Final answer:
Without specific numeric data for Data Set A and B, it is challenging to confirm any claims about mean, standard deviation, or degree of skewness. Skewness affects the relationship between mean and median, while standard deviation indicates spread. Data Set B is skewed right as its mean is greater than the median.
Step-by-step explanation:
When analyzing data sets in Mathematics, it's important to understand concepts like symmetry, skewness, mean, median, mode, and standard deviation. To address the statements given in the question:
- Skewness determines the asymmetry of the data distribution from the normal distribution. A symmetric data set has the mean and median close to each other, while the degree of skewness indicates whether data is skewed left (mean < median) or skewed right (mean > median).
- The mean is the average of data points and is sensitive to skewness. In a right-skewed distribution, it tends to be higher than the median.
- The standard deviation is a measure of the data's dispersion or spread. A larger standard deviation indicates more spread among data points.
From the provided information, we note:
- The mean is not necessarily indicative of symmetry or skewness, as it can be affected by outliers.
- Data Set B is mentioned to be skewed right, which suggests the mean is greater than the median.
- Data Set A is not provided, but skewness can be implied if the mean and median are close in value, possibly indicating symmetry.
- Without exact data, it's challenging to confirm any claims about the mean, standard deviation, or spread of the distribution quantitatively.