Skewness and outliersEdexcel International A Level Maths: Mind map

Exam questions on Skewness and outliers

1. The ages of customers at a shop have lower quartile 24 years, median 28 years and upper quartile 40 years. A value is classed as an outlier if it is more than $1.5\times IQR$ above the upper quartile or more than $1.5\times IQR$ below the lower quartile.
   The two oldest customers are aged 62 and 71. Determine which of these ages are outliers.2 marks
2. The numbers of text messages sent in one day by a sample of students have mode 8, median 10 and mean 12.
   Explain why the median is a more suitable measure of location than the mean for these data.2 marks
3. The daily rainfall, in mm, at a weather station over 15 days has smallest value 0, lower quartile 2, median 5, upper quartile 11 and largest value 40. The next largest value is 19. A value is classed as an outlier if it is more than $1.5\times IQR$ above the upper quartile or more than $1.5\times IQR$ below the lower quartile.
   Show that 40 mm is an outlier, and determine whether 19 mm is an outlier.3 marks