Solution:

Given data:

Class Frequency
(10-20) 4
(20-30) 8
(30-40) x
(40-50) 12
(50-60) 10
(60-70) 4
(70-80) y

Total frequency, N = 50

To find the value of x and y, we need to calculate the mode of the given data.

Mode:

The mode of a set of data is the value that appears most frequently in the data set.

To find the mode, we need to find the class with the highest frequency.

Here, the class with the highest frequency is (40-50) with a frequency of 12.

Therefore, the mode of the given data is 45.

Now, let's find the value of x and y.

Finding x:

To find the value of x, we need to determine the frequency of the class (30-40).

We know that the mode is 45 and it falls in the class (40-50).

Also, we know that the class (30-40) has a frequency that is greater than or equal to the frequencies of the classes (20-30) and (40-50).

Therefore, the frequency of the class (30-40) is either 8 or 10.

If the frequency of the class (30-40) is 8, then the total frequency becomes 46 (4 + 8 + 12 + 10 + 4 + y = 46).

But the given total frequency is 50.

Therefore, the frequency of the class (30-40) is 10.

Hence, x = 10.

Finding y:

To find the value of y, we can use the given total frequency and the frequencies of the other classes.

Total frequency = 50

Frequency of class (10-20) = 4

Frequency of class (20-30) = 8

Frequency of class (30-40) = 10

Frequency of class (40-50) = 12

Frequency of class (50-60) = 10

Frequency of class (60-70) = 4

Therefore, y = Total frequency - (Frequency of class (10-20) + Frequency of class (20-30) + Frequency of class (30-40) + Frequency of class (40-50) + Frequency of class (50-60) + Frequency of class (60-70))

y = 50 - (4 + 8 + 10 + 12 + 10 + 4)

y = 2

Hence, y = 2.

Therefore, the values of x and y are 10 and 2 respectively.