There are several methods that are generally considered to give accurate results. Often as a first step, the data are plotted as a histogram and the fitted normal distribution is plotted over the data. You could also construct a q-q plot that plots the observed quantiles with the quantiles of the fitted normal distribution. In each of these cases, the 'normality' of the data is assessed visually. For a more formal 'test' of normality, there are the Anderson-Darling and Shapiro-Wilk tests. Most statistical software packages are able to compute these tests.
The Shapiro-Wilk test is implemented in R via the following command:
Some statisticians argue that visual inspection is sufficient to make the 'normality' assumption. However, tests such as the Shapiro-Wilk are frequently used.
I don't think that I will plot the graph and visual check. I will use software
for Shapiro-Wilk test. Do you know which stat software which is easy to use. SAS ? Systat ? SPSS?
Currently I have SAS JMP in my desktop. I will explore more to check this software.
Thanks million for your valuabel advice
Analyze -> Distribution
Select your response, add it to the Y, Columns box, OK
Click red triangle next to the response -> Fit Distribution -> Normal
Click red triangle next to Fitted Normal -> Goodness of Fit
This is how the Shapiro-Wilk W test is done, for small data sets.