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(D) To find the class mark $(x_i)$ for each interval,the following relation is used:Class mark $(x_i) = \frac{	ext{Upper class limit} + 	ext{Lower c

Vedclass · Accepted Answer

$8.1$

Vedclass · Answer

(D) To find the class mark $(x_i)$ for each interval,the following relation is used:Class mark $(x_i) = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$The values of $x_i$ and $f_ix_i$ are calculated as follows:Number of plantsNumber of houses $(f_i)$$x_i$$f_ix_i$$0-2$$1$$1$$1 	imes 1 = 1$$2-4$$2$$3$$2 	imes 3 = 6$$4-6$$1$$5$$1 	imes 5 = 5$$6-8$$5$$7$$5 	imes 7 = 35$$8-10$$6$$9$$6 	imes 9 = 54$$10-12$$2$$11$$2 	imes 11 = 22$$12-14$$3$$13$$3 	imes 13 = 39$Total$\sum f_i = 20$$\sum f_ix_i = 162$From the table,we have $\sum f_i = 20$ and $\sum f_ix_i = 162$.The mean $\bar{x}$ is given by $\bar{x} = \frac{\sum f_ix_i}{\sum f_i}$.Mean $= \frac{162}{20} = 8.1$.Therefore,the mean number of plants per house is $8.1$.The direct method is used here because the numerical values of $x_i$ and $f_i$ are small,making the calculations simple.

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Concentration of $SO_{2}$ (in $ppm$)	Frequency
$0.00-0.04$	$4$
$0.04-0.08$	$9$
$0.08-0.12$	$9$
$0.12-0.16$	$2$
$0.16-0.20$	$4$
$0.20-0.24$	$2$

Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Monthly consumption (in units)	Number of consumers
$65-85$	$4$
$85-105$	$5$
$105-125$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$8$
$185-205$	$4$

Similar Questions

The wickets taken by a bowler in $10$ cricket matches are as follows:
$2, 6, 4, 5, 0, 2, 1, 3, 2, 3$
Find the mode of the data.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is $Rs. 18$. Find the missing frequency $f$.
Daily pocket allowance (in $Rs.$) $11-13$ $13-15$ $15-17$ $17-19$ $19-21$ $21-23$ $23-25$
Number of children $7$ $6$ $9$ $13$ $f$ $5$ $4$

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Number of plants	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$	$12-14$
Number of houses	$1$	$2$	$1$	$5$	$6$	$2$	$3$