Sketch frequency polygon for the following table:
$x$
$1 - 3$
$3 - 5$
$5 - 7$
$7 - 9$
$9 - 11$
$11 - 13$
frequency
$2$
$1$
$4$
$2$
$3$
$6$

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Solution

X

Frequency

$1 - 3$

$2$

$3 - 5$

$1$

$5 - 7$

$4$

$7 - 9$

$2$

$9 - 11$

$3$

$11 - 13$

$6$

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3, 4, 6, 1, 2, 6, 6, 4, 3, 1, 3, 6, 7, 8, 1, 5, 8, 9, 5, 9, 4, 3, 7, 1, 7

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Daily savings (in Rs.)	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$
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x

y

f (3)

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

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