To find out the concentration of SO_{2} in th | vedclass

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(B) To find the class marks $(x_{i})$ for each interval,we use the formula:$x_{i} = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$The

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$0.099$

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(B) To find the class marks $(x_{i})$ for each interval,we use the formula:$x_{i} = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$The class size $(h)$ is $0.04 - 0.00 = 0.04$.Let the assumed mean $(a)$ be $0.14$.We calculate $d_{i} = x_{i} - a$ and $u_{i} = \frac{d_{i}}{h}$.Concentration of $SO_{2}$ $(ppm)$Frequency $(f_{i})$Class mark $(x_{i})$$d_{i} = x_{i} - 0.14$$u_{i} = \frac{d_{i}}{0.04}$$f_{i}u_{i}$$0.00-0.04$$4$$0.02$$-0.12$$-3$$-12$$0.04-0.08$$9$$0.06$$-0.08$$-2$$-18$$0.08-0.12$$9$$0.10$$-0.04$$-1$$-9$$0.12-0.16$$2$$0.14$$0$$0$$0$$0.16-0.20$$4$$0.18$$0.04$$1$$4$$0.20-0.24$$2$$0.22$$0.08$$2$$4$Total$\Sigma f_{i} = 30$$\Sigma f_{i}u_{i} = -31$Using the step-deviation method:Mean $\bar{x} = a + \left( \frac{\Sigma f_{i}u_{i}}{\Sigma f_{i}} ight) 	imes h$$\bar{x} = 0.14 + \left( \frac{-31}{30} ight) 	imes 0.04$$\bar{x} = 0.14 - \frac{1.24}{30}$$\bar{x} = 0.14 - 0.04133...$$\bar{x} \approx 0.09867 \approx 0.099\, ppm$.Thus,the mean concentration of $SO_{2}$ in the air is $0.099\, ppm$.

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

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

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

Number of letters	$1-4$	$4-7$	$7-10$	$10-13$	$13-16$	$16-19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

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

Similar Questions

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

Similar Questions

$A$ 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 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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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.