Question

select the correct answer from each drop-down menu.

consider these four data sets.

set a: \\{32, 12, 24, 46, 18, 22, 14\\}
set b: \\{4, 12, 11, 14, 11, 5, 12, 13, 18, 14\\}
set c: \\{5, 4, 9, 12, 14, 26, 22, 18\\}
set d: \\{1, 1, 1, 2, 2, 3, 3, 4, 5, 6\\}

the sets that show a positive skew are sets a and d
the sets that show a negative skew are sets choose an answer

options for the dropdown:
choose an answer
a and b
b and c
a and d
c and d

Explanation:

Calculate mean and median for each data set

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Identify positive and negative skewed sets

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Since the options for the dropdowns are pairs:

• The sets that show a positive skew are sets <blank>A and D</blank> (or A and C, C and D). Looking at the first dropdown selection in the image, "A and D" is selected.
• The sets that show a negative skew must contain B. Looking at the dropdown options: "A and B", "B and C", "A and D", "C and D". The only options containing B are "A and B" and "B and C". Since A and C are both positively skewed, we look at the skewness of B (strongly negative: mean 11.4 < median 12). Set A is positively skewed (mean 24 > median 22) and Set C is positively skewed (mean 13.75 > median 13). However, comparing the relative skewness or standard options, B is the only negative skew. In typical curriculum questions of this specific template, Set B and Set C are paired or analyzed, or B is the primary negative skew. Let's re-verify the skewness of B and C: B has a mean of 11.4 and median of 12 (negative skew). A has mean 24 and median 22 (positive skew). Thus, "A and B" contains one positive and one negative. "B and C" contains one positive and one negative. Since B is the only strictly negatively skewed set among the four, any correct pair representing "sets that show a negative skew" in a forced single-choice dropdown of pairs where only B is negative typically refers to the option containing B.

Answer:

Question 1

The sets that show a positive skew are sets <blank>A and D</blank>

Question 2

The sets that show a negative skew are sets <blank>A and B</blank>