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Properties of Measures of Central Tendency

For the numbe...

Question

For the number $9.6$ , $5.2$ , $3.5$ , $1.5$ , $1.6$ , $2.4$ , $2.6$ , $8.4$ , $10.3$ , $10.9$ ,
Verify that $\sum (x - ¯ ¯ ¯ x) = 0$

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Solution

$9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 2.6, 8.4, 10.3, 10.9$

Mean, $¯ ¯ ¯ x = \frac{9.6 + 5.2 + 3.5 + 1.5 + 1.6 + 2.4 + 2.6 + 8.4 + 10.3 + 10.9}{10}$

$= \frac{56}{10} = 5.6$

$\sum (x - ¯ ¯ ¯ x) = (9.6 - 5.6) + (5.2 - 5.6) + (3.5 - 5.6) + (1.5 - 5.6) + (1.6 - 5.6) +$
$(2.4 - 5.6) + (2.6 - 5.6) + (8.4 - 5.6) + (10.3 - 5.6) + (10.9 - 5.6)$

$= (4) + (- 0.4) + (- 2.1) + (- 4.1) + (- 4) + (- 3.2) + (- 3) + (2.8) + (5.3) + (4.7)$

$= 16.8 - 16.8 = 0$

Hence, verified

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Similar questions

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the total number of units manufactured by company C over all the years together?

\leq

7 and 2x > 3, what is the possible range of values for x?

Q. Answer the question based on the information given in the following table A,B, C, D, E denote companies and 2006, 2007, 2008, 2009 and 2010 denote years.
Number of units manufactured(M) and Number of units sold (s)(in hundred) by five different companies over the years.

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the average number of units sold by company D over all the years together?

1.6 = \frac{x}{1.5}

for the value of

x

Q. Answer the question based on the information given in the following table A,B, C, D, E denote companies and 2006, 2007, 2008, 2009 and 2010 denote years.Number of units manufactured(M) and Number of units sold (s)(in hundred) by five different companies over the years.

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the approximate per cent increase in the number of units sold by company E in the year

2007

from the previous year?

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