Question

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

Explanation:

• Option A: In a symmetric, bell - shaped (normal) distribution, the mean, median, and mode coincide at the center of the distribution. This is a key property of the normal distribution.
• Option B: For skewed data, the mean (not the mode) is farther out in the longer tail than the median. The mode is the most frequently occurring value and is not pulled in the direction of the skew like the mean.
• Option C: To identify the shape of a distribution (skewness, symmetry), we can look at the relationship between the mean, median, and mode, but also visual inspection of the data (like histograms) is used. However, more importantly, the statement is incorrect as the mean and median alone are not the primary tools for identifying the shape; also, the mode is also a factor. But more critically, the main error here is that the way to identify the shape is not just by mean and median.
• Option D: Data skewed to the right (positively skewed) has a longer right tail, not left tail. Data skewed to the left (negatively skewed) has a longer left tail.

Answer:

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