Final answer:
The statement is true; the standard deviation is a measure of how spread out the data are in a distribution, with a larger value indicating more variation from the mean.
Step-by-step explanation:
The statement is true: the standard deviation is a measure that tells how spread out scores are in a distribution. The standard deviation is the square root of the variance and helps us understand the variability within a set of data. It is always positive or zero and is particularly useful for comparing the spread of data to the mean. A small standard deviation indicates that the data points are close to the mean, while a large standard deviation indicates that the data points are spread out over a wider range of values, showing more variation. The greater the standard deviation, the greater the spread around the mean.
When the standard deviation is zero, it means that all data values are identical. On the other hand, a larger standard deviation would suggest the presence of outliers or a wide range of data points. In other words, it measures how far data values are from their mean. This makes the standard deviation a critical tool for statisticians and researchers to compare individual data points or entire sets of data to the overall mean.