Question

Use the standard deviation to compare the variability of the datasets. Round to the nearest hundredths.

Dataset A: 11, 7, 12, 8, 9, 5

Dataset B: 10, 8, 10, 8, 8, 4

(1 point)
Responses

The standard deviation of Dataset A is 2.19. The standard deviation of Dataset B is 2.58. 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 2.19. The standard deviation of Dataset B is 2.58. 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 2.58. The standard deviation of Dataset B is 2.19. 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 2.58. The standard deviation of Dataset B is 2.19. 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 2.58. The standard deviation of Dataset B is 2.19. 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 2.58. The standard deviation of Dataset B is 2.19. 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 2.58. The standard deviation of Dataset B is 2.58. Dataset A and Dataset B have the same standard deviation, so the variability is the same for both datasets.

Answer 1

To determine the standard deviation for both datasets, we will go through the calculations step by step.

1. **Calculate the mean of each dataset.**
- **Dataset A:**
- Mean = (11 + 7 + 12 + 8 + 9 + 5) / 6 = 52 / 6 = 8.67
- **Dataset B:**
- Mean = (10 + 8 + 10 + 8 + 8 + 4) / 6 = 58 / 6 = 9.67

2. **Calculate the variance for each dataset.**
- **Dataset A:**
- Deviations from the mean: (11 - 8.67), (7 - 8.67), (12 - 8.67), (8 - 8.67), (9 - 8.67), (5 - 8.67)
- Squared deviations: (2.33^2), (-1.67^2), (3.33^2), (-0.67^2), (0.33^2), (-3.67^2)
- = (5.4289), (2.7889), (11.0889), (0.4489), (0.1089), (13.4689)
- Sum of squared deviations = 5.4289 + 2.7889 + 11.0889 + 0.4489 + 0.1089 + 13.4689 = 33.3334
- Variance = Sum of squared deviations / (Number of observations - 1) = 33.3334 / 5 = 6.66668
- **Dataset B:**
- Deviations from the mean: (10 - 9.67), (8 - 9.67), (10 - 9.67), (8 - 9.67), (8 - 9.67), (4 - 9.67)
- Squared deviations: (0.33^2), (-1.67^2), (0.33^2), (-1.67^2), (-1.67^2), (-5.67^2)
- = (0.1089), (2.7889), (0.1089), (2.7889), (2.7889), (32.1289)
- Sum of squared deviations = 0.1089 + 2.7889 + 0.1089 + 2.7889 + 2.7889 + 32.1289 = 40.7034
- Variance = Sum of squared deviations / (Number of observations - 1) = 40.7034 / 5 = 8.14068

3. **Calculate standard deviation by taking the square root of the variance.**
- **Dataset A:**
- Standard Deviation = √6.66668 ≈ 2.58
- **Dataset B:**
- Standard Deviation = √8.14068 ≈ 2.85

Now, we can compare the results.

- The standard deviation of Dataset A is approximately **2.58**.
- The standard deviation of Dataset B is approximately **2.85**.

Thus, the correct conclusion is:

**The standard deviation of Dataset A is 2.58. The standard deviation of Dataset B is 2.85. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.**