Standard Deviation and Normal Distribution

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.

The symbol 'σ' represents Standard Deviation.

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

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

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

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

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

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.

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.

The mean is the central value around which the data is distributed in a normal distribution.