Uche -

Not being familiar with your work, and what you are trying to do, I may be misunderstanding your question, but let's just say that a standard error is a standard deviation of a parameter such as a mean or a regression coefficient.  A standard deviation of a population is a fixed number that we estimate.  But a standard error is reduced with sample size.  Either a standard deviation or a standard error could be said to be the positive square root of a variance.  Just remember that standard errors of parameters, such as means, are based on standard deviations, but are reduced with increased sample size.

I do not know what you are doing, but perhaps you are interested in standard errors to form confidence intervals.  The confidence interval depends also on the form of a distribution.  For an estimated mean with a large sample size of continuous data, the Central Limit Theorem will probably let you use a Gaussian distribution (generally called a "normal" distribution) to construct a confidence interval about that estimated mean.  But do not make the mistake of assuming populations should necessarily be "normally distributed." 

Note that for a regression, the estimated "prediction interval" may take advantage of the Central Limit Theorem with regard to the variance of the "errors" of the "predictions" for y given x, so this involves estimated residuals, but the y data and x data themselves, that is, the dependent variable and independent variable data distributions, can have any distributional form.  (For work I did on energy establishment survey data, for official statistics, these distributions were very highly skewed.) 

You may be interested in researching other statistical concepts and terms such as bias, moving averages, time series, autocorrelation, and/or perhaps others. 

Hope some of the above might be useful and not misleading for your purposes.

Cheers - Jim

Standard deviation, variance, mean absolute deviation are measures of dispersion. Knowing them is extremely important in order to have a common base. When you run some statistical test such as comparing means from two data-sets or testing how significantly certain independent variables change a dependent variable, you actually test against the unexplained dispersion.    

Dispersion measures like stranded deviation and variance are helpful in describing the variability of observations. Its possible to have same central tendency measures for two different population . For example let say that u have the marks of 3 student all of them got 15 marks and another group of three students got 10, 15 and 20 both of them has mean 15 but they have different variances

There is no guaranteed for anything, a flower getting pollinated, fruit formation, healthy and tasty fruit, fruit being sold for a price, fruit being eaten and digested by buyer

Or

My last breath for continuous living, bullet from a weapon hitting an intended target etc. There is a likelihood for an event and it all begins with PROBABILITY (see Papoulis Textbook) of YES or NO. Law of large numbers when you have millions of flower to fruits in a forest or millions of people waiting to breath last.

For large population of events, you may fit different distributions- beta, Rayleigh…. (beginning with random number, random variable, Cumulative Fn, density fn, random processes, 3D distributions and it goes on..)

Let us understand it from practical and layman engineer point of view

.... you take physics exam for 10 times in a day (same paper or same topics). You will get a score with maximum of 100. You can take mean (first order) and the difference of score from the mean will be your SD (second order) .... there are 3rd, 4th, 5th order parameters of a distribution. 

Normal or Gaussian - is widely used and as per Central Limit Theorem:

For either large number of samples or infinite time every distribution will converge to Gaussian.... enabling us to calculate mean, SD or 1sr, 2nd, 3rd, 4th, 5th order moments easily...

Let’s us apply Central Theorem

A car thief has "infinite number of samples of keys" to break in or has infinite time to break in. Whatever may the distribution of efforts by thief to break into a car, one can approximate it with Normal/Gaussian distribution and can calculate mean time to break-in and SD of time for break-in from the mean

Now take 10 thieves..... and generate a pool for same model of car

Further, let 100 thieves break into 10 different car models 

Hope it is helpful to understand the simple Stochastic Processes that are indeed very simple but taught in a dry and complicated ways as pure math without applications oriented mind. 

Hope it is helpful

Dear seeker

Mean and SD are equivalent of alphabet A, B of probability, large sample meeting your DESIGN criterion or what you expect from a given pool of mangoes from a tree!!

It also gives you the mean of good men left in society and how the good man deviated from expected mean from a pool of say. City or country population

.....you can apply this to a nuclear reaction where the mean time to reach a target and begin nuclear reaction in uranium and also then deviation from from expected mean time to begin reaction ..... for more advanced there are higher order "moments"... physics, Advance calculus etc

Have fun. Read Papoulis book .... master it!. There is NO or YES. There is a probability of YES and NO. mean time for boss to hire/fore an employee and SD from.mean time to hire or fire you!!