Frequency Curve

A smooth curve obtained by smoothing the frequency polygon.

When the number of intervals gets large, the frequency polygon will consist of a large number of line segments, and the frequency polygon approaches a smooth curve. Useful to have some idea about the shape of the frequency distribution.

Properties

Skewness

Measure of asymmetry.

Kurtosis

Measure of peakedness, relative to a normal distribution.

High kurtosis indicates a more peaked distribution. They have a distinct peak near the mean, decline rapidly, and have heavy tails.

Low kurtosis indicates a more flat distribution. They have a flat top near the mean, decline slowly, and have light tails.

Measures of central tendency

Describes the distribution in a single value. Any measure indicating a centre of a distribution is called the measure of central tendency.

A measure of location is a quantity that locates a particular position in the frequency distribution.

Mean, median and mode are the commonly used measures of central location.

Types

Symmetric

A distribution is symmetric iff it is the same on both sides of the mean.

Skewed

A distribution is skewed iff it is not symmetric. One tail of the curve is longer than the other.

Positively skewed

When the long tail is on the right side of the curve.

Negatively skewed

When the long tail is on the left side of the curve.