Question

What does the standard deviation tell you?

-it tells how spread out the data is.
-it tells you how many data points are above the mean.
-it tells the average value of all the data.
-it tells you if the data is normally distributed.

Answer 1

The standard deviation is a measure of the spread of data points around the mean in a data set. A small value indicates little spread, while a large value indicates more variability.

Step-by-step explanation:

The standard deviation is a statistical measure that tells us how spread out the data points are around the mean of a data set. It is a critical concept in descriptive statistics that helps to understand the variability or dispersion of the data. A small standard deviation indicates that the data points tend to be close to the mean, showing little variation, while a large standard deviation suggests a wider spread and greater variation around the mean.

Descriptive statistics include the mean and standard deviation to summarize and describe data. By understanding standard deviation, one can assess whether individual data points are close to or far from the average value. It's also important to note that standard deviation can be influenced by outliers, which can significantly increase the calculated value when data points are very spread out.

Graphical representations, such as histograms or box plots, can complement the numerical measure of standard deviation. While standard deviation is very useful for symmetrical data distributions, it might be less informative for skewed distributions, where looking at individual quartiles and the median could provide better insights.