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 choose an answer.
the sets that show a negative skew are sets choose an answer.

Explanation:

Calculate mean and median for each data set

• Set A: \(\{12, 14, 18, 22, 24, 32, 46\}\)
• \(\text{Mean} = \frac{12+14+18+22+24+32+46}{7} = \frac{168}{7} = 24\)
• \(\text{Median} = 22\)
• Since \(\text{Mean} > \text{Median}\) (\(24 > 22\)), Set A is positively skewed.

• Set B: \(\{4, 5, 11, 11, 12, 12, 13, 14, 14, 18\}\)
• \(\text{Mean} = \frac{4+5+11+11+12+12+13+14+14+18}{10} = \frac{114}{10} = 11.4\)
• \(\text{Median} = \frac{12+12}{2} = 12\)
• Since \(\text{Mean} < \text{Median}\) (\(11.4 < 12\)), Set B is negatively skewed.

• Set C: \(\{4, 5, 9, 12, 14, 18, 22, 26\}\)
• \(\text{Mean} = \frac{4+5+9+12+14+18+22+26}{8} = \frac{110}{8} = 13.75\)
• \(\text{Median} = \frac{12+14}{2} = 13\)
• Since \(\text{Mean} > \text{Median}\) (\(13.75 > 13\)), Set C is positively skewed.

• Set D: \(\{1, 1, 1, 2, 2, 3, 3, 4, 5, 6\}\)
• \(\text{Mean} = \frac{1+1+1+2+2+3+3+4+5+6}{10} = \frac{28}{10} = 2.8\)
• \(\text{Median} = \frac{2+3}{2} = 2.5\)
• Since \(\text{Mean} > \text{Median}\) (\(2.8 > 2.5\)), Set D is positively skewed.

Determine the positive and negative skewed sets

• Positively skewed sets: Set A, Set C, and Set D
• Negatively skewed sets: Set B

Answer:

Question 1

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

Question 2

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