Question

Following frequency distribution shows the ages of 560 girls at the time of their marriage

in a city. If mode age of the data is 24 years, find the missing frequencies x and y.

Age

(in years)

18-23 23-28 28-33 33-38 38-43 43-48 48-53

Number of girls x 170 y 50 38 10 2

Answer 1

Answer:

The frequencies  x = 160  and  y = 130

Step-by-step explanation:

Given data

Following frequency distribution shows the ages of 560 girls  

ages(years)     18-23    23-28    28-33    33-38    38-43    43-48    48-53  

No of girls        x           170         y           50         38          10            2

mode of the data  = 24

here we need to find the missing values  x and y

from given data  number of girls =  560      

       ⇒      x + 170 + y + 50 + 38 + 10 + 2 = 560

                                              270 + x + y = 560

                                                        x + y = 290  _ (1)  

now calculate the mode of the given data  

ages              18-23     23-28    28-33    33-38    38-43    43-48    48-53  

No of girls       x           170         y           50         38          10            2

from given data mode of the data is 24 which is lies in the class  23-28

∴  modal class of the data is  23-28

 the formula for mode is given by  

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

here  l = lower limit of modal class = 23

   f₁ = frequency of modal class  = 170

   f₀=  frequency of the class preceding the modal class  = x

   f₂ = frequency of the class succeeding the modal class  = y

   h = size of the class = 5  

 mode of the given data = $23 + [ \frac{170 - x }{ 2(170) - x -y } ] 5 = 24$

                                            $[ \frac{170 - x }{ 340 - x -y } ] 5 = 24 - 23$

                                            $(170 - x) 5 = }{ 340 - x -y$  

                                            850 - 5x +x + y = 340  

                                             - 4x + y = -510  _ (2)

now subtract  (1) from  (2)

                           - 4x + y - x - y = - 510 - 290

                            - 5x = - 800  

                                x = 160

substitute x = 160 in  (1)

                            160 + y = 290

                            y = 290 - 160 = 130

the values of  x = 160 and y = 130    

Answer 2

Answer:

Step-by-step explanation:

given total frequency is 560

 so, x + y + 270 = 560

 x + y - 290 -----(I)

 or) x = 290-y

 now given mode age 24 lies in class intravel (23-28)

mode = l+(f1-f0)/2f1-f0-f2) × h

24 = 23 + 170-x / 340 -x-y × 5

or) 4x -y = 510 ------ (ii)

sub (i) and (ii) we get

x = 160

again sub x in (i) we get

y = 130