In a given set of data, if the mean is 20 and the mode is 15, what can be inferred about the data distribution?

In this scenario, where the mean is 20 and the mode is 15, the data distribution can be inferred to be positively skewed.

When a distribution is positively skewed, it means that the tail on the right side of the distribution is longer or fatter than the left side. In such cases, the mean is typically greater than the mode, as is seen here. The higher mean indicates that there are higher values in the dataset pulling the average up, while the mode, which is the most frequently occurring value, is lower.

Thus, the presence of a mean significantly greater than the mode suggests that most of the data points cluster at a lower value (in this case, around 15), while there are some higher values that raise the mean to 20. This pattern is common in positively skewed distributions, confirming that the correct inference about the data distribution based on the given mean and mode is that it is positively skewed.