1. 1
   The numbers of books read over the summer holiday by eight students, in the order they were recorded, are 3, 7, 2, 9, 6, 7, 4, 10.

   (a)

   Find the mean number of books read.

   [1 mark]

   • A$6.86$
   • B$6$
   • C$7$
   • D$6.5$

   (b)

   Find the median number of books read.

   [1 mark]

   • A$7.5$
   • B$6$
   • C$6.5$
   • D$7$

   (c)

   A ninth student is added to the group. The mean number of books read by the nine students is 7. Find the number of books read by the ninth student.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The noon temperature at a weather station was recorded on 30 days. The temperatures have mean $18.4\,^{\circ}\mathrm{C}$ and standard deviation $3.5\,^{\circ}\mathrm{C}$. Each temperature $C$ in degrees Celsius is converted to degrees Fahrenheit using $F = 1.8C + 32$.

   (a)

   Find the mean of the 30 temperatures in degrees Fahrenheit.

   [1 mark]

   • A$33.12$
   • B$50.4$
   • C$90.72$
   • D$65.12$

   (b)

   Find the standard deviation of the 30 temperatures in degrees Fahrenheit.

   [1 mark]

   • A$6.3$
   • B$38.3$
   • C$3.5$
   • D$11.34$

   (c)

   Find the variance of the 30 temperatures in degrees Fahrenheit.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The finishing times, $t$ minutes, of 80 runners in a 5 km park run are grouped as follows: 8 runners with $20 \le t < 25$; 22 runners with $25 \le t < 30$; 26 runners with $30 \le t < 35$; 16 runners with $35 \le t < 40$; 8 runners with $40 \le t < 45$. A calculator may be used in this question.

   (a)

   Write down the modal class, and find an estimate of the mean time.

   [3 marks]

   (b)

   Use your calculator to find an estimate of the standard deviation of the times, and write down an estimate of the variance. Explain why your answers to (a) and (b) are estimates and not exact values.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A café records the number of cups of coffee, $x$, it sells on each of 11 consecutive days: 42, 38, 51, 45, 47, 39, 44, 120, 46, 41, 48. The value 120 was recorded on the day of a street festival. The café's daily profit, in dollars, is modelled by $P = 2.5x - 60$. A calculator may be used in this question.

   (a)

   (i) Find the mean and the standard deviation of the number of cups sold.
   (ii) Find the median and the interquartile range of the number of cups sold.
   (iii) The café owner wants to describe the number of cups sold on a typical day and how much this varies. State, with a reason, which of the two pairs of measures from (i) and (ii) she should use.

   [6 marks]

   (b)

   (i) Find the mean and the standard deviation of the café's daily profit over the 11 days.
   (ii) The festival day is removed from the data. Show that the mean daily profit of the remaining 10 days is more than 25% lower than the mean daily profit of all 11 days.

   [6 marks]

   Total for question 4: 12 marks

End of questions