Find the mean,median and mode of the followin | vedclass

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

Question

(N/A) $1$. Mean: The class marks $(x_i)$ are $7.5, 12.5, 17.5, 22.5, 27.5, 32.5$. The sum of frequencies $(sum f_i)$ is $100$. The sum of products $(s

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) $1$. Mean: The class marks $(x_i)$ are $7.5, 12.5, 17.5, 22.5, 27.5, 32.5$. The sum of frequencies $(sum f_i)$ is $100$. The sum of products $(sum f_i x_i)$ is $(11 \times 7.5) + (20 \times 12.5) + (35 \times 17.5) + (20 \times 22.5) + (8 \times 27.5) + (6 \times 32.5) = 82.5 + 250 + 612.5 + 450 + 220 + 195 = 1810$. Mean $= \frac{\sum f_i x_i}{\sum f_i} = \frac{1810}{100} = 18.1$.
$2$. Median: $N/2 = 50$. The cumulative frequencies are $11, 31, 66, 86, 94, 100$. The median class is $15-20$. Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 15 + \left( \frac{50 - 31}{35} \right) \times 5 = 15 + \left( \frac{19}{35} \right) \times 5 = 15 + \frac{19}{7} \approx 15 + 2.71 = 17.71$.
$3$. Mode: The modal class is $15-20$ (highest frequency $35$). Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 15 + \left( \frac{35 - 20}{2(35) - 20 - 20} \right) \times 5 = 15 + \left( \frac{15}{70 - 40} \right) \times 5 = 15 + \left( \frac{15}{30} \right) \times 5 = 15 + 2.5 = 17.5$.

Class	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$
Frequency	$11$	$20$	$35$	$20$	$8$	$6$

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Number of students	$26$	$26$	$x$	$110$	$84$	$y$	$36$	$32$

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

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

Class $5-10$ $10-15$ $15-20$ $20-25$ $25-30$ $30-35$

Frequency $11$ $20$ $35$ $20$ $8$ $6$

Similar Questions

For a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

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

In the formula $Z = l + \left( \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}} \right) \times c$ for the mode,$f_{0} = \ldots \ldots \ldots$

The frequency distribution of marks obtained by $400$ students is given below. If the mean of the frequency distribution is $41.2$,find the missing frequencies $x$ and $y$.
Marks $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Number of students $26$ $26$ $x$ $110$ $84$ $y$ $36$ $32$

The median of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $5$ $x$ $20$ $15$ $y$ $5$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Find the mean,median and mode of the following frequency distribution: Class $5-10$ $10-15$ $15-20$ $20-25$ $25-30$ $30-35$ Frequency $11$ $20$ $35$ $20$ $8$ $6$