Flashcard Normal Distributions & the Empirical Rule

Front

What is the Empirical Rule?

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

What percentage of data falls within 1 standard deviation according to the Empirical Rule?

Back

68%.

Front

What percentage of data falls within 2 standard deviations according to the Empirical Rule?

Back

95%.

Front

What percentage of data falls within 3 standard deviations according to the Empirical Rule?

Back

99.7%.

Front

If a dataset is normally distributed with a mean of 50 and a standard deviation of 10, what is the range that contains approximately 68% of the data?

Back

The range is from 40 to 60.

Front

If a dataset is normally distributed with a mean of 100 and a standard deviation of 15, what is the range that contains approximately 95% of the data?

Back

The range is from 70 to 130.

Front

What is a normal distribution?

Back

A 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.

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central value around which the data is distributed, and in a normal distribution, it is also the point of symmetry.

Front

What does it mean for data to be normally distributed?

Back

It means that the data follows a bell-shaped curve where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

How do you calculate the standard deviation?

Back

Standard deviation is calculated as the square root of the variance, which is the average of the squared differences from the mean.