Standard deviation or standard error, which is right to present along with average as error bar?

If for standard error you mean Standar error.. it is a simply multiplier of standard deviation. standardError = standardDevieation / sqr(numberOfSamples)

You can use what you prefer, but meaning is quite different: Standard deviation is calculated on the mean value of a dataset, instead standard error is evaluated on the uncertainty of single values. The standar error implies a gaussian distribution of all dataset values.

However you can use exponential values of every measure to encrease their relatives differences. (^2,^3..) you have only to specify on your legend.

You should also use Variance , that is the squared deviation.

hope that could help you.

Neither is "correct", they are different things that answer different questions.

Take the height of 100 people. The standard deviation is a measure of the spread of the heights in the population, and answers questions like "how many people weigh less than 70kg?". If you measure another 100, or another 1000 people the standard deviation should remain roughly the same.

The standard error, specifically the standard error on the mean is an estimate of how well we know the mean of the population from the samples. It answers the question "What's the mean of the measure in the population likely to be?"

Suppose we only sampled three people from the population - our estimate of the mean of the whole population isn't likely to be very good, so the standard error on the mean will be quite large. If we sample 1,000,000 people our sample distribution will look very similar to our entire population, and so the standard error on the mean is smaller. If we could sample everyone in the population the standard error on the mean becomes zero, because we have the exact number.