# Distributions

Jump to navigation
Jump to search

# Discrete Variable

## Frequency tables

- containing the number of occurrences in each class of data
- often used to create histograms and frequency polygons

Colour | Frequency | |
---|---|---|

Brown | 17 | |

Yellow | 18 | |

Red | 7 | |

Green | 7 | |

Blue | 2 | |

Orange | 4 |

## Frequency Distribution

- the distribution of empirical data
- consists of a count of the number of occurrences of each value
- For a discrete random variable, a probability distribution contains the probability of each possible outcome
- The sum of all probabilities is always 1.0

Frequency Distribution | Probability Distribution |
---|---|

# Continuous Variable Distribution

Problems?

Response time (in millisecond) 568 577 581 640 641 645 657 673 696 703 720 728 729 777 808 824 825 865 875 1007

## Grouped Frequency Distribution

- a frequency distribution in which frequencies are displayed for ranges of data rather than for individual values.
**Histogram**is a graphical representation of a distribution .- It partitions the variable on the x-axis into various contiguous class intervals of (usually) equal widths.

- Example

Range | Frequency | |
---|---|---|

500-600 | 3 | |

600-700 | 6 | |

700-800 | 5 | |

800-900 | 5 | |

900-1000 | 0 | |

1000-1100 | 1 |

# A probability density function

A probability density function is a formula that can be used to compute probabilities of a range of outcomes for a continuous random variable.

## Normal Distribution

- one of the most common continuous distributions
- sometimes referred to as a "bell-shaped distribution.

## Skewness

A distribution is skewed if one tail extends out further than the other.

- A distribution has positive skew (is skewed to the right) if the tail to the right is longer
- A distribution has a negative skew (is skewed to the left) if the tail to the left is longer

## Kurtosis

- Leptokurtic is a distribution with long tails relative to a normal distribution
- Platykurtic is a distribution with short tails relative to a normal distribution

# Quiz