Question
Use the standard deviation to compare the variability of the datasets. Round to the nearest hundredths.
Dataset A: 4, 5, 6, 12, 13
Dataset B: 4, 5, 7, 9, 10
(1 point)
Responses
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability.
The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.
The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
The standard deviation of Dataset A is 3.64. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
Dataset A: 4, 5, 6, 12, 13
Dataset B: 4, 5, 7, 9, 10
(1 point)
Responses
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability.
The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.
The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
The standard deviation of Dataset A is 3.64. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
Answers
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Answered by
GPT-4o mini
To calculate the standard deviation for both datasets, we will follow these steps:
1. Find the mean of each dataset.
2. Calculate the squared differences from the mean.
3. Find the average of those squared differences.
4. Take the square root of that average to find the standard deviation.
### Dataset A: 4, 5, 6, 12, 13
1. **Mean**:
\((4 + 5 + 6 + 12 + 13) / 5 = 40 / 5 = 8\)
2. **Squared differences from the mean**:
- \( (4 - 8)^2 = 16 \)
- \( (5 - 8)^2 = 9 \)
- \( (6 - 8)^2 = 4 \)
- \( (12 - 8)^2 = 16 \)
- \( (13 - 8)^2 = 25 \)
3. **Average of squared differences**:
\((16 + 9 + 4 + 16 + 25) / 5 = 70 / 5 = 14\)
4. **Standard deviation**:
\( \sqrt{14} \approx 3.74 \)
### Dataset B: 4, 5, 7, 9, 10
1. **Mean**:
\((4 + 5 + 7 + 9 + 10) / 5 = 35 / 5 = 7\)
2. **Squared differences from the mean**:
- \( (4 - 7)^2 = 9 \)
- \( (5 - 7)^2 = 4 \)
- \( (7 - 7)^2 = 0 \)
- \( (9 - 7)^2 = 4 \)
- \( (10 - 7)^2 = 9 \)
3. **Average of squared differences**:
\((9 + 4 + 0 + 4 + 9) / 5 = 26 / 5 = 5.2\)
4. **Standard deviation**:
\( \sqrt{5.2} \approx 2.28 \)
### Comparison:
- **Standard Deviation of Dataset A**: 3.74
- **Standard Deviation of Dataset B**: 2.28
Based on these calculations, we find that the standard deviation of Dataset A is larger than that of Dataset B. Thus, Dataset A has more variability.
### Final Answer:
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
1. Find the mean of each dataset.
2. Calculate the squared differences from the mean.
3. Find the average of those squared differences.
4. Take the square root of that average to find the standard deviation.
### Dataset A: 4, 5, 6, 12, 13
1. **Mean**:
\((4 + 5 + 6 + 12 + 13) / 5 = 40 / 5 = 8\)
2. **Squared differences from the mean**:
- \( (4 - 8)^2 = 16 \)
- \( (5 - 8)^2 = 9 \)
- \( (6 - 8)^2 = 4 \)
- \( (12 - 8)^2 = 16 \)
- \( (13 - 8)^2 = 25 \)
3. **Average of squared differences**:
\((16 + 9 + 4 + 16 + 25) / 5 = 70 / 5 = 14\)
4. **Standard deviation**:
\( \sqrt{14} \approx 3.74 \)
### Dataset B: 4, 5, 7, 9, 10
1. **Mean**:
\((4 + 5 + 7 + 9 + 10) / 5 = 35 / 5 = 7\)
2. **Squared differences from the mean**:
- \( (4 - 7)^2 = 9 \)
- \( (5 - 7)^2 = 4 \)
- \( (7 - 7)^2 = 0 \)
- \( (9 - 7)^2 = 4 \)
- \( (10 - 7)^2 = 9 \)
3. **Average of squared differences**:
\((9 + 4 + 0 + 4 + 9) / 5 = 26 / 5 = 5.2\)
4. **Standard deviation**:
\( \sqrt{5.2} \approx 2.28 \)
### Comparison:
- **Standard Deviation of Dataset A**: 3.74
- **Standard Deviation of Dataset B**: 2.28
Based on these calculations, we find that the standard deviation of Dataset A is larger than that of Dataset B. Thus, Dataset A has more variability.
### Final Answer:
The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.
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