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.
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.

Answer 1

To calculate the standard deviation for both Dataset A and Dataset B, follow these steps:

### Dataset A: 4, 5, 6, 12, 13
1. **Calculate the mean**:
\[
\text{Mean} = \frac{4 + 5 + 6 + 12 + 13}{5} = \frac{40}{5} = 8
\]

2. **Calculate the squared differences from the mean**:
\[
(4-8)^2 = 16, \quad (5-8)^2 = 9, \quad (6-8)^2 = 4, \quad (12-8)^2 = 16, \quad (13-8)^2 = 25
\]
Squared differences: 16, 9, 4, 16, 25

3. **Calculate the variance**:
\[
\text{Variance} = \frac{16 + 9 + 4 + 16 + 25}{5} = \frac{70}{5} = 14
\]

4. **Calculate the standard deviation**:
\[
\text{Standard Deviation} = \sqrt{14} \approx 3.74
\]

### Dataset B: 4, 5, 7, 9, 10
1. **Calculate the mean**:
\[
\text{Mean} = \frac{4 + 5 + 7 + 9 + 10}{5} = \frac{35}{5} = 7
\]

2. **Calculate the squared differences from the mean**:
\[
(4-7)^2 = 9, \quad (5-7)^2 = 4, \quad (7-7)^2 = 0, \quad (9-7)^2 = 4, \quad (10-7)^2 = 9
\]
Squared differences: 9, 4, 0, 4, 9

3. **Calculate the variance**:
\[
\text{Variance} = \frac{9 + 4 + 0 + 4 + 9}{5} = \frac{26}{5} = 5.2
\]

4. **Calculate the standard deviation**:
\[
\text{Standard Deviation} = \sqrt{5.2} \approx 2.28
\]

### Summary of Results
- The standard deviation of Dataset A is approximately **3.74**
- The standard deviation of Dataset B is approximately **2.28**

### Conclusion
The correct response is:
**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.**