A survey regarding the heights (in cm) of 51 | vedclass

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(B) To calculate the median height,we first convert the cumulative frequency distribution into a standard frequency distribution table.Class intervals

Vedclass · Accepted Answer

$149.03$

Vedclass · Answer

(B) To calculate the median height,we first convert the cumulative frequency distribution into a standard frequency distribution table.Class intervalsFrequency $(f)$Cumulative frequency $(cf)$Below $140$$4$$4$$140-145$$7$$11$$145-150$$18$$29$$150-155$$11$$40$$155-160$$6$$46$$160-165$$5$$51$Here,$n = 51$. So,$\frac{n}{2} = \frac{51}{2} = 25.5$.The cumulative frequency just greater than $25.5$ is $29$,which corresponds to the class interval $145-150$. Thus,the median class is $145-150$.Here,$l = 145$,$cf = 11$,$f = 18$,and $h = 5$.Using the median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$$	ext{Median} = 145 + \left( \frac{25.5 - 11}{18} ight) 	imes 5$$	ext{Median} = 145 + \left( \frac{14.5}{18} ight) 	imes 5 = 145 + \frac{72.5}{18} = 145 + 4.027... \approx 149.03 \ cm$.

Height (in $cm$)	Number of girls
Less than $140$	$4$
Less than $145$	$11$
Less than $150$	$29$
Less than $155$	$40$
Less than $160$	$46$
Less than $165$	$51$

Weight (in $kg$)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$	$75-80$
Number of persons	$4$	$4$	$13$	$5$	$6$	$5$	$2$	$1$

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$6$	$10$	$5$	$6$	$4$	$2$	$2$

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

Similar Questions

The formula to find the median of a grouped data is $\ldots \ldots \ldots \ldots .$

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

The median class of the following frequency distribution is ...........
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $6$ $10$ $5$ $6$ $4$ $2$ $2$

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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$A$ survey regarding the heights (in $cm$) of $51$ girls of Class $X$ of a school was conducted and the following data was obtained:Height (in $cm$)Number of girlsLess than $140$$4$Less than $145$$11$Less than $150$$29$Less than $155$$40$Less than $160$$46$Less than $165$$51$Find the median height.