1. establishment of standard 2. fixation of the standard 3. compairing actual performance with standard performance 4. finding out the deviation 5. correcting the deviation
I am not entirely sure I understand correctly what you mean by "essence". However, the idea of finding the standard deviation is to determine, as a general tendency, whether most data points are close to the average, or whether there is a large spread in the data. The standard deviation means, more or less, "How far is the typical data point from the average?"
The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.
The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities. However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference. The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.
The standard deviation of a set of data is a measure of the random variability present in the data. Given any two sets of data it is extremely unlikely that their means will be exactly the same. The standard deviation is used to determine whether the difference between the means of the two data sets is something that could happen purely by chance (ie is reasonable) or not.Also, if you wish to take samples of a population, then the inherent variability - as measured by the standard deviation - is a useful measure to help determine the optimum sample size.
The question is excellent. If two independent random variable with different pdf's are multiplied together, the mathematics of calculating the resultant distribution can be complex. So, I would prefer to use Monte-Carlo simulation to calculate the resultant distribution. Generally, I use the Matlab program. If this is not a satisfactory answer, it would be good to repost your question.
The formula for finding probability depends on the distribution function.
Standard deviation is a statistical tool used to determine how tight or spread out your data is. In effect, this is quantitatively calculating your precision, the reproducibility of your data points. Here's how you find it: 1). Take the average of all the data points in your set. 2). Find the deviation of each point by finding the difference between each data point and the mean. 3). Add the squares of each deviation together. 4). Divide by one less than the number of data points. If there are 20 data points, divide by 19. 5). Take the square root of this value. 6). Done.
The frequency distribution usually refers to empirical measurement and there is no formula for finding it. You simply count the number of times an observation falls within a given range.
its very simple...do you want further details plz click here...http://www.business-analysis-made-easy.com/What Is Standard Deviation? google_protectAndRun("render_ads.js::google_render_ad", google_handleError, google_render_ad);To answer the question of what is standard deviation you must refer to the question raised in mean average. The mean or average have little value without some measure of the variability of the data. Standard deviation to the rescue!The EquationThe standard deviation equation is:It must be noted that this formula is for the sample and not for the population. If you don't know what this means, don't worry about it. For simple applications it makes little difference.Now that you have seen the formula, let's describe what is happening in simpler terms. The formula is simply finding the average distance each data point is from the dataset mean. The squared numbers is a mathematical way of making all of the distances positive. So here is our measure of a datset: First we find the average of the data points, then we find the average of the distance each data point is from the mean or average of the data. This gives us a good beginning in describing the data within a datset.SummaryThe question of explaining standard deviation has been addressed herein. It is the average of the distance from the mean of all the data points in the dataset. To see an example of how this parameter is calculated go to Standard Deviation Calculation.
25% to 33%.
The basic function of an average is so that you have just one value to represent your entire data with. You don't have to say that your data range lies within this boundaries - you just have to quote the average and standard deviation and that more or less, gives significant information about your data.