# Frequencies, Percentiles and Quartiles

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Frequency

1. Frequency Distribution

Frequency is a number of times a particular value occurs. By counting frequencies, frequency distribution can be constructed. A frequency distribution consists of class interval and corresponding frequencies. In excel best way to construct frequency distribution is using Pivot table.

2. 2k Rule

According to 2k rule, 2k >= n; where k is the number of classes and n is the number of data points.

k | 2k |

0 | 1 |

1 | 2 |

2 | 4 |

3 | 8 |

4 | 16 |

5 | 32 |

6 | 64 |

7 | 128 |

8 | 256 |

The width of a class interval is determined by:

3. Relative Frequency

Relative frequency is the percentage of observations on a particular class interval.

3. Cumulative Relative Frequency

Cumulative frequency is defined as the sum of all relative frequencies preceding the relative frequency of particular class interval.

Percentile

The 99 values which divide data (arranged in ascending order) into 100 equal parts are known as percentiles.

For un-grouped data percentiles can be calculated using following formula:

For grouped data percentiles can be calculated using following formula:

Quartiles

The 3 values which divide data (arranged in ascending order) into four equal parts are known as quartiles. They are named as first (lower quartile), second (median) and third (upper quartile) quartiles which are denoted by Q1, Q2 and Q3 respectively.

For un-grouped data quartiles can be calculated using following formula:

For grouped data quartiles can be calculated using following formula:

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