Final answer:
In a normal distribution, the mean, median, and mode are all equal. This reflects the symmetrical nature of the distribution, where all three measures of central tendency coincide. Skewness can affect these measures in non-symmetrical distributions, pulling the mean towards the tail of the distribution.
Step-by-step explanation:
In a normal distribution, which is symmetrical, the measures of central tendency—the mean, median, and mode—are all equal. This means that the mean, which is the arithmetic average of all data points, the median, which is the middle value when the data points are arranged in order, and the mode, which is the most frequently occurring value, coincide at the center of the distribution.
To illustrate, if we have a perfectly symmetrical bell-shaped curve (normal distribution), there would be no skewness. In such a distribution, the mean is not affected by extreme values or outliers. As the data is symmetrically distributed, every section of the data to the left of the central point is mirrored to the right. This symmetry ensures that the median and mode fall exactly at the same point as the mean.
When analyzing a data set, if there is skewness—meaning the data is not symmetrically distributed—the mean will be pulled in the direction of the long tail of the distribution. Therefore, if the distribution is skewed to the left, the mean will be less than the median, which is often less than the mode. Conversely, if the distribution is skewed to the right, the mode is often less than the median, which is less than the mean.