What does standard deviation measure in a data set?

Standard deviation measures the spread of data values in a data set. It quantifies how much the individual data points deviate or vary from the mean (average) of the set. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation signifies that the values are spread out over a wider range. This measure is crucial in fields such as engineering and statistics because it provides insight into the variability and consistency of the data, allowing for better decision-making and risk assessment.

Other options do not precisely define what standard deviation represents. The average value of the data relates to the mean, while the difference between the highest and lowest values describes the range. The most frequently occurring value pertains to the mode, which is another measure of central tendency. Each of these alternative options addresses different statistical concepts, highlighting the unique role standard deviation plays in understanding data variability.