Standard Deviation and Normal Distribution

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

What does the symbol 'σ' represent in statistics?

Back

The symbol 'σ' represents Standard Deviation.

Front

According to the empirical rule, what percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68% of the data falls within 1 standard deviation of the mean.

Front

What percentage of data falls within 2 standard deviations of the mean according to the empirical rule?

Back

95% of the data falls within 2 standard deviations of the mean.

Front

What percentage of data falls within 3 standard deviations of the mean according to the empirical rule?

Back

99.7% of the data falls within 3 standard deviations of the mean.

Front

In a normal distribution, what does the area under the curve represent?

Back

The area under the curve represents the total probability, which is equal to 1 (or 100%).

Front

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

Back

The range of values that fall within 1 standard deviation is from 45 to 55.

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

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

Back

To calculate the standard deviation, find the mean of the data set, subtract the mean from each data point, square the result, find the average of those squared differences, and then take the square root of that average.

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 in a normal distribution.