In a perfectly normal distribution, mean, median, and mode are

In a perfectly normal distribution, mean, median, and mode are

• A. All identical and located at the center
• B. Distinct and spread evenly
• C. Mean and median but not mode
• D. All different

Answer: (A)

All three measures of central tendency line up at the center of a perfectly normal distribution. The normal curve is perfectly symmetric around its mean, so the mean is the balance point, the median is the middle value, and the most frequent value (the mode) occurs at that same central point. Because of this symmetry, mean, median, and mode are identical and located at the center. The other ideas don’t fit because symmetry in a normal distribution makes the center the same point for all three measures, not distinct or separated values, and not the mean and median alone without the mode.

All three measures of central tendency line up at the center of a perfectly normal distribution. The normal curve is perfectly symmetric around its mean, so the mean is the balance point, the median is the middle value, and the most frequent value (the mode) occurs at that same central point. Because of this symmetry, mean, median, and mode are identical and located at the center. The other ideas don’t fit because symmetry in a normal distribution makes the center the same point for all three measures, not distinct or separated values, and not the mean and median alone without the mode.