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 3.64. 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.
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 4.18. The standard deviation of Dataset B is 2.55. 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 4.18. The standard deviation of Dataset B is 2.55. 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 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same 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 3.64. 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.
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 4.18. The standard deviation of Dataset B is 2.55. 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 4.18. The standard deviation of Dataset B is 2.55. 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 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability.
Answers
GPT-4o mini
To compare the variability of the datasets using standard deviation, we first need to calculate the standard deviation for both Dataset A and Dataset B.
### 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 variance:
\[
\text{Variance} = \frac{(4-8)^2 + (5-8)^2 + (6-8)^2 + (12-8)^2 + (13-8)^2}{5}
\]
\[
= \frac{16 + 9 + 4 + 16 + 25}{5} = \frac{70}{5} = 14
\]
3. 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 variance:
\[
\text{Variance} = \frac{(4-7)^2 + (5-7)^2 + (7-7)^2 + (9-7)^2 + (10-7)^2}{5}
\]
\[
= \frac{9 + 4 + 0 + 4 + 9}{5} = \frac{26}{5} = 5.2
\]
3. Calculate the standard deviation:
\[
\text{Standard Deviation} = \sqrt{5.2} \approx 2.28
\]
### Comparison:
- The standard deviation of Dataset A is approximately **3.74**.
- The standard deviation of Dataset B is approximately **2.28**.
### Conclusion:
The standard deviation of Dataset A is larger than that of Dataset B, meaning that Dataset A has more variability.
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.**
### 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 variance:
\[
\text{Variance} = \frac{(4-8)^2 + (5-8)^2 + (6-8)^2 + (12-8)^2 + (13-8)^2}{5}
\]
\[
= \frac{16 + 9 + 4 + 16 + 25}{5} = \frac{70}{5} = 14
\]
3. 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 variance:
\[
\text{Variance} = \frac{(4-7)^2 + (5-7)^2 + (7-7)^2 + (9-7)^2 + (10-7)^2}{5}
\]
\[
= \frac{9 + 4 + 0 + 4 + 9}{5} = \frac{26}{5} = 5.2
\]
3. Calculate the standard deviation:
\[
\text{Standard Deviation} = \sqrt{5.2} \approx 2.28
\]
### Comparison:
- The standard deviation of Dataset A is approximately **3.74**.
- The standard deviation of Dataset B is approximately **2.28**.
### Conclusion:
The standard deviation of Dataset A is larger than that of Dataset B, meaning that Dataset A has more variability.
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.**