Question

the mode of the following frequency table is 26 .find the missing frequencies if the total is 50 class 0-10,10-20,20-30,30-40,40-50,50-60 frequency 3,f1,15,f2,8,4

Answer 1

Answer:

hey here is your answer in above pics

pls mark it as brainliest

Answer 2

Answer:

The missing frequencies  f₁ = 9 and  f₂ = 11    

Step-by-step explanation:

Given data:

class                 0-10   10-20    20-30    30-40    40-50    50- 60

frequencies        3         f₁          15             f₂           8             4          

sum of the frequencies  = 50  

mode of the data = 26  

here we need to find missing frequencies  f₁ and f₂  

from given data sum of frequencies = 50

             3 + f₁ + 15 + f₂ + 8 + 4 = 50

                 30 + f₁ + f₂ = 50

                          f₁ + f₂ = 20 _(1)  

from given data mode of the data is 26 which is lies in 20-30

∴ modal class of the given data is 20-30

the formula for mode is given by  

                $mode = l + [ \frac{f_{1} - f_{0} }{2 f_{1} - f_{0} - f_{2} } ] h$        

here   l = lower limit of modal class  = 20

         f₀ =  frequency of preceding the modal class = f₁  

         f₁ =  frequency of the modal class = 15  

         f₂ = frequency of succeeding the modal class = f₂  

         h =  size of the class = 10  

   $mode =20 + [ \frac{ 15 - f_{1} }{2 (15)- f_{1} - f_{2} } ] 10$          

            $=20 + [ \frac{ 15 - f_{1} }{30 - (f_{1} + f_{2} ) } ] 10$  

            $=20 + [ \frac{ 15 - f_{1} }{30 - (20) } ] 10$              [ from (1) ]

           $=20 + [ \frac{ 15 - f_{1} }{10 } ] 10$  

           = 20 + (15 - f₁ )      which is equals to 26  from given data      

⇒        20 + (15 - f₁ )  = 26  

                    f₁ = 35 - 26

                     f₁ = 9

now substitute f₁ = 9  in  (1)

                         9 + f₂ = 20  

                               f₂ =  11