Question

the mean of the following frequency distribution is 25.2.And sum of it is 50.find xand y. ​

Answer 1

x = 12, y = 11

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Answer 2

Answer:

x=12 and y=11

Step-by-step explanation:

C.I.                    0-10              10-20            20-30          30-40           40-50

Frequency          8                   x                    10                  y                   9

Given

Now make a table,

           CI                 Frequency           Mid Values

                            $f_{i}$        $x_{i}$        $f_{i}x_{i}$

       

          0-10                       8                             5                            40

         10-20                     x                             15                           15x

        20-30                    10                            25                          250

        30-40                     y                             35                           35y

        40-50                     9                             45                          405

The mean of the following frequency distribution is 25.2

sum of the frequency $\sum{f_{i}}=50$

That means,  

$\sum{f_{i}}=8+x+10+y+9\\\\\Rightarrow50=x+y+27\\\\\Rightarrow{x+y}=50-27\\\\\Rightarrow{x+y}=23\text{ ....................equation-1$

$\sum{f_{i}x_{i}}=40+15x+250+35y+405\\\\\\sum{f_{i}x_{i}}=15x+35y+695$

Mean value

$\frac{f_{i}x_{i}}{f_{i}}=25.2\\\\\Rightarrow\frac{15x+35y+695}{50}=25.2\\\\\Rightarrow{15x+35y+695}=25.2\times50\\\\\Rightarrow{15x+35y+695}=1260\\\\\Rightarrow{15x+35y=565$

$\\\\\Rightarrow{3x+7y=113\text{ .....................equation-2}$

Now multiply the equation 1 by 3 we get

$3x+3y=69\text{ ....................equation-3$

Now subtracting equation 3 from equation 2 we get

$(3x+7y)-(3x+3y)=113-69\\\\\Rightarrow3x+7y-3x-3y=44\\\\\Rightarrow4y=44\\\\\Rightarrow{y}=11$

Putting the value of y in equation 1 we get

$x+y=23\\\\\Rightarrow{x}=23-y\\\\\Rightarrow{x}=23-11\\\\\Rightarrow{x}=12$