"That's mean I have a normally distributed data."

No. It only means that the normal probability distribution seems to be a (hopefully) sufficiently good approximation to the frequency distribution of your data.

If you don't *see* outliers, then you don't have a problem with outliers. If there are (very few!) realy obvious outlying points, then you might want to find out what the reason is for this observation. If you can't find any reason, than these values are to be kept in the analysis.

Refer these articles before taking a decision on data collected on likert scale measurements and outliers; interestingly data falls in a bounded region eg. if rating is 1 to 5 for 5 questions, the scores can be 1 to 25. 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.113.2197&rep=rep1&type=pdf

http://stats.stackexchange.com/questions/203/group-differences-on-a-five-point-likert-item

Please note that an outlier is an observation that appears to deviate markedly from other observations in the sample.Identification of potential outliers is important for the following reasons:

1) An outlier may indicate bad data. For example, the data may have been coded incorrectly or an experiment may not have been run correctly. If it can be determined that an outlying point is in fact erroneous, then the outlying value should be deleted from the analysis (or corrected if possible). 

2) In some cases, it may not be possible to determine if an outlying point is bad data. Outliers may be due to random variation or may indicate something scientifically interesting. In any event, we typically do not want to simply delete the outlying observation. However, if the data contains significant outliers, we may need to consider the use of robust statistical techniques.

Identifying an observation as an outlier depends on the underlying distribution of the data. If the normality assumption for the data being tested is not valid, then a determination that there is an outlier may in fact be due to the non-normality of the data rather than the prescence of an outlier.

For this reason, it is recommended that you generate a normal probability plot of the data before applying an outlier test. The box plot can also be useful graphical tools in checking the normality assumption and in identifying potential outliers. The lower and upper tails of the box plot can be a useful graphical technique for identifying potential outliers. 

Dear @Mahdi Safarpour,

Do you mean we shall identify the outlier and see what we can do to improve the dataset instead of ignoring outlier? I personally thk outlier do exist in my dataset. For example, there will be one or two ppl who may give extreme value (scale 1 or 5) as compare to those in normal range. In Likert, this is unavoidable. It is respondent personal opinion. Therefore I would not delete those outlier as per suggested by some scholars. In fact, I would retain them for analysis. I am not sure, what is the purpose for me to identify outlier since I don't intend to delete them? And since my data is normally distributed, the presence of outlier doesn't seems to affect my dataset. What do u thk?

If you don't intend doing anything if you'd "know" about outliers - then there is really no need to identify possible outliers at all (what for?, I'd ask).

You seem to have data in the domain (1..5). I don't think it makes sense to even try identifying possible outlieres at all,except in "strange" cases. One such case would be that all, really all values are 1, and there is only a single value at 5 (or the other way around). In your case this could indicate that the respondent got the question wrong (he was thinking of "aggrement" but the question was for "disaggreement" or so). If you can go back to that respondent and clarify the issue, then you could possible correct this value (or confirm that the value is in fact ok an should thus be taken serious).

If the distribution is less clear, it is hard to impossible if one (or two) of the respondents got something wrong. If they got the possibility to answer what you translate as 1 or 5, why should't they do so?

I see the bigger problem in the definition of your random variable (i.e. how you come from the answers to the numerical values 1..5). If this has no somehow physical basis (what I assume) then the numerical/quantitative interpretation of your results has no such basis, too. Statistics like the mean may not be (sensibly) interpretable.

Dear Michael Teng Loong Ing,

Normal distribution data can have outliers. Well-known statistical techniques (for example, Grubb's test, student's t-test) are used to detect outliers (anomalies) in a data set under the assumption that the data is generated by a Gaussian distribution.

See, for example:

Grubbs, F. (1969). Procedures for detecting outlying observations in samples. Technometrics 11, 1, 1-21.

http://webspace.ship.edu/pgmarr/Geo441/Readings/Grubbs%201969%20-%20Detecting%20outlying%20observations%20in%20samples.pdf

For smaller databases, the Q-test can be used to eliminate an obvious outlier at 1 end of the distribution:

Dean, R.B., and W.J. Dixon. 1951. Simplified statistics for small numbers of observations. Analytical Chemistry 23: 636-638 (https://pdfs.semanticscholar.org/7b6f/cfbf2a68d11cd4f444e1311e35309be0ae76.pdf).

Hawkins, C.E., and J.H. Niewahner. 1983. Data analysis, graphing and report writing. 1st ed. Mohican Textbook. Loudonville, OH. 92 pp.

It gets trickier if there are “outliers” at both ends of the distribution. I wouldn’t recommend any data removal in that case. You could always do a stat. transformation to improve normality.

Belatedly, Bob Vadas, Jr.