Discrete - Standard Deviation Review

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Front

How do you calculate the mean of a data set?

Back

To calculate the mean, add all the numbers in the data set together and then divide by the total number of values.

Front

What is variance?

Back

Variance is the average of the squared differences from the mean. It measures how far a set of numbers is spread out.

Front

What is an outlier in a data set?

Back

An outlier is a data point that differs significantly from other observations in the data set. It can skew the results of statistical analyses.

Front

How do you identify an outlier?

Back

An outlier can be identified using the interquartile range (IQR) method or by looking for values that are significantly higher or lower than the rest of the data.

Front

What does a higher standard deviation indicate about a data set?

Back

A higher standard deviation indicates that the data points are more spread out from the mean, suggesting greater variability.

Front

What is the relationship between mean and standard deviation?

Back

The mean provides a measure of central tendency, while the standard deviation provides a measure of variability around that mean.

Front

What is the formula for calculating variance?

Back

Variance (σ²) = Σ (xi - μ)² / N for population variance, or Σ (xi - x̄)² / (n - 1) for sample variance, where xi is each value, μ is the mean, and N is the number of values.

Front

What does it mean if two data sets have the same mean but different standard deviations?

Back

It means that while the average value is the same, the spread of the data points around the mean differs, indicating different levels of variability.

Front

What is the purpose of squaring the differences when calculating variance?

Back

Squaring the differences prevents negative values from canceling out positive values and emphasizes larger differences.