To determine which of the provided options accurately describes standard deviation values, we can analyze each option in detail to understand which one fits best.
Option A: Range associated with the difference between the highest and lowest values around the mean value.
The range is defined as the difference between the highest and lowest values in a data set, but it is not specific to values "around" the mean. This option incorrectly links the concept of range with the mean.
Option B: Range associated with the difference between the highest and lowest values around the median value.
Similar to Option A, this description ties the range to values around the median, which is not correct. Range is related to the overall spread between the extremes, not specifically to values around the median.
Option C: Confidence interval for the value set.
Confidence intervals are related to estimating a population parameter (like mean) from a sample, rather than describing the variability of the data set itself. Standard deviation does not describe a confidence interval.
Option D: Range of values obtained for 50% of the subjects.
This option is related to the interquartile range (IQR), which measures the middle 50% of values around the median. It does not describe standard deviation, which measures overall variability around the mean.
Option E: Variability associated with the scattering of data around the mean value.
This option correctly defines standard deviation. The standard deviation is a measure of the amount of variation or dispersion in a set of values around the mean. A smaller standard deviation indicates that the data points tend to be close to the mean, while a larger standard deviation indicates that the data points are spread out over a wider range of values.
Given the detailed explanation, the correct answer is:
E. Variability associated with the scattering of data around the mean value.
