Question

the mean of the following distribution is 50 and the sum of all the frequencies is 120 find the missing frequencies x and y.

Answer 1

.

. . x=28 and y =24

Hope it helps u

Answer 2

Answer:

The value of missing frequency x = $28$ and missing frequency y = $24$.

Step-by-step explanation:

Given,

Classes:         $0-20$   $20-40$   $40-60$   $60-80$   $80-100$      total

Frequencies:    $17$          x            $32$             y           $19$             $120$

The mean of the frequency distribution = $50$

The sum of all the frequencies = $120$

To find:

• The values of missing frequencies x and y.

Now, as we know,

• Mean = $\frac{\sum f_{i} a_{i} }{\sum f_{i} }$

Here, $f_{i}$ = frequency and $a_{i}$ = mid-value

Now, let us find out the mid values:

Classes          frequency ($f_{i}$)        mid-value ($a_{i}$)           $f_{i} a_{i}$

$0-20$                   $17$                            $10$                        $170$

$20-40$                  x                             $30$                        $30x$

$40-60$                 $32$                            $50$                        $1600$

$60-80$                  y                             $70$                         $70y$

$80-100$               $19$                             $90$                        $1710$

Total                   $120$                                                  $3480+30x+70y$

Now,

• Mean = $\frac{\sum f_{i} a_{i} }{\sum f_{i} }$
• $50$ = $\frac{3480+30x+70y}{120}$
• $3480+30x+70y$ = $6000$
• $30x+70y$ = $2520$
• $3x +7y$ = $252$          ------equation (1)

Also, as given: $17+x+32+y+19 = 120$

• $x+y = 52$              --------equation (2)

After multiplying equation (2) by $7$, we get:

• $7x +7y = 364$

After subtracting equation (1) from equation (2), we get:

• $4x = 112$
• x = $28$

After putting the value of x in equation (1), we get:

• $28+y =52$

• y = $24$

Hence, the missing frequency x = $28$ and missing frequency y = $24$.