Final answer:
Standard deviation is a key statistical tool that details how data diverges from the mean, indicating low variability with smaller values and high variability with larger values. It is less effective for skewed distributions, but it is generally valuable and should be paired with graphical data representation. Despite its downsides, standard deviation remains an essential measure of data spread.
Step-by-step explanation:
The use of standard deviations provides significant benefits when describing the variability of data. Standard deviation can distinguish how much individual data points or groups differ from the data set mean. It is a useful measure for comparing these differences numerically. When the value of the standard deviation is small, it indicates that data points are close to the mean, signifying low variability. Conversely, a larger standard deviation suggests that data points are spread out over a wide range, indicating high variability.
However, there are some downsides to consider when using standard deviations. It may not be as helpful in skewed distributions, where the variability is different on either side of the mean. In such cases, it's beneficial to also consider the median, quartiles, and extreme values for a more comprehensive view of the data spread. Nonetheless, in symmetrical distributions, standard deviation is particularly valuable. Always complement numerical measures of spread like the standard deviation with graphical representations such as histograms or box plots to gain a better understanding of data distribution.
In conclusion, despite some downsides in certain situations, the standard deviation remains a critical tool for measuring variability. It is always advisable to use calculators or software to compute standard deviations accurately, and to interpret the numbers in the context of the data distribution they represent.