In a 4*100m relay race, tota track length is 200m and time taken by one particular group is 50.2sec. ehat is the average speed and average velocity of that group?
pl mee

This is tricky, and the question could probably be written more clearly.

A " 4 x 100 m " race means that four runners each run 100 meters, for
a total of 400 meters ... very close to a quarter mile.

On a 200-meter track, each runner does halfway around the track, and
the whole team of four runners does twice around the track. 

This team did the whole thing in 50.2 seconds. The average time for each runner
was 50.2/4 = 12.55 seconds.

Velocity is a speed and a direction.  We have the speed, leaving only the puzzle of
what to do about the 'average' direction.

Here's a sneaky but easy way to dispense with the whole issue:
Define the average velocity (vector) as  (total displacement vector)/(total time).

Since the fourth runner finished in exactly the same spot as the first runner
began, the total displacement is zero, and therefore so is the average velocity.