When are the mean, median, and mode likely to be similar?

The mean, median, and mode are likely to be similar when the data is normally distributed. In a normal distribution, the data is symmetrically spread around the mean, resulting in these three measures of central tendency being equal or very close to each other. This characteristic reflects the balance of the distribution, ensuring that the values are evenly distributed on both sides of the mean.

In contrast, when data is skewed, the mean can be pulled in the direction of the skew, making it differ from the median and mode. The presence of outliers can also distort the mean significantly while leaving the median less affected, leading to a further disparity among these measures. Lastly, when the sample size is small, the measures may not be representative of the population, and their relationship may not reflect the characteristics of a normal distribution. Thus, the condition of normality is crucial for the mean, median, and mode to align closely.