Final answer:
The standard deviation is a measure of how spread out the values in a data set are from the mean. It calculates the average distance from individual data points to the mean, providing a measure of variation or spread of the data values.
Step-by-step explanation:
What is Measured by the Standard Deviation?
The standard deviation measures the spread or variation in a data set, specifically how far individual data values are from the mean (average) of the data set. It does not measure the distance between the mean of a population and a sample or between individual scores and the sample mean explicitly. Instead, it reflects the typical distance an individual data point is from the mean of the entire data set.
To calculate the standard deviation, we must first calculate the variance. The variance represents the average of the squared differences between each data value and the mean. For a population, the variance is symbolized as σ² and the standard deviation as σ, which is the square root of the variance. For a sample, the variance is symbolized as s² and the standard deviation as s, also the square root of the sample variance.
The standard deviation can be used to determine whether a particular data value is close to or far from the mean. A small standard deviation indicates that the data points are generally close to the mean, exhibiting little variation. Conversely, a larger standard deviation indicates a wider spread of data values from the mean.