class, in a school are as follows. The ages are given in years months.

14

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1,

Prepare a grouped frequency distribution table (classes; 13

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Find the value of :

$1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Q. 9, 12, 8, 14, 12, 8, 12, 4, 17, 2, 13, 2
Find the frequency of 12 in the above data.

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