What is indicated by high standard deviation in a set of data?

What is indicated by high standard deviation in a set of data?

• A. Values are very close together
• B. Values are spread out
• C. Values are all the same
• D. Values increase steadily

Answer: (B)

A high standard deviation in a set of data indicates that the values are spread out over a wide range. Standard deviation measures the amount of variation or dispersion in a set of values. When the standard deviation is high, it implies that the individual data points differ significantly from the mean (average) of the data set. This means that there are more extreme values or a greater range of values, resulting in a less consistent or more varied dataset. In contrast, a low standard deviation would suggest that the values are clustered closely around the mean. Therefore, the understanding of the standard deviation as a measure of dispersion is essential in interpreting the variability within a dataset.

A high standard deviation in a set of data indicates that the values are spread out over a wide range. Standard deviation measures the amount of variation or dispersion in a set of values. When the standard deviation is high, it implies that the individual data points differ significantly from the mean (average) of the data set. This means that there are more extreme values or a greater range of values, resulting in a less consistent or more varied dataset. In contrast, a low standard deviation would suggest that the values are clustered closely around the mean. Therefore, the understanding of the standard deviation as a measure of dispersion is essential in interpreting the variability within a dataset.