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. A low standard deviation indicates 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, sum all the values in the data set and then divide by the number of values.

Front

What is the formula for variance?

Back

Variance is calculated as the average of the squared differences from the Mean. Formula: Variance (σ²) = Σ (xi - μ)² / N, where xi is each value, μ is the mean, and N is the number of values.

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, showing greater variability.

Front

What is the relationship between variance and standard deviation?

Back

Standard deviation is the square root of variance. It provides a measure of spread in the same units as the data.

Front

How do you find the standard deviation of a sample?

Back

For a sample, the standard deviation is calculated using the formula: s = √(Σ (xi - x̄)² / (n - 1)), where x̄ is the sample mean and n is the sample size.

Front

What is the mean of the data set: 8, 7, 5, 9, 6, 13?

Back

The mean is 8.

Front

What is the standard deviation of the data set: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2?

Back

The standard deviation is 7.26.

Front

What is the variance of the data set: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2?

Back

The variance is 52.77.

Front

Which data set has the largest standard deviation: Set 1: {10, 19, 38, 50, 51}, Set 2: {5, 21, 26, 39, 51}, Set 3: {9, 38, 50, 50, 51}, Set 4: {5, 28, 28, 28, 51}?

Back

Set 1 has the largest standard deviation.