The large data setAQA A-Level Maths: Flashcards

Exam questions on The large data set

1. A large data set records, for each new car sold in a year, the fuel type (petrol, diesel or hybrid), the number of doors, the engine size in litres and the CO₂ emissions in g/km. Some records have the CO₂ emissions blank.
   Name a suitable diagram for displaying the fuel type of the cars, and explain why a histogram would not be suitable.2 marks
2. A student takes a random sample of 11 petrol cars from a large data set and records the CO₂ emissions in g/km: 110, 114, 118, 121, 124, 126, 129, 131, 134, 138, 205. Quartiles are the medians of the lower and upper halves of the ordered data, leaving out the median. A value is an outlier if it is more than $1.5\times$ IQR above the upper quartile or below the lower quartile.
   Show that 205 g/km is an outlier.2 marks
3. A student uses a large data set of daily weather records from one station. Missing readings are shown by the value $-99$. A random sample of 40 valid days gives $\sum x=612$ and $\sum x^2=9774$ for the daily mean temperature $x$ in °C. A value is an outlier if it lies more than 2 standard deviations from the mean.
   Explain what would go wrong if the readings of $-99$ were included when calculating the mean and standard deviation, and what the student should do.3 marks