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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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 $[1 m a r k]$

Observations Frequency

2 2

4 1

8 2

9 1

12 3

13 1

14 1

17 1

Frequency is the number of times a data value occurs, so frequency of 12 in the given data is 3. $[1 m a r k]$

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Q. Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

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) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Fill in the blanks.

(i) $(\frac{- 3}{17}) + (\frac{- 12}{5}) = (\frac{- 12}{5}) + (. . . . .)$

(ii) $- 9 + \frac{- 21}{8} = (. . . . . .) + (- 9)$

(iii) $(\frac{- 8}{13} + \frac{3}{7}) + (\frac{- 13}{4}) = (. . . . . .) + [\frac{3}{7} + (\frac{- 13}{4})]$

(iv) $- 12 + (\frac{7}{12} + \frac{- 9}{11}) = (- 12 + \frac{7}{12}) + (. . . . .)$

(v) $\frac{19}{- 5} + (\frac{- 3}{11} + \frac{- 7}{8}) = {\frac{19}{- 5} + (. . . . .)} + \frac{- 7}{8}$

(vi) $\frac{- 16}{7} + . . . . . = . . . . . . + \frac{- 16}{7} = \frac{- 16}{7}$

Q. 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.

Q. Emmy did a survey of how many games each of

20

friends owned, and got the following data:

5, 7, 12, 13, 4, 6, 8, 12, 9, 16, 13, 12, 5, 13, 7, 17, 3, 9, 12, 14.

Find the mean.

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

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