What is empirical rule (Meaning, definition, Formula)
Here, we will help you understand the Empirical Rule as well as its calculation and where and how to apply the Empirical Rule formula.
What is the Empirical Rule?
The Empirical Rule is basically the statistical rule that tells us that all the facts and figures will eventually fall under three of the standard deviations of the mean which is denoted by σ (and refers to as standard deviation), and where we calculate the mean by average of all of the given numbers that are available with us. This is also referred as Three Sigma Rule or the Rule of 68-95-99.7, as it comprises of the 3 set ranges of the data, which are as:
- 68 Percent of all the data – it falls within the first standard deviation of the mean
- 95 Percent of all the data, and – it falls within the two concerned standard deviations.
- 99.7 Percent of all the data– it falls within the three concerned standard deviations.
The Empirical Rule Definition:
The Definition of Empirical Rule states that for a normal distribution, approximately all of the facts and figures will fall inside the given or stated three standard deviations of the concerned mean. And those 3 groups are of the data 68 Percent, 95 Percent, and 99.7 Percent of the data.
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When to use the Empirical Rule?
The Empirical Rule is used when it is quite difficult to obtain the data or sometimes when it becomes impossible to collect the data. So, it is most probably used to forecast things.
And a rough figure is calculated using the empirical rule. Thus, mostly it is applied when the data is not available to us, or we are left out with no information.
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Empirical rule statistics
The statistics of the empirical rule involves the calculation of Mean and standard deviation that is used in the calculation of the empirical rule.
1. The Mean
Mean is calculated by adding the number of available groups and dividing the sum by the total number available. It is represented by.
2. The Standard Deviation
The standard deviation is calculated by using the following formula, that is given below:
3. The normal distribution:
The normal distribution is the actual graph that defines the range of the given data. Here, the empirical rule is applied and result is drawn out.
So, the empirical rule stats involve the usage of: the mean, standard deviation and the normal curve.
Empirical rule graph:
The empirical rule graph denotes the three groups or ranges of the rule which are as follows:
Whereas, the empirical rule percentage graph is drawn as follows:
How to do empirical rule?
The empirical rule procedure involves The Calculation for Empirical Rule:
Step 1: Firstly, you need to draw a bell shaped curve. This is a simple curve.
Step 2: Write down all the values or data in the bell shaped curve.
Step 3: Mark down each section’s percentage for which you need to calculate the following:
- You need to Calculate the Mean of the available data.
- You need to Find out the Standard Deviation of the data available.
Step 4: Apply the Empirical Rule to the derived data by use of mean and standard deviation.
Empirical rule example 1:
Taking up the example as the mean to be 40 and the standard deviation to be 200. And applying empirical rule we get the following output:
Here, the empirical rule bell curve says that:
- Roughly 99.7 Percent of all the data lies between ± 3 SD, or between 80 and 320
- Roughly 95 Percent of all the data lies between ± 2 SD, or between 120 and 280
- Roughly 68 Percent of all the data lies between ± 1 SD, or between 160 and 240
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Empirical rule example 2:
Taking up the example as the mean to be 50 and the standard deviation to be 4. And applying empirical rule we get the following output:
- Approx. 99.7 Percent of all the data lies between ± 3 SD, or between 38 and 62
- Approx. 95 Percent of all the data lies between ± 2 SD, or between 42 and 58
- Approx. 68 Percent of all the data lies between ± 1 SD, or between 46 and 54
Thus, with the use of empirical rule you can find out the data and analyse it as well. Normally, it is used where the data or facts and figures are not available. And empirical data is used to draw out a result. Though, this rule is applicable only in case on random variables and So, does not apply to the data that is not normal.
The formula used in empirical rule can be stated as follows:
- For the first standard deviation from the mean: μ ± 1σ (having 65%)
- For the second standard deviation from the mean: μ ± 2σ (having 95%)
- For the third standard deviation from the mean: μ ± 3σ (having 99.7%)
The empirical rule is used with the help of a normal distribution, that states that all the data will eventually fall within the three standard deviations of the mean. Thus, it can be seen as well as calculated in 3 parts i.e.
- 68% of concerned data
- 95% of the data and
- 99.75 of the data
The empirical rule means that all the data will fall down under the 3 data sets which in all sums up the 100%. And therefore, the 3 ranges of the empirical rule are grouped up as: 68% of the given data, 95% of the given data and 99.7% of the given data. So, the data will fall in these given and set 3 ranges only.
Some of the other names used for the empirical rule are as:the 68-95-99.7 rule or Three Sigma Rule, normal distribution, the rule of thumb, etc.