IB Maths Notes: Probability and Statistics – Quartiles and Median From Frequency Tables By Interpolation

We start with the table below which summarises the daily sales in a newspaper shop over a year for the 360 days the shop was open.

Sales |
Number of Days |

1 -200 |
166 |

201- 400 |
100 |

401 - 700 |
59 |

701 - 1000 |
30 |

1001 -1500 |
3 |

To find the lower quartile we use

whereare the lower and upper bounds of the frequency class in which the lower quartile lies,1-200,is the total number of data points,is the sum of the frequencies of the classes BELOW that class in which the lower quartile is found andis the frequency of the interval in which the lower quartile is found.

To find the median we use

whereare the lower and upper bounds of the frequency class in which the median lies, 201-300,is the total number of data points,is the sum of the frequencies of the classes ABOVE that class in which the median is found (in the table above) andis the frequency of the interval in which the median is found.

To find the upper quartile we use

whereare the lower and upper bounds of the frequency class in which the upper quartile lies, 401-700,is the total number of data points,is the sum of the frequencies of the classes BELOW that class in which the upper quartile is found andis the frequency of the interval in which the upper quartile is found.