Final answer:
The distribution of the exercise hours is positively skewed because the mean is greater than the median, and the median is greater than the mode. As such, the median would be the best measure of central tendency in this case, not the mean as indicated in option a).
Step-by-step explanation:
A researcher conducted a survey and asked participants the number of hours they exercised on average the previous six weeks, with the following results: X = 10 hours, Median = 4 hours, and Mode = 2 hours. When considering the shape of this distribution and the best measure of central tendency, we need to look at the relationship between these three statistics.
Since the mean is greater than the median, and the median is greater than the mode, we are looking at a positively skewed distribution. This means that there are a few very high values that pull the mean up, but most of the data are clustered toward the lower end.
Due to the skewness, the median is usually the best measure of central tendency since it is less affected by extreme values in the data set. Hence, the correct answer is a) Positively skewed; Mean, as the mean is not the best measure of central tendency in a positively skewed distribution, but rather the median.