Which of the following frequency tables represents a skewed data set?

• A. $\text{Class:}1-3,\text{Frequency:}8;\text{Class:}4-6,\text{Frequency:}8;\text{Class:}7-9,\text{Frequency:}8;\text{Class:}10-12,\text{Frequency:}8$
• B. $\text{Class:}1-3,\text{Frequency:}10;\text{Class:}4-6,\text{Frequency:}15;\text{Class:}7-9,\text{Frequency:}15;\text{Class:}10-12,\text{Frequency:}10$
• C. $\text{Class:}1-3,\text{Frequency:}20;\text{Class:}4-6,\text{Frequency:}12;\text{Class:}7-9,\text{Frequency:}5;\text{Class:}10-12,\text{Frequency:}2$
• D. $\text{Class:}1-3,\text{Frequency:}2;\text{Class:}4-6,\text{Frequency:}5;\text{Class:}7-9,\text{Frequency:}12;\text{Class:}10-12,\text{Frequency:}18;\text{Class:}13-15,\text{Frequency:}3$

Answer: (D)

Verified step by step guidance

1. Understand that a skewed data set is one where the frequencies are not symmetrically distributed around the center; the data tends to have a longer tail on one side.
2. Examine each frequency table to see how the frequencies change across the classes. Look for a pattern where frequencies either consistently decrease or increase, or have a long tail on one side.
3. For the first table, frequencies are equal (8, 8, 8, 8), indicating a uniform distribution, which is not skewed.
4. For the second table, frequencies increase then decrease symmetrically (10, 15, 15, 10), suggesting a roughly symmetric distribution, not skewed.
5. For the third and fourth tables, observe if frequencies start high and decrease steadily or start low and increase steadily, indicating skewness. The table with frequencies 20, 12, 5, 2 shows a decreasing pattern, indicating right skew (tail on the right), and the table with frequencies 2, 5, 12, 18, 3 shows an increase then a drop, indicating skewness as well.