GCSE Mathematics
GCSE Maths: Data & Statistics Revision
Statistics and data handling revision for GCSE and iGCSE Maths
Statistics questions are usually generous with marks and easy to lose them on: an estimated mean calculated from the wrong column, a median read from an unordered list, a frequency density confused with a frequency. This free revision engine covers the statistics and data handling content of GCSE and International GCSE Maths, from types of data through to histograms and cumulative frequency. It generates a new question every time and marks your answer as you go.
What the statistics revision engine covers
Foundation and Higher Types of data — discrete, continuous and qualitative Averages from raw data — mean, median, mode and range Averages from frequency tables — including the mean from a table Averages from grouped frequency — estimating the mean and finding the modal class Charts and diagrams — bar charts, pie charts and two-way tables Comparing distributions — using an average and a measure of spread together Higher tier as well Cumulative frequency — the median, quartiles and the interquartile range Histograms — frequency density, and finding a frequency from a bar
Statistics results you need to know
The mean. Add the values and divide by how many there are. From a frequency table, multiply each value by its frequency, add those products, then divide by the total frequency. The median. Put the values in order first, then take the middle one. With an even number of values, take the mean of the middle two. The mode. The most common value. For grouped data you can only give the modal class, not a single value. The range. Largest minus smallest. It is a measure of spread, not an average. Estimated mean for grouped data. Use the midpoint of each class as the value. It is an estimate because the original values are no longer known. Cumulative frequency. The median is at n/2, the lower quartile at n/4 and the upper quartile at 3n/4. The interquartile range is the upper quartile minus the lower quartile. Histograms. Frequency density = frequency ÷ class width. So frequency = frequency density × class width. The area of a bar gives the frequency, not its height. Comparing distributions. Always compare both an average and a measure of spread, and say what it means in context. The complement. P(not A) = 1 − P(A). This is often the quickest route, particularly for "at least one". Mutually exclusive events. P(A or B) = P(A) + P(B), when A and B cannot both happen. Independent events. P(A and B) = P(A) × P(B), when one does not affect the other. The general addition rule. P(A or B) = P(A) + P(B) − P(A and B). Expected frequency. Expected number = probability × number of trials. At least one. P(at least one) = 1 − P(none). Far quicker than adding the cases. Without replacement. After one item is removed, both the numerator and the denominator change. A bag of 5 red from 12 becomes 4 red from 11. Conditional probability. P(B given A) is worked out from the situation after A has happened.
How to use it
Choose Foundation or Higher, then pick a topic. The engine generates a question, you type your answer, and it marks it straight away. Some questions give you a table to read; others are multi-step, such as finding a missing value that produces a stated mean. Signing in saves your accuracy per topic to your GCSE skill tree.
More GCSE Maths revision
Statistics shares its arithmetic with number and its diagrams with probability, and the estimated mean is really a weighted average — so ratio work helps here too. Every topic and your progress across all of them is on the revision hub. All of our revision engines are free to use.