The percentage of marks obtained by 100 stude | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

$45.4$

Vedclass · Answer

(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 $45.4$.

Monthly income range (in $Rs.$)	Number of families
Income more than $10000$	$100$
Income more than $13000$	$85$
Income more than $16000$	$69$
Income more than $19000$	$50$
Income more than $22000$	$33$
Income more than $25000$	$15$

Class	$200-299$	$300-399$	$400-499$	$500-599$	$600-699$	$700-799$	$800-899$
Frequency	$3$	$61$	$118$	$139$	$126$	$151$	$2$

Class	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
Frequency	$4$	$5$	$13$	$20$	$14$	$7$	$4$

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

Find the mean of the following data:

Class $200-299$ $300-399$ $400-499$ $500-599$ $600-699$ $700-799$ $800-899$

Frequency $3$ $61$ $118$ $139$ $126$ $151$ $2$

Consider the data:

Class $65-85$ $85-105$ $105-125$ $125-145$ $145-165$ $165-185$ $185-205$

Frequency $4$ $5$ $13$ $20$ $14$ $7$ $4$

The difference between the upper limit of the median class and the lower limit of the modal class is:

The mode of the observations $4, 5, 6, 3, 4, 3, 3, 2, 3, 5$ is $\ldots \ldots \ldots \ldots .$

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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.