Standard Deviation Practice

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

1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Find the average of these squared differences. 4. Take the square root of that average.

Front

What does a low standard deviation indicate?

Back

The data points tend to be close to the mean, indicating low variability.

Front

What does a high standard deviation indicate?

Back

The data points are spread out over a wider range of values, indicating high variability.

Front

What is the formula for standard deviation (population)?

Back

σ = √(Σ(xi - μ)² / N) where μ is the mean, N is the number of data points.

Front

What is the formula for standard deviation (sample)?

Back

s = √(Σ(xi - x̄)² / (n - 1)) where x̄ is the sample mean and n is the sample size.

Front

What is the relationship between variance and standard deviation?

Back

Standard deviation is the square root of variance.

Front

How does standard deviation relate to the normal distribution?

Back

In a normal distribution, about 68% of data falls within one standard deviation of the mean.

Front

What is the effect of outliers on standard deviation?

Back

Outliers can significantly increase the standard deviation, indicating greater variability.

Front

How can standard deviation be used in real-life applications?

Back

It can be used in finance to assess risk, in education to evaluate test scores, and in quality control to monitor processes.