Question

Seven baseball players are trying out for a team and the coach wants to see who can throw the baseball the farthest. The distance each player threw the baseball is recorded in the list below.

74 yards, 88 yards, 94 yards, 80 yards, 95 yards, 102 yards, 91 yards.

Part 1:

Determine the median and the mean for 7 throws, to the nearest yard. Show or explain how you got your answers.

The coach allowed two additional players to try out for the team, and each player threw the ball a distance of 91 yards.

Part 2:

What effect will these two additional distances have on the median and mean you calculated? Show or explain your work and justify your answers.

Answer 1

Kindly check explanation

Explanation:

Given the data below :

74 yards, 88 yards, 94 yards, 80 yards, 95 yards, 102 yards, 91 yards.

Rearranging the data in ascending order :

74, 80, 88, 91, 94, 95, 102

The median :

1/2(n+1)th term

n = number observations = 7

1/2(7 + 1)th term

8/2 = 4th term

= 91 yards

Mean:

Σ(74 + 80 + 88 + 91 + 94 + 95 + 102) / n

= 624 / 7

= 89.14

The coach allowed two additional players to try out for the team, and each player threw the ball a distance of 91 yards.

New data :

74, 80, 88, 91, 91, 91, 94, 95, 102

n = 9

The median :

1/2(n+1)th term

n = number observations = 7

1/2(9 + 1)th term

10/2 = 5th term

= 91 yards

Mean:

Σ(74 + 80 + 88 + 91 + 91 + 91 + 94 + 95 + 102) / n

= 806 / 9

= 89.56