Consider the following frequency distribution | vedclass

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

Question

(B) Given the total frequency $N = \sum f = 584$,we have $\alpha + 110 + 54 + 30 + \beta = 584$,which simplifies to $\alpha + \beta + 194 = 584$,so $\

Vedclass · Accepted Answer

$164$

Vedclass · Answer

(B) Given the total frequency $N = \sum f = 584$,we have $\alpha + 110 + 54 + 30 + \beta = 584$,which simplifies to $\alpha + \beta + 194 = 584$,so $\alpha + \beta = 390$.The median is given as $45$,which lies in the class interval $40-50$. Thus,the lower limit $\ell = 40$,class size $h = 10$,frequency of the median class $f = 30$,and cumulative frequency of the class preceding the median class $c = \alpha + 164$.The median formula is $Median = \ell + \left[\frac{\frac{N}{2} - c}{f}ight] 	imes h$.Substituting the values: $45 = 40 + \left[\frac{292 - (\alpha + 164)}{30}ight] 	imes 10$.$5 = \frac{128 - \alpha}{3}$.$15 = 128 - \alpha$,which gives $\alpha = 113$.Since $\alpha + \beta = 390$,we have $\beta = 390 - 113 = 277$.Therefore,$|\alpha - \beta| = |113 - 277| = |-164| = 164$.

Class:	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq:	$\alpha$	$110$	$54$	$30$	$\beta$

$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$

Income group	No. of firms
$150-300$	$300$
$300-500$	$500$
$500-800$	$900$
$800-1200$	$1000$
$1200-1800$	$1200$

Consider the following frequency distribution:

Class: $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Freq: $\alpha$ $110$ $54$ $30$ $\beta$

If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$

Similar Questions

The mean of $6$ distinct observations is $6.5$ and their variance is $10.25$. If $4$ out of $6$ observations are $2, 4, 5$ and $7$,then the remaining two observations are:

If the variance of the frequency distribution is $3$,then $\alpha$ is ......

$X_i$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

Frequency $f_i$ $3$ $6$ $16$ $\alpha$ $9$ $5$ $6$

The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is:

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the following frequency distribution: Class: $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Freq: $\alpha$ $110$ $54$ $30$ $\beta$ If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$