Final answer:
Measures of dispersion, such as the standard deviation, indicate the variation or spread of data. A low standard deviation means less spread, while a high one shows more variability. In symmetrical distributions, the mean, median, and mode are similar, but in skewed distributions, the median is oftentimes more representative of the data center.
Step-by-step explanation:
Measures of dispersion are used to indicate the spread or variation of the data. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a numerical value that indicates how far data values are from their mean. A smaller standard deviation means that the data points are closer to the mean, suggesting less variability, while a larger standard deviation indicates more spread-out data and greater variability. It is important to note that when the standard deviation is zero, all data values are the same, indicating no spread or variability. Another aspect to consider is the shape of the data distribution. In a symmetrical distribution, the mean, median, and mode will all be close to each other. However, when there are outliers or the data is not symmetrical, these measures can differ significantly, and the median often becomes a more appropriate measure of the center than the mean.