Averages and spreadIB MYP Maths Extended: Subtopic test

1. 1
   The ages, in years, of seven members of a chess club are 12, 15, 13, 12, 40, 14 and 12.

   (a)

   What is the median age?

   [1 mark]

   • A$12$ years
   • B$16.9$ years
   • C$14$ years
   • D$13$ years

   (b)

   What is the mean age, to $1$ decimal place?

   [1 mark]

   • A$16.9$ years
   • B$13.0$ years
   • C$12.0$ years
   • D$28.0$ years

   (c)

   Explain which average best represents the typical age of the members.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A football team's goals scored per match over 20 matches: 0 goals in 4 matches, 1 goal in 6 matches, 2 goals in 5 matches, 3 goals in 3 matches and 4 goals in 2 matches.

   (a)

   What is the modal number of goals per match?

   [1 mark]

   • A$6$
   • B$1$
   • C$2$
   • D$4$

   (b)

   What is the median number of goals per match?

   [1 mark]

   • A$1$
   • B$2$
   • C$1.5$
   • D$1.65$

   (c)

   Find the mean number of goals per match.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The heights of 40 plants are recorded in a grouped frequency table. In centimetres, 4 plants are in the class 0 ≤ h < 10, 10 plants in 10 ≤ h < 20, 15 plants in 20 ≤ h < 30, 8 plants in 30 ≤ h < 40 and 3 plants in 40 ≤ h < 50.

   (a)

   Write down the modal class. Show that the median height lies in the class $20\leq h<30$.

   [3 marks]

   (b)

   Calculate an estimate of the mean height of the plants.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two delivery companies, Swift and Rapid, each record the time in minutes taken for five deliveries to a school. Swift: 18, 22, 20, 19 and 21. Rapid: 12, 14, 13, 15 and 36.

   (a)

   Calculate the mean and the range of the times for each company, and the median time for Rapid. Compare the two companies.

   [6 marks]

   (b)

   A school must send exam papers by a company, and the papers must arrive within $25$ minutes. Recommend a company, justifying your choice using the data. State one limitation of the data.

   [6 marks]

   Total for question 4: 12 marks

End of questions