Bot GPT 4-o mini To determine how the addition of the new boy (age 8) affects the mean, median, and standard deviation of the ages of the boys on the baseball team, we first summarize the current data from the dot plot.
Current ages represented by the dot plot:
- 10: 1 boy
- 11: 2 boys
- 12: 2 boys
- 13: 3 boys
- 14: 1 boy
Current totals:
- Ages: 10, 11, 11, 12, 12, 13, 13, 13, 14
- Total number of boys = 1 + 2 + 2 + 3 + 1 = 9
- Total age sum = 10 + 11 + 11 + 12 + 12 + 13 + 13 + 13 + 14 = 10 + 22 + 36 + 14 = 121
Adding the new boy (age 8):
- New total number of boys = 9 + 1 = 10
- New total age sum = 121 + 8 = 129
Calculating the statistics:
-
Mean:
- Current Mean = Total age / Number of boys = 121 / 9 ≈ 13.44
- New Mean = New total age / New number of boys = 129 / 10 = 12.9
- Result: Decrease
-
Median:
- Current ages (sorted): 10, 11, 11, 12, 12, 13, 13, 13, 14
- Current Median (5th value) = 12
- New ages including the new boy: 8, 10, 11, 11, 12, 12, 13, 13, 13, 14 (sorted)
- New Median (average of the 5th and 6th values) = (12 + 12) / 2 = 12
- Result: Stay the Same
-
Standard Deviation:
- Adding a value that is lower than the existing mean (most of the data is above 8) will increase the spread of the data.
- The standard deviation measures how much the ages vary from the mean, and since 8 is quite far from the previous mean and will introduce more spread, the standard deviation will increase.
- Result: Increase
Final Summary:
- Mean: Decrease
- Median: Stay the Same
- Standard Deviation: Increase
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