Standard Deviation
One of the most important measurements is standard deviation.
Standard deviation is similar to variance because it is the square root of variance.
Therefore, the formulas will differ for the population and sample.
Definition
Standard deviation is a measure of how data is spread out in relation to the mean.
Empirical Rule
The Empirical Rule, also known as the 68β95β99.7 rule, applies when the population follows a Normal Distribution. According to this rule:
- About 68% of the data falls within one standard deviation (Ο) of the mean;
- About 95% falls within two standard deviations (2Ο);
- About 99.7% falls within three standard deviations (3Ο).
When dealing with samples, the percentages might not be precisely accurate, but you can expect them to be quite close to the values in the rule, especially with larger sample sizes.
Example
To illustrate this, let's examine a sample of kitten weights measured in grams:
In this scenario, the following data is being used:
- Mean value (ΞΌ) is 100 grams;
- Standard deviation (Ο) is 20 grams.
As mentioned earlier, one standard deviation above and below the mean encompasses 68% of the values. In this instance, those values range:
from:Β ΞΌβΟ=100β20=80;to:Β ΞΌ+Ο=100+20=120.Thanks for your feedback!
Ask AI
Ask AI
Ask anything or try one of the suggested questions to begin our chat
Can you explain the difference between population and sample standard deviation?
How is the standard deviation calculated in practice?
Can you provide more examples of the Empirical Rule?
Awesome!
Completion rate improved to 2.63Standard Deviation
Swipe to show menu
One of the most important measurements is standard deviation.
Standard deviation is similar to variance because it is the square root of variance.
Therefore, the formulas will differ for the population and sample.
Definition
Standard deviation is a measure of how data is spread out in relation to the mean.
Empirical Rule
The Empirical Rule, also known as the 68β95β99.7 rule, applies when the population follows a Normal Distribution. According to this rule:
- About 68% of the data falls within one standard deviation (Ο) of the mean;
- About 95% falls within two standard deviations (2Ο);
- About 99.7% falls within three standard deviations (3Ο).
When dealing with samples, the percentages might not be precisely accurate, but you can expect them to be quite close to the values in the rule, especially with larger sample sizes.
Example
To illustrate this, let's examine a sample of kitten weights measured in grams:
In this scenario, the following data is being used:
- Mean value (ΞΌ) is 100 grams;
- Standard deviation (Ο) is 20 grams.
As mentioned earlier, one standard deviation above and below the mean encompasses 68% of the values. In this instance, those values range:
from:Β ΞΌβΟ=100β20=80;to:Β ΞΌ+Ο=100+20=120.Thanks for your feedback!
