Calculate:

1 − 2 + 3 − 4 + 5 − 6 +......+ 15 − 16

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Solution

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 + 11 − 12 + 13 − 14 + 15 − 16
= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16)
= 64 − 72
= −8

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Similar questions

Q. Calculate the standard deviation for the following data:

Class - internal	Frequency
$1 - 5$ $6 - 10$ $11 - 15$ $16 - 20$	$4$ $3$ $2$ $1$
	$N = 10$

Q. Calculate the standard deviation for the given frequency distribution :

$C . I .$	$f$
$1 - 5$ $6 - 10$ $11 - 15$ $16 - 20$	$1$ $2$ $3$ $4$

N = 10

Calculate : $(\frac{2}{3} + \frac{5}{8}) \times (\frac{4}{6} + \frac{7}{16})$

Q. Calculate the Standard Deviation and coefficient of variation for the given frequency table:

Class-interval	Frequency
$1 - 5$	$1$
$6 - 10$	$2$
$11 - 15$	$3$
$16 - 20$	$4$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

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Calculate: 1 − 2 + 3 − 4 + 5 − 6 +......+ 15 − 16

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 + 11 − 12 + 13 − 14 + 15 − 16 = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16) = 64 − 72 = −8

Calculate:

1 − 2 + 3 − 4 + 5 − 6 +......+ 15 − 16

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 + 11 − 12 + 13 − 14 + 15 − 16
= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16)
= 64 − 72
= −8