In a perfectly symmetrical distribution, the mean, median, and mode are all equal.

Yes, that statement is indeed correct. In statistics, a perfectly symmetrical distribution means that the data is evenly distributed around the center point. In such distributions, the three measures of central tendency—mean, median, and mode—coincide.

1. Mean: This is the arithmetic average of all the data points. In a symmetrical distribution, the mean represents the balance point of the distribution.

2. Median: This is the middle value when all data points are arranged in ascending order. In a perfect symmetry, the median lies at the center of the distribution, making it equal to the mean.

3. Mode: This is the value that appears most frequently in the data set. In a symmetrical distribution where values are evenly spread, the mode also aligns with the mean and median.

Examples of perfectly symmetrical distributions include the normal distribution, where the bell-shaped curve reflects this property. Hence, in such distributions, you can confidently state that the mean, median, and mode are equal. This characteristic is pivotal in understanding data sets and in applying statistical methods effectively.