# GCSE Maths Unit 1 - Frequency Distribution Tables

##### March 3, 2016

**GCSE Maths: Frequency Distribution Tables and Cumulative Frequency**

The modal class is the class interval with the highest frequency. To get the mean of a distribution, we multiply each value by its frequency; add these together and divide by the total of the frequencies.

**Example**

Find the mode and mean of the distribution summarised in the table below.

Value | 5 | 15 | 25 | 35 | 45 | 55 | 65 |

Frequency | 2 | 4 | 5 | 6 | 4 | 2 | 1 |

Mode = 35 (it has the highest frequency 6)

Mean =

A cumulative frequency distribution table is similar to a normal frequency table except that we continuously add our frequencies to give a frequency for that class or lower. Once the cumulative frequencies have been plotted, both the median and the quartiles (half-way between the median and the ends, i.e. 1/4 or 3/4 - way through the data) can be easily read from the graph.

**Example**

i) Convert the frequency distribution table below into a cumulative frequency distribution table and then plot the data as a cumulative frequency graph.

Length | 24 | 28 | 32 | 36 | 40 |

Frequency | 3 | 7 | 12 | 6 | 4 |

ii) Use this graph to determine the median and both the lower and the upper quartiles of this data.

Length | 24 | 28 | 32 | 36 | 40 |

Frequency | 3 | 7 | 12 | 6 | 4 |

Cumulative Frequency | 3 | 10 (7+3) | 22 (10+12) | 28 (22+6) | 32 (28+4) |

**Solutions**

Total cumulative frequency = 32

Lower Quartile @ frequency of 1/4 of the total

1/4 x 32 = 8, which corresponds to a length of 28

Median @ frequency of 1/2 of the total

1/2 x 32 = 16, which corresponds to a length of 30

Upper Quartile @ frequency of 3/4 of the total

3/4 x 32 = 24, which corresponds to a length of 33

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