It is one of the most common form of probability distribution and can take any values within a range.
The normal distribution is a type of continuous probability distribution.One of the most common graph bell curve occurs in this one.
The two parameters that characterized the Normal Distribution are :-
1.) Mean
2.) Variance
The normal distribution can take any values from -infinity to + infinity.There is infinite number of normal distribution ,varying upon their mean and variance.
Standard Distribution / Z-distribution :- The normal distribution with mean =0 and standard deviation =1 is called standard distribution /Z distribution.
Characteristics of Normal Distribution :-
1.)Symmetry
2.)A single most common value (uni modality)
3.)Range from -infinity to + infinity
4.)Area under curve is 1
5.)A common value for the mean,median and mode.
Examples to illustrate it :-
A normal distribution is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side. There is also only one mode, or peak, in a normal distribution. Normal distributions are continuous and have tails that are asymptotic, which means that they approach but never touch the x-axis. The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below. It follows that the mean, median, and mode are all equal in a normal distribution.
Some of the common uses of normal distribution :-
1.) Height
2.)IQ
3.)Blood pressure
4.)Salaries etc.
The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
Z-scores/Normalized Scores:-
The formula for Z-score is :
Let us take an example to understand the concept of Z-scores .
A wild pack of Chihuahuas terrorizing the countryside has a mean height of 7.5 inches, with a standard deviation of 1.5 inches. We feel sorry for the person who had to measure that. What proportion of these Chihuahuas are between 6 and 9 inches tall?
When we want to know something about probabilities or proportions of normal distributions, we need to work with Z-scores. We use them to convert a value into the number of standard deviations it is from the mean. The formula is:
μ is another fancy code name for the mean of the normal distribution, while σ is its standard deviation. We can find the Z-scores for 6 and 9 inches now.
How much of the normal distribution falls within 1 standard deviation above or below the mean? According to the Empirical Rule, that's 68% of the distribution.
Further Reading :-https://en.wikipedia.org/wiki/Normal_distribution
http://www.statisticshowto.com/probability-and-statistics/normal-distributions/
The normal distribution is a type of continuous probability distribution.One of the most common graph bell curve occurs in this one.
The two parameters that characterized the Normal Distribution are :-
1.) Mean
2.) Variance
The normal distribution can take any values from -infinity to + infinity.There is infinite number of normal distribution ,varying upon their mean and variance.
Standard Distribution / Z-distribution :- The normal distribution with mean =0 and standard deviation =1 is called standard distribution /Z distribution.
Characteristics of Normal Distribution :-
1.)Symmetry
2.)A single most common value (uni modality)
3.)Range from -infinity to + infinity
4.)Area under curve is 1
5.)A common value for the mean,median and mode.
Examples to illustrate it :-
A normal distribution is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side. There is also only one mode, or peak, in a normal distribution. Normal distributions are continuous and have tails that are asymptotic, which means that they approach but never touch the x-axis. The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below. It follows that the mean, median, and mode are all equal in a normal distribution.
Some of the common uses of normal distribution :-
1.) Height
2.)IQ
3.)Blood pressure
4.)Salaries etc.
The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
Z-scores/Normalized Scores:-
The formula for Z-score is :
Let us take an example to understand the concept of Z-scores .
A wild pack of Chihuahuas terrorizing the countryside has a mean height of 7.5 inches, with a standard deviation of 1.5 inches. We feel sorry for the person who had to measure that. What proportion of these Chihuahuas are between 6 and 9 inches tall?
When we want to know something about probabilities or proportions of normal distributions, we need to work with Z-scores. We use them to convert a value into the number of standard deviations it is from the mean. The formula is:
μ is another fancy code name for the mean of the normal distribution, while σ is its standard deviation. We can find the Z-scores for 6 and 9 inches now.
How much of the normal distribution falls within 1 standard deviation above or below the mean? According to the Empirical Rule, that's 68% of the distribution.
Further Reading :-https://en.wikipedia.org/wiki/Normal_distribution
http://www.statisticshowto.com/probability-and-statistics/normal-distributions/
Really Good blog post.provided a helpful information.I hope that you will post more updates like this Big data hadoop online Training
ReplyDeleteHyderabad
ReplyDeleteGreat Article
Final Year Projects in Python
Python Training in Chennai
FInal Year Project Centers in Chennai
Python Training in Chennai