Standard deviation Normal Distribution

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Definition: - Standard deviation is the square root of the variance.

The standard deviation is the popular measure of variability. It is used both as a separate entity and as a part of other analyses, such as computing confidence intervals and in hypothesis testing.

The population standard deviation is denoted by σ and
Sample standard deviation is denoted by s.

·         σ =√∑(x-µ)^2 / N
·         s= √∑(x- x?)^2/ (n-1)
·         Standard deviation= √ variance.

Example: Find the standard deviation of the sample when variance of sample is 25.

Solution: - Since
            Standard deviation= √ variance.
                        S = √25= 5
Therefore standard deviation of sample is 5.

Another example: - Find the standard deviation of population when variance of the population is 100.

Solution: - Standard deviation= √ variance.
                        S = √100 =10
Therefore standard deviation of population is 10.

Normal distribution is the most widely used of all distribution. It fits many individual characteristics, such as heights, lengths, speed, IQ and year of life expectancy, among others. Like their human counterpart’s living things in environment, such as trees, animals, insects, have many characteristics that are normally distributed.

Some examples of variables that could create normally distributed measurements include the yearly cost of household insurance, the cost per square foot of renting warehouse space, and manager’s satisfaction with support from ownership on a five- point scale. In addition, we can say most items are produced or filled by machines are normally distributed.


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