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

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$149.03$

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 $165$	$51$

Number of wickets	$20$-$60$	$60$-$100$	$100$-$150$	$150$-$250$	$250$-$350$	$350$-$450$
Number of bowlers	$7$	$5$	$16$	$12$	$2$	$3$

Age (in years)	$5$-$15$	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$
Number of patients	$6$	$11$	$21$	$23$	$14$	$5$

Percentage of female teachers	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$	$65$-$75$	$75$-$85$
Number of States/$U$.$T$.	$6$	$11$	$7$	$4$	$4$	$2$	$1$

Lifetimes (in hours)	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Similar Questions

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:
Lifetimes (in hours) $0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$
Frequency $10$ $35$ $52$ $61$ $38$ $29$

Determine the modal lifetimes of the components.

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Number of mangoes	$50$-$52$	$53$-$55$	$56$-$58$	$59$-$61$	$62$-$64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

$A$ 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.

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The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:Lifetimes (in hours)$0-20$$20-40$$40-60$$60-80$$80-100$$100-120$Frequency$10$$35$$52$$61$$38$$29$Determine the modal lifetimes of the components.

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The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:
Lifetimes (in hours) $0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$
Frequency $10$ $35$ $52$ $61$ $38$ $29$

Determine the modal lifetimes of the components.