Sample standard deviation
There are a lot of cases in which it is not easy to sample ye every member in the population which can require the above equation which can be modified so the standard deviation can be measured with the random sample of studying population. The common estimator of how to calculate standard deviationis the sample of standard deviation which is denoted by s. As there are many of the different equations for calculating the same.ole standard deviation as like of sample mean sample standard deviation which is not having the single estimator which is unbiased, efficient and has the maximum likelihood. The question which is provided downside is the corrected sample standard deviation. This is the correct equation which is obtained by the modification of population standard deviation equation by using the size of the sample as the size of the population which also able to remove some bias of the equation. The standard deviation of unbiased estimation is highly involved and will vary according to the distribution.
Application of the standard deviation
1 . Standard deviation is the one which is used widely in the experimental and the industrial settings test models which are against the real world of data. An example for clearly understanding the application can be to use of this in industries for quality control of some products.
2 . Standard Deviation calculation can also be used for calculating the minimum and maximum value of those products which can fall with text high percentage of time due to some aspects of that product. In such cases when the value falls down below the calculated range then it becomes necessary for making changes to the process of production of that particular product for ensuring the quality control.
3 . We are also using the standard deviation in weather determination for calculating the weather conditions of different regions. Just imagine that there are two cities from which one is at the coast and the other one is in the deep inland which is having the same temperature that is of 75°F. Now, this is just a belief or imagination that both of the cities have the same temperature this can be done only in one situation if you ignore the value of calculating standard deviation and only consider the mean value.
Coastal cities have much more stable temperature because of the regulation of temperature by large bodies of water as water is having the high capacity of heat as compared to the land. This phenomenon makes the water less susceptible for changing the temperature and the coastal areas still remain warm even in the winters and remain cool in summers due to the high amount of energy which is required for changing the temperature of water.
So as result we can say that when the temperature of coastal city has the range in between 60°F to the 80°F for the considered times then the mean value will be 75°F , whether the inland city can have to temperature which ranges from 30°F to the 110°F which results in the same mean maths value that is of 75°F.
4 . Finance section is another area in which the standard deviation is used on a large scale where it is used for measuring the risk of price fluctuations at some portfolio and some assets. In such cases, the use of the standard deviation provides the uncertainty of returns in future for the particular investment. Let us have a standard deviation example–
If we have to compare the stock A which is having the return value of average 7 % with the standard deviation percentage standard deviation of around 10 % with respect to stock B which is having the same average return but the value of standard deviation for stock B is 50 % then the first stock which is A will be much safe option as compared with the second stock which is B. We can not say that you will get the better investment option with A and will got definitive loss in B but there are high chances of getting large returns ( loss ) of stock B as compared to the A due to the high variation of value of standard deviation.
5 . By , calculating the value of standard deviation is valuable at the time when it is important or necessary to know how far will the typical value of mean can be distributed.