Question

if you are told the mean is 10.6 and the mode is 19, which of the following statements is most likely?
a. median is 27.9, and the distribution is negatively skewed
b. median is 4.4, and the distribution is positively skewed
c. median is 15.5, and the distribution is positively skewed
d. median is 4.4, and the distribution is negatively skewed
e. median is 27.9, and the distribution is positively skewed
f. median is 15.5, and the distribution is negatively skewed

Explanation:

Step1: Recall skew measure relationships

For skewed distributions:

• Negative skew: $\text{Mode} < \text{Median} < \text{Mean}$
• Positive skew: $\text{Mean} < \text{Median} < \text{Mode}$

Given $\text{Mean}=10.6$, $\text{Mode}=19$, so $\text{Mean} < \text{Mode}$, which matches positive skew, requiring $\text{Mean} < \text{Median} < \text{Mode}$, or $10.6 < \text{Median} < 19$.

Step2: Match to valid option

Check options: only option c has median $15.5$ (fits $10.6 < 15.5 < 19$) and positive skew.

Answer:

c. median is 15.5, and the distribution is positively skewed