Hi
Please explain simply what is meant by this?
Insurance companies hire the best mathematicians in the world as an "actuary" to determine the risk and based on that calculate how much insurance premiums need to be. They use statistical analysis and generally will only consider events within 3 standard deviations.
In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of data points. It indicates how spread out the values are from the mean (average) value.
When we talk about a value being "11 standard deviations away," it means that the data point is exceptionally far from the mean. In fact, it is considered extremely rare to find a value that is 11 standard deviations away from the mean in a normal distribution.
In a normal distribution, about 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. As the number of standard deviations increases, the percentage of data points within that range decreases exponentially.
To put it into perspective, if a value is 11 standard deviations away from the mean, it implies that the data point is exceptionally extreme and highly unlikely to occur by chance in a normal distribution. This would suggest either a very unusual event or a potential issue with the data or measurement process. In many practical cases, such extreme values may be considered outliers or anomalies.
If we consider 11 standard deviations away from the mean, it would imply an extremely rare occurrence. In a normal distribution, the percentage of data points within 11 standard deviations is virtually negligible, approaching zero. To be precise, it would be less than 0.0000000001% or 1 in 10 billion.
Therefore, if a data point is 11 standard deviations away from the mean, it suggests an exceptionally extreme value that is highly improbable in a normal distribution. Such an occurrence is typically considered an outlier or an anomaly.