To analyze the impact of Larry's 5th game score of 150 on his bowling scores, let's first determine the current statistics: the median, range, mean, and mode of the first four games.
Current Scores:
- Game 1: 128
- Game 2: 142
- Game 3: 136
- Game 4: 142
Step 1: Calculate the Median
To find the median, we need to sort the scores:
- 128, 136, 142, 142
The median is the average of the two middle numbers (136 and 142):
- Median = (136 + 142) / 2 = 139
Step 2: Calculate the Range
The range is determined by subtracting the lowest score from the highest score:
- Lowest score = 128
- Highest score = 142
- Range = 142 - 128 = 14
Step 3: Calculate the Mean
Mean is the average of the scores:
- Mean = (128 + 142 + 136 + 142) / 4 = 548 / 4 = 137
Step 4: Calculate the Mode
The mode is the score that occurs most frequently:
- In this case, the mode is 142 (occurs twice).
Step 5: Include the 5th Game Score of 150
Now let's update the statistics with the new score of 150.
New Scores:
- 128, 136, 142, 142, 150
New Median
- Sorted: 128, 136, 142, 142, 150
- Median = 142 (the middle score).
New Range
- New highest score = 150
- New range = 150 - 128 = 22
New Mean
- Mean = (128 + 136 + 142 + 142 + 150) / 5 = 698 / 5 = 139.6 (this means it increases, but we'll check how much).
New Mode
The mode remains the same because 142 still occurs twice while all other scores occur only once.
Summary of Changes:
- Median updated from 139 to 142 (increased).
- Range increased from 14 to 22 (increased by 8).
- Mean increased from 137 to 139.6 (increased by 2.6, approximately).
- Mode remains at 142 (not increased).
Conclusion:
The correct statement is that the range increases by 8.