Averages and Measures of Spread

What is Averages and Measures of Spread?

The summary statistics of Cambridge IGCSE Mathematics 0580 Topic 9. Core requires four, calculated for individual data given as a list or an ungrouped frequency table: the mean is the sum of the values divided by how many there are, or the sum of f times x divided by the sum of f; the median is the middle value of the ordered data, averaged across the two central values when the count is even; the mode is the most frequent value or category; the range is the largest value minus the smallest. The first three describe where the data sits and the fourth describes how spread out it is, so a complete summary quotes one of each. Extended adds three further requirements: the lower and upper quartiles and the interquartile range of individual data, which measure the spread of the middle fifty per cent and are unaffected by extreme values; an estimate of the mean for grouped data, where the class midpoint replaces the unknown individual values and makes the result an estimate; and the modal class, which is the class interval of greatest frequency and is the only mode a grouped table can identify.

This definition is part of the Statistics chapter in Cambridge IGCSE Mathematics.

Concepts related to Averages and Measures of Spread

• ordering data
• frequency table
• quartiles
• interquartile range
• class midpoint
• estimated mean
• modal class