Let x be the median of data: 33, 42, 28, 49, 32, 37, 52, 57, 35, 41.
If 32 is replaced by 36 and 41 by 63, then the median of the data, so obtained, is y. What is the value of (x + y)?

33, 42, 28, 49, 32, 37, 52, 57, 35, 41

Arrange the given data in ascending order from left to right.

28, 32, 33, 35, 37, 41, 42, 49, 52, 57

Median = $$\frac{\left(\frac{n}{2}\right)^{th}\ term\ +\left(\frac{n}{2}+1\right)^{th}\ term}{2}$$

Here n = the number of data

Median = x = $$\frac{\left(\frac{10}{2}\right)^{th}\ term\ +\left(\frac{10}{2}+1\right)^{th}\ term}{2}$$

= $$\frac{5^{th}\ term\ +\left(5+1\right)^{th}\ term}{2}$$

= $$\frac{5^{th}\ term\ +6^{th}\ term}{2}$$

= $$\frac{37+41}{2}$$

= $$\frac{78}{2}$$

x = 39

If 32 is replaced by 36 and 41 by 63, then the median of the data, so obtained, is y.

28, 36, 33, 35, 37, 63, 42, 49, 52, 57

Arrange the given data in ascending order from left to right.

28, 33, 35, 36, 37, 42, 49, 52, 57, 63

Median = y = $$\frac{\left(\frac{10}{2}\right)^{th}\ term\ +\left(\frac{10}{2}+1\right)^{th}\ term}{2}$$

= $$\frac{5^{th}\ term\ +\left(5+1\right)^{th}\ term}{2}$$

= $$\frac{5^{th}\ term\ +6^{th}\ term}{2}$$

= $$\frac{37 + 42}{2}$$

= $$\frac{79}{2}$$

y = 39.5

value of (x + y) = (39+39.5)

= 78.5