Question

Given the set of runs scored in 13 baseball games: 2 8 2 1 0 0 3 5 1 8 6 5 5 A. What is the median number. B. After recording the number of runs scored in two more games, the median increased by two. What could be one possible pair of runs scored in these two games? C. Explain how the median could be 2.5 when it is not possible to score half a run. D. Explain how it is possible to play 2 more games and have no change in the value of the range.

Answer 1

Explanation:

Given:

Games:

0

0

1

1

2

2

3

5

5

5

6

8

8

A.

Median is the middle value after the ste of values are arranged in ascending order, M which is the 7th value = 3

B.

Median increased by 2, M + 2

Therefore, new Median = 5

This means that the 2 runs are less than the previous median, 3 or greater than the new median, 5.

Possible pairs:

1, 2 or 6, 8

C.

Median can be 2.5 when the total number of runs scored are even numbers, therefore if the middle numbers are 2 and 3. In this case a number greater than or equal to 2;

The median = (2 + 3)/2

= 2.5

D.

Range is the difference between the highest value of runs scored to the lowest value of runs. In the data given above, range = 8 - 0

= 8.

It is possible to play 2 more games and no change in the range, 8 if the value of the 2 games (or 1 game) is/are greater than 0, the lowest value of runs scored and/or less than 8, which is the greatest value of runs scored.