Is bell shaped curve always be symmetrical?
Hans is correct, the traditional bell-shaped curve is the Gaussian or Normal distribution, which is characterized as having zero skewness. However, there are versions of the Normal distribution probability density function (PDF) which allow for the Normal distribution to have a nonzero skewness. Many distributions are skewed (not symmetrical) and are widely used, such as the GEV family of distributions, the Pearson family of distributions, the log-Normal distribution, etc. etc. So to answer your question, no it’s not technically bell-shaped unless it strictly follows the Normal (Gaussian) distribution. Sometimes it’s easier to quantify the properties of the graph using numeric values to describe the shape, such as mean, variance, skewness, kurtosis, mode, median, etc. etc.
