For all your cases you may either show SD or SEM (if available). Which one to show is not related to your cases but to the features you want to present, the features that are important to you (and presumably to the reader).

Here you must decide which aspect is the relevant aspect for your story/research/conclusion. First of all, giving the standard deviation at all makes sense only if the assumption of normal distributed data is reasonable. The value (estimate) of the standard deviation obtained from small samples (

As Jochen made clear. SD is about the variation in a variable, whereas Standard error is about a statistic (calculated on a sample of observations of a variable) and SEM about the specific statistic mean. You want to describe the variation of a (normal distributed) variable - use SD; you want to describe the uncertaintly of the population mean relying on a sample mean (when the central limit theorem is applicable) - use SEM.

Dear Venkatesha Venkatasubbaiah,

Dr. Jochen Wilhelm and Dr. Kenneth Carling has made the concept very clear for the use of SD or SEM. I would like to add here a point that we often use SD for the results obtained in analyatical experiments while for the biological experiments SEM is widely preferred over SD.

Kindly folow these links to get a clear idea about SD and SEM.

http://jcb.rupress.org/content/177/1/7.full

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3148365/

http://www.medicine.mcgill.ca/epidemiology/hanley/IntMedResidents/SD-SE.pdf

Yes, explanation is clear. Thank you so much Jochen, Kenneth, and Bhavesh.

Bhavesh, appreciated for the link to relevant articles.

I clearly support everyone's explanation

Just in case, minimum sample size recommended for SEM is 200. 

yeah the link has a proper description with examples.

From this paper:

"So the range determined by m1 ± 1.96 × se (in lieu of equation M7 ± 1.96 × sdm) provides the range of values that includes the true value of the population with a 95% probability: this is the 95% confidence interval."

That's plain wrong.

It would mean following: take one particular interval, maybe one shown in Fig.1. Look at this interval. What is the probability that it "includes the true value of the population"?

After this it gets even worst: "we can be confident that there is a 95% probability that the mean size of the tumor "... what is this? How can one hope that people will understand the concept of probability and confidence if these terms are used in the wrong context and in such weird ways?!

Later on there is another statement that is more confusing than helpful:

"If one wishes to provide a description of the sample, then the standard deviations of the relevant parameters are of interest." - Either the authors talk about a description or about a model (inference). A "relevant parameter" is a property of a model (not of the data), and it is confusing why they use this. Some lines earlier they said that the "standard deviation" of such parameters are called "standard errors" (what is somewhat correct), but here they seem to confuse the average of the values with the expected value of the random variable. The former is a description, the latter is the result of an inference, involving probabilities and all that. A reason for this confusion might be that both things are numerically identical.

I think this is very likely to be a major source of confusion in this whole context - that the word "mean" is used for both, the mere average of (a sample of) values and the expected value of random variable. And that the concept of the expected value is not explained but substituted by the concept of the exitence of some "true population mean". At a first glance, this concept seems attractive, easy to understand, and to make things simple. But later on it causes many problems (what is the "truth"? what is the "population"?).

"If a researcher is interested in estimating the mean tumor size in the population, then he or she would have to provide the mean and standard deviation of tumor size to describe the sample observed and the standard error or confidence interval to infer to the population." - Again very confusing. The "mean and standard deviation of tumor size" just describe what we can infer about the "population of tumor sizes" from the sample. This tells us in what range we expect a tumor size to be if we would measure the size of some yet unseen tumor. The question is different if we ask for the expected value of the tumor size. This value is usually not very interesting to any researcher. It is rather interesting to find the expected value of a difference or change in tumor size, e.g. between different tumor types, treatment, or environmental factors. Here is the question: what change in tumor size (due to the treatment)  can we expect? Here we have/nee an underlying stochastic model, and the difference we look for is one of the parameters in this model. And we can use some kown data to estimate the value of this parameter and we can give a confidence interval for this parameter. This is where expected values, standard errors, and confidence intervals start making some sense. Unfortunately most mediacl papers would report the "mean ±standard error" for the tumor sizes of the individual groups (like "treated" and "placebo") instead of providing the most interesting statistic: the expected difference between the groups. I think this is a nice example: one should report the tumor sizes in the groups descriptively (median, mean, IQR, standard deviation, range, whatever one feels to be a good/useful description of the data) and report the expected difference between the groups as the point estimate together with its confidence interval. That would be nice, and it would make sense.

Article "Mean ± SEM" or "Mean (SD)"?

I would add this article in as a brief and less technical paper on the topic.

Article Statistics notes: Standard deviations and standard errors