Standard Deviation

Front

What is Standard Deviation?

Back

Standard Deviation is 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

A low Standard Deviation indicates that the data points tend to be close to the mean, showing less variability.

Front

What does a high Standard Deviation indicate?

Back

A high Standard Deviation indicates that the data points are spread out over a wider range of values, showing more variability.

Front

If two data sets have the same mean, can they have different Standard Deviations?

Back

Yes, two data sets can have the same mean but different Standard Deviations, indicating different levels of variability.

Front

What is the relationship between Standard Deviation and reliability in data?

Back

A lower Standard Deviation indicates more reliability in predicting outcomes, as the data points are closer to the mean.

Front

What does it mean if a data set has a Standard Deviation of 0?

Back

A Standard Deviation of 0 means that all the data points are identical and there is no variability.

Front

How does Standard Deviation relate to the normal distribution?

Back

In a normal distribution, about 68% of the data falls within one Standard Deviation of the mean, and about 95% falls within two Standard Deviations.

Tags

CCSS.HSS.ID.A.4

Front

What is the formula for Standard Deviation for a sample?

Back

s = sqrt(Σ(xi - x̄)² / (n - 1)), where xi is each value, x̄ is the sample mean, and n is the number of values.

Front

What is the difference between population Standard Deviation and sample Standard Deviation?

Back

Population Standard Deviation uses N in the denominator, while sample Standard Deviation uses (n-1) to account for sample variability.