Step-by-step EXPLANATION:

Given Question:-

From the given data, Find the missing frequencies x and y.

Solution:-

The mode of the given data = 33

Modal class = 30-40

Total number of frequencies = 100

=>56+x+y = 100

=>x+y = 100-56

=>x+ y= 44------(1)

so we have

frequency of the modal class (F 1) = 28

frequency of the preceding the modal class

=(f 0) = X

frequency of the succeeding the modal class

= (f 2) = Y

Lower limit of the modal class (l) = 30

Size of the class (h)=10

We KNOW that

Mode = l +[(f1-f0)/(2f1 -f0-f2)]×h

On Substituting all the values in the formula then

=>33=30+[(28-X)/(2(28)-X-Y)]×10

=>33-30 = (28-X)/(56-X-Y)]×10

=>3=(28-X)/(56-(X+Y)]×10

=>3 = [(28-X)/(56-44)]×10 (from (1))

=>3 = [(28-X)/12]×10

=>3=[(28-X)×10]/12

=>3×12 = (28-X)10

=>36=(28-X)10

=>36/10 = 28-X

=>3.6 = 28-X

=>28- X = 3.6

=>X = 28-3.6

=>X = 24.4

From (1)

X+Y = 44

=>24.4+Y=44

=>Y=44-24.4

=>Y= 19.6

The VALUE of X = 24.4

The value of Y = 19.6

Answer:-

The values of Missing numbers in the given data are :

The value of X = 24.4

The value of Y = 19.6

Used formula:-

• Mode (z)=l +[(f1-f0)/(2f1 -f0-f2)]×h