Measures of locationEdexcel International A Level Maths: Subtopic test

1. 1
   A hockey team scored the following numbers of goals in its first 10 matches of a season: 0, 1, 1, 2, 2, 2, 3, 3, 4, 6.

   (a)

   Find the mean number of goals scored per match.

   [1 mark]

   • A$2$
   • B$2.18$
   • C$2.4$
   • D$2.67$

   (b)

   Find the median number of goals scored.

   [1 mark]

   • A$2$
   • B$2.4$
   • C$2.5$
   • D$3$

   (c)

   The team plays two more matches. The mean number of goals per match over all 12 matches is then 2.5. Find the total number of goals scored in the two extra matches.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The times, in minutes, taken by 40 students to complete a puzzle are summarised as follows: 0 to under 10 minutes, 4 students; 10 to under 20 minutes, 10 students; 20 to under 30 minutes, 16 students; 30 to under 50 minutes, 10 students. Assume that times are spread evenly within each class.

   (a)

   Write down the modal class.

   [1 mark]

   • A$0$ to under $10$ minutes
   • B$10$ to under $20$ minutes
   • C$30$ to under $50$ minutes
   • D$20$ to under $30$ minutes

   (b)

   Estimate the mean time taken.

   [1 mark]

   • A$23.75$ minutes
   • B$24.25$ minutes
   • C$21.25$ minutes
   • D$242.5$ minutes

   (c)

   Use linear interpolation to estimate the median time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The masses, $m$ grams, of a sample of 20 packets of rice are coded using $y=\frac{m-500}{10}$. It is given that $\sum y=36$.

   (a)

   Find the mean mass of the 20 packets.

   [3 marks]

   (b)

   A second sample of 30 packets has a coded mean $\bar y=0.6$. Find the mean mass of all 50 packets.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A small company employs nine people. Their annual salaries, in thousands of pounds, are 20, 22, 22, 24, 25, 28, 30, 33 and 102. The highest salary belongs to the owner.

   (a)

   (i) Find the mean, the median and the mode of the salaries.
   (ii) The company advertises that its 'typical salary is £34 000'. Evaluate whether this is a fair description.

   [6 marks]

   (b)

   (i) Each of the nine salaries is increased by 3% and then £500 is added. Find the new mean and the new median.
   (ii) Instead, the owner leaves and is not replaced. Find the mean and median of the remaining eight salaries and use them to compare how the mean and median respond to an extreme value.

   [6 marks]

   Total for question 4: 12 marks

End of questions