The lower quartile, median and upper quartile are usually denoted by Q_1, Q_2 and Q_3. To find them you must first arrange the data in order of size.

If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.

To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.

If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.

To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.

## Software/Applets used on this page

## Glossary

### median

the middle value of a set of data that has been arranged in order of magnitude; half the data values are above it and half are below.

### quartile

In an ordered set of data 25% are below the first (Q

_{1}), 50% are below the second (Q_{2}), 75% are below the third (Q_{3}).### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location |

AQA AS Maths 2017 | Statistics | Data Presentation and Interpretation | Measures of Central Tendency |

AQA AS/A2 Maths 2017 | Statistics | Data Presentation and Interpretation | Measures of Central Tendency |

CBSE XI (India) | Statistics and Probability | Statistics | Range, mean deviation, variance and standard deviation of grouped data |

CCEA A-Level (NI) | S1 | Summarising data | Measures of location |

CIE A-Level (UK) | S1 | Summarising data | Measures of location |

L Statistics - Data | L3 Central Tendency and Variation | Measures of Central Tendency | |

Edexcel A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location |

Edexcel AS Maths 2017 | Statistics | Measures of Data | Measures of Central Tendency |

Edexcel AS/A2 Maths 2017 | Statistics | Measures of Data | Measures of Central Tendency |

I.B. Standard Level | 5 | Summarising data | Measures of location |

Methods (UK) | M14 | Summarising data | Measures of location |

I.B. (MSSL) | 6 | Summarising data | Measures of location |

OCR A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location |

OCR AS Maths 2017 | Statistics | Central Tendency and Variation | Measures of Central Tendency |

OCR MEI AS Maths 2017 | Statistics | Central Tendency and Variation | Measures of Central Tendency |

OCR-MEI A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location |

Pre-U A-Level (UK) | Prob | Summarising data | Measures of location |

Scottish (Highers + Advanced) | HS | Summarising data | Measures of location |

Scottish Highers | S | Summarising data | Measures of location |

Universal (all site questions) | S | Summarising data | Measures of location |

WJEC A-Level (Wales) | S1 | Summarising data | Measures of location |