Empirical Rule

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The use of the Empirical Rule
When the mean=median and the values often tend to cluster around the mean and median, producing a bell-shaped distribution. Then we can use the empirical rule to examine the variability. Usually in this bell-shaped data set, we can calculate the mean the standard deviation. The mean means the average value of this set of data. The standard deviation means the average scatter around the mean. If we allow[pic]to represents the mean and[pic]to represents the standard deviation. Then we can say 68% of the data are within[pic], 95% of the data are within[pic], 99.7% of the data are within[pic]. [pic]

The picture gives us a clear overview of what the empirical rule look like. The Empirical Rule is useful for estimating the possibility of each interval for a bell-shaped distribution. For example, if we have 100 data for a variable which has a bell-shaped distribution. Then we can say that: approximately 68 data are lie within[pic],

95 data are lie within[pic],
27 (95-68=27) data are lie within[pic],
4.7 (99.7-95) data are lie within[pic],
0.3 data lies within[pic].
Here is an example of the use of the Empirical Rule: Suppose that the distribution of monthly earning for all people who possess a bachelor’s degree is known to be bell-shaped and symmetric with a mean of $2000 and a standard deviation of $500. How do we know the percentage of the individuals with a bachelor’s degree earn less than 1500 per month? Well, Z=[pic]. The data should be lie within[pic], The percentage should be 1-(50+68/2)%=16%

B. How do we know the percentage of a individual with bachelor’s degree earns more than 1000 per month?

The data are lie within[pic], the percentage should be (50+95/2)%=97.5%

C. How do we know the percentage of a individual with a bachelor’s degree earns between 3000 and 3500 per month?

[pic] [pic]
The data are lie within[pic]. The percentage should...
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