The number of faults found on each of 70 cars is summarised in the table below, where a a\,a and b b\,b are positive integers.
| Number of faults | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Frequency | 12 | aaa | 20 | bbb | 6 |
The mean number of faults per car is exactly 2.
Show that a+b=32a + b = 32a+b=32 and a+3b=76a + 3b = 76a+3b=76.
Find the value of a a\,a and the value of bbb.
Write down the mode of the number of faults.
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.