Normal Distribution/Gaussian
Normal Distribution(ND) refers to data Population or Sample.
ND is also called as Bell Curve or Normal Curve.
ND describes the tendency for data to cluster around a central value.
In fact, this central value is the population mean ‘mu’ which is always located in the middle of the curve. So for any normal distribution we can say that some data points will fall under below the mean and other data points will fall above the mean, but most of the values located near the mean.
Example for ND in Exam Score: Some people do great on exams, some people do poorly on exams. But large majority of the people score near the average or the mean. In this example the average score is 50 because it is located in the middle of the curve.
Parameter: A number that describes the data from population.
Statistic: A number that describes data from a sample.
Representation:
Population Mean(Mu) & Population St. Deviation(Sigma), both of these tell us important information about how the Normal Distribution looks.
Population Mean (Mu):
Characterizes the position of the Normal Distribution. If we increase the Mean the curve follows and move towards right.
If we decrease the Mean the curve follows and move towards left.
This happens because the data will always cluster around the mean in Normal Distributed Populations. As a result the value of the mean determines the position of Normal Distribution.
Population Standard Deviation (Sigma):
Sigma characterizes the spread of Normal Distribution. The larger the St.Deviation the more spread out the distribution will be and small the St.Deviation the lesser the spread out.
Note: The reason for this is Normal Distribution is a density curve. And the total area of the any density curve must remain equal to 1 or 100%. So the changes in the width of the curve must be compensated for the changes in height of the curve & vice-versa.
Overview of Normal Distribution:
- Normal Distribution is Unimodal. This means that the distribution has a single peak.
- The normal curve is symmetric about its mean so we can see that the distribution can be cut into two equal halves.
- The parameters Mu & Sigma completely characterizes the Normal Distribution.
• The population mean Mu determines the location of the distribution and where the data tends to cluster around.
• The population standard deviation (or) Sigma determines how spread out the distribution will be. - X ~ N(Mu, Sigma)
• For variable X it follows a Normal Distribution and as the Mean Mu with St.Deviation of Sigma.
