Final answer:
Standard deviation is a statistical measure of variability within a data set, representing the spread of the data points around the mean. It is the square root of the variance, and a higher standard deviation signifies more spread out data. This measure is denoted by 's' for a sample and 'σ' for a population.
Step-by-step explanation:
The standard deviation is a key statistical measure that tells us how spread out the numbers in a data set are around the mean, which is the average. To be more precise, it is the square root of the variance; 's' represents the sample standard deviation and 'σ' represents the population standard deviation. Importantly, when the standard deviation is zero, there is no variability as all data values are the same. Otherwise, if the standard deviation is larger, the data points are more widely spread out from the mean.
The standard deviation serves as a numerical measure of the amount of variation within a data set. When you have a low standard deviation, the data points tend to be close to the mean, indicating a small amount of variability. Conversely, a high standard deviation indicates that the data points are spread out over a large range of values and thus, show a greater amount of variability or spread.
To compute the standard deviation, we first determine the variance, which is the average of the squared deviations from the mean. The standard deviation is then obtained by taking the square root of the variance, providing insight into the overall spread of the data set.