Final answer:
Knowing both the mean and standard deviation allows us to understand the central tendency and variability of a data set.
Step-by-step explanation:
The mean and standard deviation (or variance) provide us with valuable information about a data set. Knowing both the mean and standard deviation allows us to understand the central tendency and variability of the data. The mean represents the average value of the data set, while the standard deviation measures how spread out the data points are from the mean.
For example, let's say we have two data sets A and B. Both data sets have a mean of 50. However, the standard deviation of data set A is 10, while the standard deviation of data set B is 30. This means that the data points in data set A are closer to the mean, indicating less variability, while the data points in data set B are further from the mean, indicating greater variability.
By knowing both the mean and standard deviation, we can determine whether a particular data value is close to or far from the mean, and we can also compare individual data points or classes to the overall data set numerically.