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

I have monthly sea surface temperature data set for 1 year.

I need to present seasonal average as bar chart and error bar to show deviation in each season.

for example,
season 1 = nov+dec+jan+feb/4
season 2 = mar+apr+may+jun/4
season 3 = jul+aug+sep+oct/4

Now I have seasonal average.I should show the error bar.
To show the error bar, can I use standard error?
or should I use standard deviation?

Standard error looks good when add to the bar chart (error bar is smaller than the mean).

But the error bar of standard deviation is longer than the mean, when deviation is higher.

Which one is correct method?

## 2 Answers

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.

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.

• How to explain the standard error (SE)? Is it error? If yes, is there any acceptable range? – Karnan May 27 '19 at 15:12
• The standard deviation is a number that show how much "numbers" changes from the mean: if standard deviation is 0 => every "number" is equal to the mean of dataset. The Standard error (also is a number) is a recalibration of the standard deviation by the number of data (useful because it changes proportionally by the nuber of data). – Marco May 27 '19 at 19:08
• If you want to use a standard deviation you have to think that it is the error of the mean value of a dataset: is not an index about single value. If you want to compare a single data to standard deviation (or standard error) you can do it thinking that: the distance from data to mean should be equal to standard deviation if the data was quite near to the mean (68% in a gaussian distribution, more complicated if otherwise) If |x-mean| > stdDev => more distant from mean, |if x-mean| < stdDev => very near to mean – Marco May 27 '19 at 19:16
• I can't add comment to @spacedman post but: if you have the height of 3 people from 100 but they are exactly height in the mean, the standard deviation is 0.. – Marco May 27 '19 at 19:52