The lengths of 40 leaves of a plant are measu | vedclass

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(C) The given data does not have continuous class intervals. The difference between the upper limit of one class and the lower limit of the next class

Vedclass · Accepted Answer

$146.75$

Vedclass · Answer

(C) The given data does not have continuous class intervals. The difference between the upper limit of one class and the lower limit of the next class is $127 - 126 = 1$. Therefore,we subtract $0.5$ from the lower limit and add $0.5$ to the upper limit of each class to make them continuous.Continuous class intervals and cumulative frequencies are as follows:Length (in mm)Frequency $(f_i)$Cumulative Frequency $(cf)$$117.5-126.5$$3$$3$$126.5-135.5$$5$$8$$135.5-144.5$$9$$17$$144.5-153.5$$12$$29$$153.5-162.5$$5$$34$$162.5-171.5$$4$$38$$171.5-180.5$$2$$40$Here,$n = 40$,so $\frac{n}{2} = 20$. The cumulative frequency just greater than $20$ is $29$,which corresponds to the class interval $144.5-153.5$.Median class $= 144.5-153.5$,lower limit $(l)$ $= 144.5$,class size $(h)$ $= 9$,frequency $(f)$ $= 12$,and cumulative frequency of the preceding class $(cf)$ $= 17$.Using the median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$$	ext{Median} = 144.5 + \left( \frac{20 - 17}{12} ight) 	imes 9 = 144.5 + \left( \frac{3}{12} ight) 	imes 9 = 144.5 + 2.25 = 146.75$.Thus,the median length of the leaves is $146.75 	ext{ mm}$.

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Daily expenditure (in $Rs.$)	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
Number of households	$4$	$5$	$12$	$2$	$2$

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

Class interval	Frequency
$0-10$	$5$
$10-20$	$x$
$20-30$	$20$
$30-40$	$15$
$40-50$	$y$
$50-60$	$5$
Total	$60$

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 $60$	$100$

Similar Questions

The table below shows the daily expenditure on food of $25$ households in a locality.
Daily expenditure (in $Rs.$) $100-150$ $150-200$ $200-250$ $250-300$ $300-350$
Number of households $4$ $5$ $12$ $2$ $2$

Find the mean daily expenditure on food by a suitable method.

$A$ 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.

If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.
Class interval Frequency
$0-10$ $5$
$10-20$ $x$
$20-30$ $20$
$30-40$ $15$
$40-50$ $y$
$50-60$ $5$
Total $60$

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Length (in mm)	Number of leaves
$118-126$	$3$
$127-135$	$5$
$136-144$	$9$
$145-153$	$12$
$154-162$	$5$
$163-171$	$4$
$172-180$	$2$

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre,and the data obtained is represented in the following table:Length (in mm)Number of leaves$118-126$$3$$127-135$$5$$136-144$$9$$145-153$$12$$154-162$$5$$163-171$$4$$172-180$$2$Find the median length of the leaves.

Similar Questions

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.Runs scoredNumber of batsmen$3000-4000$$4$$4000-5000$$18$$5000-6000$$9$$6000-7000$$7$$7000-8000$$6$$8000-9000$$3$$9000-10000$$1$$10000-11000$$1$Find the mode of the data.

The table below shows the daily expenditure on food of $25$ households in a locality.Daily expenditure (in $Rs.$)$100-150$$150-200$$200-250$$250-300$$300-350$Number of households$4$$5$$12$$2$$2$Find the mean daily expenditure on food by a suitable method.

$A$ 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.