In a normal distribution, what three measures coincide at the center of the distribution?

In a normal distribution, the mean, median, and mode all have the same value and coincide at the center of the distribution. The mean represents the average value of the data set, providing a central point calculated by summing all values and dividing by the number of observations. The median is the middle value when the data is arranged in ascending or descending order, and in a symmetric distribution like the normal distribution, this value aligns with the mean. The mode is the most frequently occurring value in the data set, which also aligns at the center in a perfectly normal distribution where the peak occurs at the mean.

This characteristic of the normal distribution underlines its symmetry, indicating that the distribution is equally balanced around the center. Thus, when considering a normal distribution, it is essential to recognize that the three measures of central tendency—mean, median, and mode—are not just related but identical in value, reflecting the nature of this specific type of statistical distribution. The other options include measures that do not coincide at the center or describe different aspects of the data, such as range, variance, or standard deviation.