Understanding Standard Deviation

Front

What is standard deviation?

Back

A measure of the amount of variation or dispersion in a set of values.

Front

How is standard deviation calculated?

Back

It is calculated as the square root of the variance.

Front

What does a high standard deviation indicate?

Back

It indicates that the data points are spread out over a wider range of values.

Front

What does a low standard deviation indicate?

Back

It indicates that the data points are closely clustered around the mean.

Front

What is the empirical rule in statistics?

Back

It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

What is the significance of a five Sigma result?

Back

It indicates a very low probability (1 in 3.5 million) that the result is due to random fluctuation.

Front

How does standard deviation relate to the normal curve?

Back

Standard deviation determines the width of the normal curve; a smaller standard deviation results in a steeper curve.