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 analyze the test scores for each class and determine the statistics:
### Class A:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2)
- Mean calculation:
\[
\text{Mean} = \frac{(17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2)}{1 + 3 + 4 + 2} = \frac{(17) + (54) + (76) + (40)}{10} = \frac{187}{10} = 18.7
\]
### Class B:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2), 23 (1)
- Mean calculation:
\[
\text{Mean} = \frac{(17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2) + (23 \times 1)}{1 + 3 + 4 + 2 + 1} = \frac{(17) + (54) + (76) + (40) + (23)}{11} = \frac{210}{11} \approx 19.09
\]
### Class C:
- Scores: 14 (1), 17 (1), 18 (3), 19 (4), 20 (2)
- Mean calculation:
\[
\text{Mean} = \frac{(14 \times 1) + (17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2)}{1 + 1 + 3 + 4 + 2} = \frac{(14) + (17) + (54) + (76) + (40)}{11} = \frac{201}{11} \approx 18.27
\]
### Summary of Means:
- **Class A Mean:** 18.7
- **Class B Mean:** 19.09
- **Class C Mean:** 18.27
### Conclusions:
- **Lowest Mean:** Class A (18.7)
- **Highest Mean:** Class B (19.09)
### Standard Deviation Comparison:
To determine the smallest standard deviation, we consider the dispersion of each class's scores.
**Class A:**
- Scores (deviations): (17-18.7), (18-18.7), (19-18.7), (20-18.7)
- Standard deviation is likely to be lower as the scores are closer together.
**Class B:**
- Score 23 greatly increases the spread of the data, likely resulting in a higher standard deviation.
**Class C:**
- The inclusion of the score 14 could also increase the spread, meaning Class C will likely have a larger standard deviation compared to Class A.
### Final Matching:
- 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 A** (as it has the scores most tightly clustered)
So the final answer will be:
- 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 A**
### Class A:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2)
- Mean calculation:
\[
\text{Mean} = \frac{(17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2)}{1 + 3 + 4 + 2} = \frac{(17) + (54) + (76) + (40)}{10} = \frac{187}{10} = 18.7
\]
### Class B:
- Scores: 17 (1), 18 (3), 19 (4), 20 (2), 23 (1)
- Mean calculation:
\[
\text{Mean} = \frac{(17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2) + (23 \times 1)}{1 + 3 + 4 + 2 + 1} = \frac{(17) + (54) + (76) + (40) + (23)}{11} = \frac{210}{11} \approx 19.09
\]
### Class C:
- Scores: 14 (1), 17 (1), 18 (3), 19 (4), 20 (2)
- Mean calculation:
\[
\text{Mean} = \frac{(14 \times 1) + (17 \times 1) + (18 \times 3) + (19 \times 4) + (20 \times 2)}{1 + 1 + 3 + 4 + 2} = \frac{(14) + (17) + (54) + (76) + (40)}{11} = \frac{201}{11} \approx 18.27
\]
### Summary of Means:
- **Class A Mean:** 18.7
- **Class B Mean:** 19.09
- **Class C Mean:** 18.27
### Conclusions:
- **Lowest Mean:** Class A (18.7)
- **Highest Mean:** Class B (19.09)
### Standard Deviation Comparison:
To determine the smallest standard deviation, we consider the dispersion of each class's scores.
**Class A:**
- Scores (deviations): (17-18.7), (18-18.7), (19-18.7), (20-18.7)
- Standard deviation is likely to be lower as the scores are closer together.
**Class B:**
- Score 23 greatly increases the spread of the data, likely resulting in a higher standard deviation.
**Class C:**
- The inclusion of the score 14 could also increase the spread, meaning Class C will likely have a larger standard deviation compared to Class A.
### Final Matching:
- 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 A** (as it has the scores most tightly clustered)
So the final answer will be:
- 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 A**