Question
The data set shown by the dot plot represents the ages of the boys on a baseball team.
The dot plot shows one dot above 10, two dots above 11, two dots above 12, three dots above 13, and one dot above 14.
A new boy, who is 8, has joined the baseball team since the dot plot has been made.
Determine whether the value of each statistic, for the ages of the boys, will increase, stay the same, or decrease once the age of the new boy is added to the data set. Select Increase, Stay the Same, or Decrease for each statistic.
Increase Stay the Same Decrease
Mean
Median
Standard Deviation
The dot plot shows one dot above 10, two dots above 11, two dots above 12, three dots above 13, and one dot above 14.
A new boy, who is 8, has joined the baseball team since the dot plot has been made.
Determine whether the value of each statistic, for the ages of the boys, will increase, stay the same, or decrease once the age of the new boy is added to the data set. Select Increase, Stay the Same, or Decrease for each statistic.
Increase Stay the Same Decrease
Mean
Median
Standard Deviation
Answers
GPT-4o mini
To determine how the addition of a new boy aged 8 will affect the mean, median, and standard deviation of the ages of the boys on the baseball team, we need to analyze the data before and after the addition.
**Original ages based on the dot plot:**
- 10: 1 boy
- 11: 2 boys
- 12: 2 boys
- 13: 3 boys
- 14: 1 boy
**Current data counts:**
- Total number of boys = 1 + 2 + 2 + 3 + 1 = 9 boys
- Total age sum = (10*1) + (11*2) + (12*2) + (13*3) + (14*1) = 10 + 22 + 24 + 39 + 14 = 109
- Mean = Total sum / Count = 109 / 9 ≈ 12.11
**New data with the addition of the new boy aged 8:**
- Total number of boys = 9 + 1 = 10 boys
- Total age sum = 109 + 8 = 117
- New Mean = 117 / 10 = 11.7
**Impact on the Mean:**
- The mean will decrease because the new mean (11.7) is less than the original mean (≈ 12.11).
**Median Calculation:**
- Original sorted ages: 10, 11, 11, 12, 12, 13, 13, 13, 14
- The median for 9 boys (middle value) is 12.
- With the addition of age 8, the sorted list is: 8, 10, 11, 11, 12, 12, 13, 13, 13, 14
- The median for 10 boys (average of the 5th and 6th values) is (12 + 12) / 2 = 12.
**Impact on the Median:**
- The median will stay the same since the two middle numbers remain 12.
**Standard Deviation:**
- The current ages are concentrated around higher values (10 to 14).
- The introduction of the age 8 (which is further from the mean) will increase the spread of the ages.
**Impact on the Standard Deviation:**
- The standard deviation will increase due to the addition of a value (8) that is further from the mean than the current ages.
**Final Results:**
- Mean: Decrease
- Median: Stay the Same
- Standard Deviation: Increase
**Summary:**
- Mean: Decrease
- Median: Stay the Same
- Standard Deviation: Increase
**Original ages based on the dot plot:**
- 10: 1 boy
- 11: 2 boys
- 12: 2 boys
- 13: 3 boys
- 14: 1 boy
**Current data counts:**
- Total number of boys = 1 + 2 + 2 + 3 + 1 = 9 boys
- Total age sum = (10*1) + (11*2) + (12*2) + (13*3) + (14*1) = 10 + 22 + 24 + 39 + 14 = 109
- Mean = Total sum / Count = 109 / 9 ≈ 12.11
**New data with the addition of the new boy aged 8:**
- Total number of boys = 9 + 1 = 10 boys
- Total age sum = 109 + 8 = 117
- New Mean = 117 / 10 = 11.7
**Impact on the Mean:**
- The mean will decrease because the new mean (11.7) is less than the original mean (≈ 12.11).
**Median Calculation:**
- Original sorted ages: 10, 11, 11, 12, 12, 13, 13, 13, 14
- The median for 9 boys (middle value) is 12.
- With the addition of age 8, the sorted list is: 8, 10, 11, 11, 12, 12, 13, 13, 13, 14
- The median for 10 boys (average of the 5th and 6th values) is (12 + 12) / 2 = 12.
**Impact on the Median:**
- The median will stay the same since the two middle numbers remain 12.
**Standard Deviation:**
- The current ages are concentrated around higher values (10 to 14).
- The introduction of the age 8 (which is further from the mean) will increase the spread of the ages.
**Impact on the Standard Deviation:**
- The standard deviation will increase due to the addition of a value (8) that is further from the mean than the current ages.
**Final Results:**
- Mean: Decrease
- Median: Stay the Same
- Standard Deviation: Increase
**Summary:**
- Mean: Decrease
- Median: Stay the Same
- Standard Deviation: Increase