Final answer:
The question relates to the Mean Absolute Deviation (M.A.D.) as a measure of variability, with reference to class datasets, box plots, and skewness of data. Without the specific plot, Class 2 is implied to have a lower M.A.D. due to less variability, though the definitive answer cannot be determined from the given information.
Step-by-step explanation:
The question is regarding the concept of Mean Absolute Deviation (M.A.D.), which is a measure of variability in a data set. When considering which class data would have a lower M.A.D., we should look for the data set with less variability between the mean and its data points. Statement C suggests that Class 2 has less variability between the mean and its data points, which would indicate a lower M.A.D. for Class 2. Without the box and whisker plot provided, we cannot make a definitive conclusion, and thus, option D applies. However, additional statements provided give insight into the variability of the data. For instance, if a data set has more values clustered close to the median and small whiskers on a box plot, this suggests less variability, potentially leading to a lower M.A.D. Regarding outliers, a value of 7 would more likely be an outlier for the data set with a smaller spread and a lower maximum, typically indicated by the upper whisker on a box plot being closer to the median than in the other data set.
For visual representations of data like histograms and box plots, skewness and the spread indicated by the Interquartile Range (IQR) can be observed. The IQR shows the range within which the central 50 percent of the data falls, and a larger IQR indicates more variability. Therefore, the dataset with a wider spread for the middle 50 percent of the data, or a larger IQR, suggests more variability and potentially a higher M.A.D. Furthermore, when discussing the shape of the data and appropriate measures of center, the median is typically more resistant to outliers and non-symmetrical distributions than the mean. The mode may be considered in cases with high frequency of a particular value.
When displaying categorical data, such as the color of cars, a bar graph is more appropriate because it allows for non-numerical categories to be represented, while a histogram is used for continuous numerical data. Percentiles, such as in test scores, reflect the percentage of the population that scores lower than a certain value, providing a measure of how a score compares to others.