Normal Distribution

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 are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of the data falls within one standard deviation of the mean.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average of all data points and is the center of the normal distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations.

Front

What does a z-score represent?

Back

A z-score indicates how many standard deviations an element is from the mean.

Front

If a data point has a z-score of 2, what does that mean?

Back

It means the data point is 2 standard deviations above the mean.