Final answer:
The true statement about standard deviation is that removing an outlier will decrease the standard deviation. Standard deviation measures how spread out the data values are from the mean, and outliers can artificially inflate this measurement. Therefore, the correct option is C.
Step-by-step explanation:
The true statement about the standard deviation is that removing an outlier will decrease the standard deviation. Standard deviation is a measure of the spread of data values around the mean. When outliers, which are extreme values, are present in a data set, they can significantly increase the standard deviation because they contribute to a larger overall spread. By removing an outlier, the remaining data points are usually closer to the mean, resulting in a smaller standard deviation.
It is important to note that standard deviation is not the difference between the minimum and maximum values—that would be the range of the data. Likewise, it is not the difference between the first and third quartile—that measure is known as the interquartile range (IQR).
When analyzing data, one should also consider the distribution shape. In symmetrical distributions, the standard deviation can effectively describe the spread, but in skewed distributions, it may be less informative, and therefore, measures like quartiles, median, or IQR might provide more insight.