In a normal distribution, which measures of central tendency are equal?

In a normal distribution, which measures of central tendency are equal?

• A. They are equal
• B. They are unequal
• C. Only mean equals median
• D. Only mode equals mean

Answer: (A)

In a normal distribution the mean, median, and mode coincide at the same central value. This happens because the distribution is perfectly symmetric around its center, so the balance point (the mean) is exactly at the peak of the chart (the mode) and at the middle of the data (the median). In short, the center of symmetry makes all three measures equal, typically denoted by mu in N(mu, sigma^2). If the data were skewed or multimodal, these measures could differ, but for a normal distribution they align.

In a normal distribution the mean, median, and mode coincide at the same central value. This happens because the distribution is perfectly symmetric around its center, so the balance point (the mean) is exactly at the peak of the chart (the mode) and at the middle of the data (the median). In short, the center of symmetry makes all three measures equal, typically denoted by mu in N(mu, sigma^2). If the data were skewed or multimodal, these measures could differ, but for a normal distribution they align.