Question

3.

Karen's bowling scores for her last eight games
are listed below.
128
156
154 148
120 130 142 162
Karen found the median of her eight scores. In
her ninth game, Karen's bowling score was 140.
How does the median of the scores change when
Karen's bowling score from her ninth game is
included?
A. The median of the scores decreases by 3.
B. The median of the scores increases by 4.
C. The median of the scores decreases by 5.
D. The median of the scores does not change.

Answer 1

The median of Karen's bowling scores decreases by 3 when including her ninth game score of 140, changing the median from 145 to 142. So the correct answer is: A.

Step-by-step explanation:

To find out how the median of Karen's bowling scores changes when her ninth game score is included, we first need to find the median of her eight games.

The scores in ascending order are: 120, 128, 130, 142, 148, 154, 156, 162. With eight scores, the median is the average of the fourth and fifth scores, which are 142 and 148. Therefore, the median of the first eight games is (142 + 148) / 2 = 145.

When Karen's ninth game score of 140 is included, the scores in ascending order are: 120, 128, 130, 140, 142, 148, 154, 156, 162. With nine scores, the median is now the fifth score, which is 142. Comparing the new median of 142 with the original median of 145, we can see that the median has decreased.

Thus, the median of the scores decreases by 3 when Karen's ninth game score of 140 is included.

So the correct answer is: A. The median of the scores decreases by 3.