Question
Four graphs of different data sets are shown. Which data set has the greatest standard deviation?(1 point)
Responses
data set a is symetrical and has a steeper incline
data set b is symetrical and has a less steeper incline
data set c is skewed left
data set d is skewed right
Responses
data set a is symetrical and has a steeper incline
data set b is symetrical and has a less steeper incline
data set c is skewed left
data set d is skewed right
Answers
GPT-4o mini
To determine which data set has the greatest standard deviation among the options provided, we can analyze the characteristics of each data set based on their descriptions:
1. **Data set a**: Symmetrical with a steeper incline.
2. **Data set b**: Symmetrical with a less steep incline.
3. **Data set c**: Skewed left.
4. **Data set d**: Skewed right.
**Standard deviation** measures the amount of variation or dispersion in a set of values. Generally, several factors can influence the standard deviation:
- **Steeper Incline**: A steeper incline may indicate data points that are closer to the mean (lower variability), suggesting a smaller standard deviation.
- **Less Steep Incline**: A less steep incline may indicate that data points are more spread out from the mean, potentially resulting in a larger standard deviation.
- **Skewness**: Data that is skewed (either left or right) can have higher standard deviations if the tails of the data set are further from the mean, suggesting increased variability.
Given these considerations, data set **c** (skewed left) and data set **d** (skewed right) could have large standard deviations due to potential outliers or a spread of values away from the mean. However, typically, symmetrical data sets (like a normal distribution) have lower standard deviations, especially if they are steeper (data set a) compared to less steep (data set b).
Without specific numerical data, the best assumption based on the descriptions is likely that **data set d** (skewed right) could have the greatest standard deviation due to the presence of larger values in the tail, indicating more variability.
Therefore, the data set with the greatest standard deviation is likely **data set d** (skewed right).
1. **Data set a**: Symmetrical with a steeper incline.
2. **Data set b**: Symmetrical with a less steep incline.
3. **Data set c**: Skewed left.
4. **Data set d**: Skewed right.
**Standard deviation** measures the amount of variation or dispersion in a set of values. Generally, several factors can influence the standard deviation:
- **Steeper Incline**: A steeper incline may indicate data points that are closer to the mean (lower variability), suggesting a smaller standard deviation.
- **Less Steep Incline**: A less steep incline may indicate that data points are more spread out from the mean, potentially resulting in a larger standard deviation.
- **Skewness**: Data that is skewed (either left or right) can have higher standard deviations if the tails of the data set are further from the mean, suggesting increased variability.
Given these considerations, data set **c** (skewed left) and data set **d** (skewed right) could have large standard deviations due to potential outliers or a spread of values away from the mean. However, typically, symmetrical data sets (like a normal distribution) have lower standard deviations, especially if they are steeper (data set a) compared to less steep (data set b).
Without specific numerical data, the best assumption based on the descriptions is likely that **data set d** (skewed right) could have the greatest standard deviation due to the presence of larger values in the tail, indicating more variability.
Therefore, the data set with the greatest standard deviation is likely **data set d** (skewed right).