Final answer:
The range is the best measure for determining the variation among a set of scores as it provides the difference between the largest and smallest values in the data set, directly indicating the spread of the data.
Step-by-step explanation:
The question is asking which statistical measure is best for determining variation among a set of scores. Variation is best determined by the range of the data, which is calculated by subtracting the smallest value from the largest value within a data set. The range provides a simple measure of the spread of scores and can quickly indicate how dispersed the data points are from each other. While the mean, median, and mode can all provide useful information about the center of a data set, they do not directly measure variation or spread.The mode tells us the most frequently occurring value in the data set. In a symmetrical distribution, the mean, median, and mode will all be equal. However, the mean is highly sensitive to outliers, which is why in such cases, the median might be a more appropriate measure of the center because it is not affected by extreme values. When assessing the distribution for averages, if the mean, median, and mode are equal, and the distribution is symmetrical, the area under the curve should be 1. This is because the symmetrical distribution is generally a reference to the normal distribution, where the total area under the curve indeed equals 1.It is important to consider the shape of the data when deciding which measures to use. If the data are skewed, the mean will reflect that skewing more than the median or mode. However, for determining variation, the range remains the best option among the choices provided.