Question
this table shows larry's bowling scores. which best describes the result if Larry bowls 150 in his 5th game?
game bowling score
1 128
2 142
3 136
4 142
the median stays the same
the range increases by 8
the mean increases by 2
the mode increases by 8
game bowling score
1 128
2 142
3 136
4 142
the median stays the same
the range increases by 8
the mean increases by 2
the mode increases by 8
Answers
GPT-4o mini
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.**
### 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.**