Question

the mean of the following frequency table is 53.But the frequencies f1 and f2 in the classes 20-40 and 60-80 are missing.Find the missing frequencies.

Answer 1

Here is your solution

Answer 2

Answer:

18 and 29 are the required missing frequencies.

Step-by-step explanation:

Explanation:

Given , mean $\bar {x}$ = 53

$\sum{fi}$ = 100

Therefore we have $\sum{fi} = 53 +f_{1} +f_{2}$  =100

⇒   $f_{1} +f_{2} = 100-53 = 47$ .........(i)

Now , we find out $xi$  (class mark ) which is calculated by    

  ($\frac{upper limit + lower limit}{2}$)

So, xi = 10, 30 , 50 ,70,90

and fixi = 150 , 30$f_{1}$ , 1050, 70$f_{2}$ , 1530.

Where fixi is the product of frequency and class mark.

Step1:

∴$\sum{fixi}$ = 2730+30$f_{1}$ +70$f_{2}$

Mean = $\frac{\sum{fixi}}{\sum{fi}}$  = $\frac{2730+30f_{1}+70f_{2} }{100}$ = 53     (53 is mean given in the question )

⇒5300 = ${2730+30f_{1}+70f_{2} }$

⇒5300-2730 = ${30f_{1}+70f_{2} }$

⇒2570 = 10(${3f_{1}+7f_{2} }$)

⇒257 = ${3f_{1}+7f_{2} }$ .......(ii)

Step2:

Compare equation(i) and equation(ii)

$f_{1} +f_{2} = 47$ and ${3f_{1}+7f_{2} } =257$

we get , $f_{2}$ = 29 and $f_{1}$= 18 .

Final answer:

Hence , the value of $f_{1}$ is 18 and $f_{2}$ is 29.