Representation and summary of data

Sample questions

Original practice questions written in the style of the exam.

1. Question 15 marks

   The times, $x$ minutes, taken by 20 students to complete a puzzle are summarised by $\sum x = 364, \qquad \sum x^2 = 6892.$

   (a) Find the mean and the standard deviation of $x$.

   (b) The data are coded using $y = \dfrac{x - 10}{2}$. Find the mean and the standard deviation of $y$.

   Mark scheme

   • (a) Mean $\bar{x} = \dfrac{364}{20} = 18.2$ (1)
   • M1 Variance $={\displaystyle }$ (1)
2. Question 25 marks

   The numbers of text messages sent by 15 people on one day are:

   3	5	7	8	8	9	10	11	12	12	13	14	15	17	31

   (a) Find the median and the lower and upper quartiles.

   (b) An outlier is a value more than $1.5 \times$ the interquartile range above $Q_3$ or below $Q_1$. Determine whether there are any outliers.