Question

which of the following is always true? choose the correct answer below. a. data skewed to the right have a longer left tail than right tail. b. for skewed data, the mode is farther out in the longer tail than the median. c. in a symmetric and bell - shaped distribution, the mean, median, and mode are the same. d. the mean and median should be used to identify the shape of the distribution.

Explanation:

• Option A: Data skewed to the right (positively skewed) has a longer right tail, not left. So A is false.
• Option B: For skewed data, the mean (not mode) is farther out in the longer tail than the median. So B is false.
• Option C: In a symmetric, bell - shaped (normal) distribution, the mean, median, and mode coincide (are the same). This is a key property of normal distributions.
• Option D: To identify the shape of a distribution, we look at the relative positions of mean, median, and mode, but also the overall shape (like skewness, presence of peaks). Also, the mean and median alone aren't sufficient to fully identify the shape. And typically, we use measures of center and spread along with visualizations (like histograms) to identify the shape. So D is false.

Answer:

C. In a symmetric and bell - shaped distribution, the mean, median, and mode are the same.