The CO2 _2\,2 emissions, x x\,x g/km, of the cars in two extracts are summarised below.
Extract A contains 40 cars, with ∑x=8400\sum x = 8400∑x=8400 and ∑x2=1 780 000\sum x^2 = 1\,780\,000∑x2=1780000.
Extract B contains 60 cars, with ∑x=10 800\sum x = 10\,800∑x=10800 and ∑x2=1 968 000\sum x^2 = 1\,968\,000∑x2=1968000.
Find the mean and the standard deviation of the CO2 _2\,2 emissions in extract A.
Find the mean and the standard deviation of the CO2 _2\,2 emissions in extract B.
Find the mean and the standard deviation of the CO2 _2\,2 emissions of all 100 cars.
Explain why the standard deviation found in part (c) is greater than the standard deviation of either extract on its own.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.