Final answer:
The set of data A and D are symmetrically distributed; set B is left-skewed; and set C is right-skewed. Set E is also symmetrically distributed. Skewness affects the relative positions of the mean, median, and mode.
Step-by-step explanation:
Skewness and the distribution of data can tell us a lot about the behavior of mean, median, and mode. When analyzing whether data is left-skewed, right-skewed, or symmetrically distributed, one must look at the general shape and balance of the data given.
- Set A: 3, 5, 5, 3 - This dataset appears to be symmetrically distributed because it is balanced around a central value, which in this case is 4.
- Set B: 1, 1, 3, 1 - This dataset is left-skewed because the majority of the data is concentrated on the right side (higher values), creating a tail on the left end (lower values).
- Set C: 7, 9, 9, 11 - This dataset is right-skewed. It has a concentration of values on the left, with the single high value of 11 creating the skewed tail on the right.
- Set D: 5, 5, 3, 3 - This data set also appears to be symmetrically distributed with an even spread around the central value of 4.
- Set E: 19, 21, 21, 19 - Again, this dataset appears to be symmetrically distributed, as values are balanced around the central value of 20.
In general, when data are symmetrically distributed, the mean and median are close or the same, while in skewed distributions, the mean tends to be pulled towards the long tail.