Final answer:
The outlier value of 30 would increase the mean of the dataset, resulting in a positively skewed distribution where the mean is greater than the median.
Step-by-step explanation:
The inclusion of an outlier value of 30 in the dataset comprising values 3, 8, 4, 10, 12, 13, 2 would significantly affect the mean of the dataset by increasing it. This is due to the nature of the mean, which is calculated by summing all the values and dividing by the number of values, and hence is highly sensitive to outliers. The presence of such a high outlier would result in a positively skewed distribution, as the long tail of the distribution would be to the right, and the mean would be greater than the median.
When considering measures of central tendency like the median and the mode, these are more robust to outliers. While the mode remains unaffected by outliers, the median might only change slightly if the outlier is a part of a much larger dataset. The mean, however, can be drastically altered by a single extreme value, thus more accurately reflecting any skewness in the data. When data is skewed, the mean will often be pulled towards the tail, and in this specific case, towards the higher values.