Stats 3-3 (part 2) Measures of Variation

Front

What is the Empirical Rule in statistics?

Back

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

Front

Define 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

What is Chebyshev's Theorem?

Back

Chebyshev's Theorem states that for any data set, regardless of distribution, at least (1 - 1/k²) of the data values will fall within k standard deviations of the mean, where k is any positive integer greater than 1.

Front

Calculate the range of a data set: 5, 10, 15, 20, 25.

Back

Range = Maximum - Minimum = 25 - 5 = 20.

Front

What is variance in statistics?

Back

Variance is the average of the squared differences from the mean, indicating how much the data points differ from the mean.

Front

How do you find the mean of a data set?

Back

To find the mean, sum all the values in the data set and divide by the number of values.

Front

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

Back

Approximately 95% of the data lies within two standard deviations of the mean in a normal distribution.

Front

If the mean is 50 and the standard deviation is 5, what is the range for at least 75% of the data according to Chebyshev's Theorem?

Back

The range is 50 ± 2(5) = 40 to 60.

Front

What is the formula for calculating sample variance?

Back

Sample Variance (s²) = Σ(xi - x̄)² / (n - 1), where xi is each value, x̄ is the sample mean, and n is the number of values.

Front

Define normal distribution.

Back

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.