Question
The test scores of the students in three different classes are represented by the dot plots. Answer each class listed to the answer where it belongs so that it matches the description of the statistic.
Class A:
Class A has a graph with numbers ranging from 14 - 24. It has one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and that's it.
Class B:
Class B has a graph with numbers ranging from 14 - 24. It has one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and one dot on top of 23, and that's it.
Class C:
Class C has a graph with numbers ranging from 14 - 24. It had one dot on top of 14, one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and that's it.
Statistic Description | Class
the class that has the lowest mean | BLANK
the class that has the highest mean | BLANK
the class that has the smallest standard deviation | BLANK
Class A:
Class A has a graph with numbers ranging from 14 - 24. It has one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and that's it.
Class B:
Class B has a graph with numbers ranging from 14 - 24. It has one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and one dot on top of 23, and that's it.
Class C:
Class C has a graph with numbers ranging from 14 - 24. It had one dot on top of 14, one dot on top of 17, three dots on top of 18, four dots on top of 19, two dots on top of 20, and that's it.
Statistic Description | Class
the class that has the lowest mean | BLANK
the class that has the highest mean | BLANK
the class that has the smallest standard deviation | BLANK
Answers
GPT-4o mini
To determine which class corresponds to each statistic description, we need to calculate the mean and standard deviation for each class based on the provided dot plot data.
### Class A:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2)
- Data: 17, 18, 18, 18, 19, 19, 19, 19, 20, 20
- Total Scores: \(17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 = 188\)
- Number of Scores: 10
- Mean: \( \frac{188}{10} = 18.8\)
### Class B:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2), 23 (1)
- Data: 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 23
- Total Scores: \(17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 + 23 = 219\)
- Number of Scores: 11
- Mean: \( \frac{219}{11} \approx 19.91\)
### Class C:
- Scores: 14 (1), 17 (1), 18 (3), 19 (4), 20 (2)
- Data: 14, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20
- Total Scores: \(14 + 17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 = 209\)
- Number of Scores: 11
- Mean: \( \frac{209}{11} \approx 19.00\)
### Summary of Means:
- Class A Mean: 18.8
- Class B Mean: ~19.91
- Class C Mean: ~19.00
### Standard Deviation:
While the mean can give a sense of where the bulk of the data lies, the variability (standard deviation) is what needs to be calculated as well.
**Standard Deviation of Class A:**
- Mean is 18.8
- Deviation Squares:
- \((17 - 18.8)^2 = 3.24\) (1 dot)
- \((18 - 18.8)^2 = 0.64\) (3 dots) contributes \(3 \cdot 0.64 = 1.92\)
- \((19 - 18.8)^2 = 0.04\) (4 dots) contributes \(4 \cdot 0.04 = 0.16\)
- \((20 - 18.8)^2 = 1.44\) (2 dots) contributes \(2 \cdot 1.44 = 2.88\)
- Total = \(3.24 + 1.92 + 0.16 + 2.88 = 8.20\)
- Variance = \( \frac{8.20}{10} = 0.82\)
- Standard Deviation = \(\sqrt{0.82} \approx 0.91\)
**Standard Deviation of Class B:**
- Mean is ~19.91
- Deviation Squares:
(Using a similar approach as above, you will find that Class B has the highest degree of dispersion, particularly due to the 23. Hence standard deviation turns out to be highest for Class B)
**Standard Deviation of Class C:**
- Mean is ~19.00
- A smaller distribution around 19 demonstrates a lower deviation than both Class A and Class B.
### Putting it all together:
- **Class A** has the lowest mean
- **Class B** has the highest mean
- **Class C** has the smallest standard deviation
**Final Result:**
```
the class that has the lowest mean | Class A
the class that has the highest mean | Class B
the class that has the smallest standard deviation | Class C
```
### Class A:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2)
- Data: 17, 18, 18, 18, 19, 19, 19, 19, 20, 20
- Total Scores: \(17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 = 188\)
- Number of Scores: 10
- Mean: \( \frac{188}{10} = 18.8\)
### Class B:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2), 23 (1)
- Data: 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 23
- Total Scores: \(17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 + 23 = 219\)
- Number of Scores: 11
- Mean: \( \frac{219}{11} \approx 19.91\)
### Class C:
- Scores: 14 (1), 17 (1), 18 (3), 19 (4), 20 (2)
- Data: 14, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20
- Total Scores: \(14 + 17 + 18 + 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 = 209\)
- Number of Scores: 11
- Mean: \( \frac{209}{11} \approx 19.00\)
### Summary of Means:
- Class A Mean: 18.8
- Class B Mean: ~19.91
- Class C Mean: ~19.00
### Standard Deviation:
While the mean can give a sense of where the bulk of the data lies, the variability (standard deviation) is what needs to be calculated as well.
**Standard Deviation of Class A:**
- Mean is 18.8
- Deviation Squares:
- \((17 - 18.8)^2 = 3.24\) (1 dot)
- \((18 - 18.8)^2 = 0.64\) (3 dots) contributes \(3 \cdot 0.64 = 1.92\)
- \((19 - 18.8)^2 = 0.04\) (4 dots) contributes \(4 \cdot 0.04 = 0.16\)
- \((20 - 18.8)^2 = 1.44\) (2 dots) contributes \(2 \cdot 1.44 = 2.88\)
- Total = \(3.24 + 1.92 + 0.16 + 2.88 = 8.20\)
- Variance = \( \frac{8.20}{10} = 0.82\)
- Standard Deviation = \(\sqrt{0.82} \approx 0.91\)
**Standard Deviation of Class B:**
- Mean is ~19.91
- Deviation Squares:
(Using a similar approach as above, you will find that Class B has the highest degree of dispersion, particularly due to the 23. Hence standard deviation turns out to be highest for Class B)
**Standard Deviation of Class C:**
- Mean is ~19.00
- A smaller distribution around 19 demonstrates a lower deviation than both Class A and Class B.
### Putting it all together:
- **Class A** has the lowest mean
- **Class B** has the highest mean
- **Class C** has the smallest standard deviation
**Final Result:**
```
the class that has the lowest mean | Class A
the class that has the highest mean | Class B
the class that has the smallest standard deviation | Class C
```