Final answer:
After analyzing each data set for patterns such as uniformity, symmetry, and skewness, it is apparent that none of the provided matching options a-d perfectly align with the characteristics of the given data sets; each set displays unique skewness and none are perfectly symmetrical or uniform.
Step-by-step explanation:
To match each data set with the shape of its graphical form, we should look for patterns such as the uniformity, symmetry, or skewness in the data sets. Skewness refers to the degree to which data tails off to one side.
- Data set A (2, 2, 2, 1, 3, 4, 5): Most of the numbers are around 2, with a slight tail towards the higher numbers. This set is skewed to the right because it has a longer tail on the high-value side.
- Data set B (1.4, 2, 3, 4, 5, 6.4, 7): The numbers steadily increase, suggesting a somewhat uniform distribution; however, this set is still slightly skewed to the right.
- Data set C (3, 4, 2, 3, 1, 2, 4, 1): This set has no clear mode and looks fairly even on a graph. However, since there are more low-value numbers, it's mildly skewed to the left.
- Data set D (2, 4, 5, 1, 5, 3, 6, 5): The mode here is 5, and the data has a slight imbalance with the repeated 5s, which would create a peak in the graph. This set could be described as having a non-uniform shape despite the mode.
Therefore, option (b) Data set A: Skewed to the right, Data set B: Skewed to the left, Data set C: Uniform, Data set D: Symmetrical is not entirely correct as none of the sets are perfectly uniform or symmetrical, and their skews don't fit the given description. As such, none of the provided options a-d perfectly match the characteristics of the given data sets.