Ten values have mean 10. Nine of the values are
5, 7, 8, 8, 9, 11, 12, 14, 15 5,\ 7,\ 8,\ 8,\ 9,\ 11,\ 12,\ 14,\ 15\,5, 7, 8, 8, 9, 11, 12, 14, 15
For this question, a value is defined to be an outlier if it is more than two standard deviations from the mean.
Find the tenth value.
Show that the standard deviation of the ten values is exactly 3.
Find, using set notation, the set of values that would be classed as outliers for this data set.
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.