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 $45.4$.

Class	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Frequency	$6$	$3$	$8$	$2$	$1$

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	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$
Frequency	$8$	$15$	$16$	$20$	$12$	$9$

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

For the calculation of mode of the following frequency distribution,$f_{0} = \dots \dots \dots \dots \dots$

Class $1-3$ $3-5$ $5-7$ $7-9$ $9-11$

Frequency $6$ $3$ $8$ $2$ $1$

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 $Rs.$).

While computing the mean of grouped data,we assume that the frequencies are

Find the mean,median and mode of the following frequency distribution:

Class $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$

Frequency $8$ $15$ $16$ $20$ $12$ $9$

In the formula $\bar{x} = A + \frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}} \times c$,$u_{i} =$ .........

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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.