Dec 4 B1 BW Stats Ch 2.4 Measures of Variation

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 means that the values are spread out over a wider range.

Front

How do you calculate the standard deviation of a data set?

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 this average.

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 in the data.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

Front

What percent of data falls within 1 standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What percent of data falls within 2 standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Front

What percent of data falls within 3 standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

If the mean of a data set is 50 and the standard deviation is 5, what is the range of values that fall within 1 standard deviation?

Back

The range is from 45 to 55.

Front

What is variance in statistics?

Back

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

Front

How is variance related to standard deviation?

Back

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