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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

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$8.1$

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(D) To find the class mark $(x_i)$ for each interval,the following relation is used:Class mark $(x_i) = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$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.

Number of cars	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$7$	$14$	$13$	$12$	$20$	$11$	$15$	$8$

Production yield (in kg/ha)	Number of farms
$50-55$	$2$
$55-60$	$8$
$60-65$	$12$
$65-70$	$24$
$70-75$	$38$
$75-80$	$16$

Family size	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Number of families	$7$	$8$	$2$	$2$	$1$

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 table gives the production yield per hectare of wheat of $100$ farms of a village.
Production yield (in kg/ha) Number of farms
$50-55$ $2$
$55-60$ $8$
$60-65$ $12$
$65-70$ $24$
$70-75$ $38$
$75-80$ $16$

Change the distribution to a 'more than type' distribution,and draw its ogive.

$A$ survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
Family size $1-3$ $3-5$ $5-7$ $7-9$ $9-11$
Number of families $7$ $8$ $2$ $2$ $1$

Find the mode of this data.

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

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.

$A$ student noted the number of cars passing through a spot on a road for $100$ periods each of $3\, \text{minutes}$ and summarized it in the table given below. Find the mode of the data:Number of cars$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$$70-80$Frequency$7$$14$$13$$12$$20$$11$$15$$8$

The following table gives the production yield per hectare of wheat of $100$ farms of a village.Production yield (in kg/ha)Number of farms$50-55$$2$$55-60$$8$$60-65$$12$$65-70$$24$$70-75$$38$$75-80$$16$Change the distribution to a 'more than type' distribution,and draw its ogive.