Suppose you have four distributions: A is symmetric and centered at $0$, B is right-skewed with most values above $0$, C is left-skewed with most values below $0$, and D is uniform between $-5$ and $5$. Which of these distributions is likely to have the largest mean?

• A. Distribution C, because left-skewed distributions have higher means.
• B. Distribution D, because uniform distributions always have the largest mean.
• C. Distribution A, because symmetric distributions always have the largest mean.
• D. Distribution B, because right-skewed distributions with most values above $0$ tend to have higher means.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the meaning of skewness in a distribution. A right-skewed distribution has a longer tail on the right side, meaning it has some larger values pulling the mean to the right (higher values). Conversely, a left-skewed distribution has a longer tail on the left side, pulling the mean to the left (lower values).
2. Step 2: Analyze each distribution's characteristics: Distribution A is symmetric and centered at 0, so its mean is approximately 0. Distribution B is right-skewed with most values above 0, suggesting the mean is pulled to the right and is greater than 0. Distribution C is left-skewed with most values below 0, so the mean is pulled to the left and is less than 0. Distribution D is uniform between -5 and 5, so its mean is the midpoint, which is 0.
3. Step 3: Recall that the mean is sensitive to extreme values (outliers) and skewness. Since Distribution B is right-skewed with most values above 0, the mean will be influenced by the larger values on the right tail, making it larger than the means of the other distributions.
4. Step 4: Compare the expected means: Distribution A and D both have means around 0 due to symmetry and uniformity, Distribution C has a mean less than 0 due to left skewness, and Distribution B has a mean greater than 0 due to right skewness and values mostly above 0.
5. Step 5: Conclude that Distribution B is likely to have the largest mean because its right skewness and concentration of values above 0 pull the mean higher than the other distributions.