Choose the best answer.
If necessary, use the paper you were given.
Mary Ann played a game 5 times. Her scores for the first 4 times are shown:
72
84
72
81
Of the following scores, which could Mary Ann have gotten on her 5th game so the range of the scores was 25?
The correct answer and explanation is:
To find the score Mary Ann could have gotten on her 5th game, we need to calculate the range of the scores. The range is the difference between the highest and lowest scores.
Given her first four scores:
- 72
- 84
- 72
- 81
We first identify the minimum and maximum scores:
- The minimum score is 72.
- The maximum score is 84.
The range of the first four scores is:
Range = 84 – 72 = 12.
Now, we want the range of all five scores to be 25. The new minimum and maximum scores must differ by 25.
- If the lowest score remains 72, the highest score must be 72 + 25 = 97.
- If the highest score remains 84, the lowest score must be 84 – 25 = 59.
Thus, for the range to be 25, Mary Ann’s 5th score could either be 97 (to make the maximum 97) or 59 (to make the minimum 59).
Therefore, the correct answer is 97 or 59, depending on what the 5th score was.
To determine which score Mary Ann could have gotten, we consider the options provided. If 97 or 59 is listed, one of them would be the correct answer. If neither is available, the range would not be achievable based on the scores.