Final answer:
A more leptokurtic distribution is characterized by being more peaked than a normal distribution, with data significantly clustered around the mean and having fatter tails. It is different from skewness, which refers to the symmetry or asymmetry of the data. The correct answer to the question is b) It has a more peaked distribution.
Step-by-step explanation:
If someone says one distribution of scores is more leptokurtic than another, they are referring to the shape of the distribution. Specifically, a leptokurtic distribution is more peaked than a normal distribution, indicating that the data are more clustered around the mean, and it has fatter tails, meaning there are more extreme values or outliers. This contrasts with a flatter distribution, which would be described as platykurtic, and neither a leptokurtic distribution nor a platykurtic distribution is necessarily skewed left or right. Skewness refers to the asymmetry in the distribution of the data. For instance, a left (negative) skew means the tail is on the left side of the distribution, indicating that the distribution has more high values, and the mean is less than the median, which is in turn often less than the mode. A right (positive) skew means the tail is on the right side, indicating more low values, where the mode is often less than the median, which is less than the mean.
A proper understanding of skewness and kurtosis is essential when evaluating the normality of the data. The Central Limit Theorem, for instance, assumes that as the sample size increases, the distribution of sample means approximates a normal distribution, which is unimodal and symmetric. In such a symmetrical distribution, the mean, median, and mode are all located at the same place. In contrast, a leptokurtic distribution deviates from this pattern by having a sharper peak and heavier tails.
Based on this explanation, the correct answer to the question is option b: It has a more peaked distribution.