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(B) To find the class mark $(x_{i})$ for each interval,the following relation is used:$x_{i} = \frac{	ext{Upper class limit} + 	ext{Lower class limi

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$20$

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(B) To find the class mark $(x_{i})$ for each interval,the following relation is used:$x_{i} = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$Given that,mean pocket allowance,$\bar{x} = Rs. 18$.Taking $18$ as assumed mean $(a)$,$d_{i}$ and $f_{i}d_{i}$ are calculated as follows:Daily pocket allowance (in $Rs.$)Number of children $(f_{i})$Class mark $(x_{i})$$d_{i} = x_{i} - 18$$f_{i}d_{i}$$11-13$$7$$12$$-6$$-42$$13-15$$6$$14$$-4$$-24$$15-17$$9$$16$$-2$$-18$$17-19$$13$$18$$0$$0$$19-21$$f$$20$$2$$2f$$21-23$$5$$22$$4$$20$$23-25$$4$$24$$6$$24$Total$\sum f_{i} = 44 + f$$\sum f_{i}d_{i} = 2f - 40$From the table,we obtain:$\sum f_{i} = 44 + f$$\sum f_{i}d_{i} = 2f - 40$Using the formula for mean:$\bar{x} = a + \frac{\sum f_{i}d_{i}}{\sum f_{i}}$$18 = 18 + \left(\frac{2f - 40}{44 + f}ight)$$0 = \frac{2f - 40}{44 + f}$$2f - 40 = 0$$2f = 40$$f = 20$Hence,the missing frequency $f$ is $20$.

Life time (in hours)	Number of lamps
$1500-2000$	$14$
$2000-2500$	$56$
$2500-3000$	$60$
$3000-3500$	$86$
$3500-4000$	$74$
$4000-4500$	$62$
$4500-5000$	$48$

Daily income (in Rs.)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Marks obtained $(x_{i})$	$10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$	$1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

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

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

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 $7$ $6$ $9$ $13$ $f$ $5$ $4$

Similar Questions

The following table gives the distribution of the lifetime of $400$ neon lamps:
Life time (in hours) Number of lamps
$1500-2000$ $14$
$2000-2500$ $56$
$2500-3000$ $60$
$3000-3500$ $86$
$3500-4000$ $74$
$4000-4500$ $62$
$4500-5000$ $48$

Find the median lifetime of a lamp.

The following distribution gives the daily income of $50$ workers of a factory.
Daily income (in Rs.) $100-120$ $120-140$ $140-160$ $160-180$ $180-200$
Number of workers $12$ $14$ $8$ $6$ $10$

Convert the distribution above to a less than type cumulative frequency 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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Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

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$

Similar Questions

The following table gives the distribution of the lifetime of $400$ neon lamps:Life time (in hours)Number of lamps$1500-2000$$14$$2000-2500$$56$$2500-3000$$60$$3000-3500$$86$$3500-4000$$74$$4000-4500$$62$$4500-5000$$48$Find the median lifetime of a lamp.

The following distribution gives the daily income of $50$ workers of a factory.Daily income (in Rs.)$100-120$$120-140$$140-160$$160-180$$180-200$Number of workers$12$$14$$8$$6$$10$Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

$A$ 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$

$A$ 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.