The percentage of marks obtained by 100 stude | vedclass

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(B) 						Marks (Class)			Frequency $(f)$			Cumulative Frequency $(cf)$							$30-35$			$14$			$14$							$35-40$			$16$			$30$							$40-45$			$18$

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$45.4$

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(B) 						Marks (Class)			Frequency $(f)$			Cumulative Frequency $(cf)$							$30-35$			$14$			$14$							$35-40$			$16$			$30$							$40-45$			$18$			$48$							$45-50$			$23$			$71$							$50-55$			$18$			$89$							$55-60$			$8$			$97$							$60-65$			$3$			$100$			Here,$n = 100$.Therefore,$\frac{n}{2} = \frac{100}{2} = 50$.The cumulative frequency just greater than $50$ is $71$,which corresponds to the class interval $45-50$. Thus,the median class is $45-50$.$l$ (lower limit of median class) $= 45$$cf$ (cumulative frequency of class preceding median class) $= 48$$f$ (frequency of median class) $= 23$$h$ (class size) $= 5$Median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$$	ext{Median} = 45 + \left( \frac{50 - 48}{23} ight) 	imes 5$$	ext{Median} = 45 + \left( \frac{2}{23} ight) 	imes 5$$	ext{Median} = 45 + \frac{10}{23} \approx 45 + 0.4347 \approx 45.43$Rounding to one decimal place,the median percentage of marks is $45.4$.

Weekly income	Number of families
$0-1000$	$250$
$1000-2000$	$190$
$2000-3000$	$100$
$3000-4000$	$40$
$4000-5000$	$15$
$5000-6000$	$5$
Total	$600$

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$5$	$x$	$20$	$y$	$2$

Speed $(km/h)$	$85-100$	$100-115$	$115-130$	$130-145$
Number of players	$11$	$9$	$8$	$5$

Class	$60-70$	$70-80$	$80-90$	$90-100$	$100-110$	$110-120$
Frequency	$5$	$15$	$20$	$30$	$20$	$8$

The percentage of marks obtained by $100$ students in an examination are given below:

Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$

Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$

Determine the median percentage of marks.

Similar Questions

Weekly income of $600$ families is tabulated below:

Weekly income Number of families

$0-1000$ $250$

$1000-2000$ $190$

$2000-3000$ $100$

$3000-4000$ $40$

$4000-5000$ $15$

$5000-6000$ $5$

Total $600$

Compute the median income (in $Rs.$).

The median of the following frequency distribution is $50$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.

Class $0-20$ $20-40$ $40-60$ $60-80$ $80-100$

Frequency $5$ $x$ $20$ $y$ $2$

For a given frequency distribution,the frequencies of the first,second,and third class are $8$,$15$,and $18$ respectively. Then,the cumulative frequency of the third class is $\ldots \ldots \ldots \ldots .$

The maximum bowling speeds,in $km/h$,of $33$ players at a cricket coaching centre are given as follows:

Speed $(km/h)$ $85-100$ $100-115$ $115-130$ $130-145$

Number of players $11$ $9$ $8$ $5$

Calculate the median bowling speed (in $km/h$).

Find the median of the following frequency distribution:

Class $60-70$ $70-80$ $80-90$ $90-100$ $100-110$ $110-120$

Frequency $5$ $15$ $20$ $30$ $20$ $8$

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Marks	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$
Frequency	$14$	$16$	$18$	$23$	$18$	$8$	$3$

The percentage of marks obtained by $100$ students in an examination are given below: Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$ Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$ Determine the median percentage of marks.