Frequency polygon and frequency curve:

A frequency polygon is a many sided closed figure. It is constructed by plotting the class frequencies against their corresponding class marks (mid-points) and then joining the resulting points by means of straight lines.

Frequency polygon typically uses straight lines and points. But frequency curve is a smoothed curve.

The frequency curve should be smooth and it should be as close as possible to the corner points of the polygon. It is subjective approach and different people will draw the different curve

Positive and Negative Skewed Curve:

A frequency distribution or curve is said to be skewed when it departs from symmetry. If the right tail is longer the distribution is positively skewed and if the left tail of the distribution is longer, the distribution is said to be negatively skewed.

First and third quartile:

One fourth of the data lies below the Q1 (first quartile) and three quarters of the data lies below Q3 (third quartile).