4.3 Measures of central tendency and dispersionIB Maths: Applications and Interpretation HL: Subtopic test

1. 1
   A hockey team scores the following numbers of goals in 10 matches: 2, 0, 3, 1, 4, 1, 2, 5, 1, 1. Treat these 10 matches as the whole population.

   (a)

   Write down the mode of the number of goals.

   [1 mark]

   • A2
   • B1.5
   • C1
   • D5

   (b)

   Find the median number of goals.

   [1 mark]

   • A1
   • B2
   • C2.5
   • D1.5

   (c)

   Use your GDC to find the standard deviation and the variance of the number of goals.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The waiting times, $t$ minutes, of 50 patients at a clinic are recorded. $0\le t<10$: 6 patients; $10\le t<20$: 14 patients; $20\le t<30$: 18 patients; $30\le t<40$: 9 patients; $40\le t<50$: 3 patients.

   (a)

   Which is the modal class?

   [1 mark]

   • A$10\le t<20$
   • B$20\le t<30$
   • C$30\le t<40$
   • D$0\le t<10$

   (b)

   Which is the mid-interval value of the class $30\le t<40$?

   [1 mark]

   • A35
   • B30
   • C40
   • D9

   (c)

   Estimate the mean waiting time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The daily maximum temperature in a town over a month has mean $30\,^\circ$C and standard deviation $4\,^\circ$C. A visitor converts each temperature to degrees Fahrenheit using $F=1.8C+32$.

   (a)

   Find the mean temperature in degrees Fahrenheit, and write down the variance of the temperatures in degrees Celsius.

   [3 marks]

   (b)

   Find the standard deviation and the variance of the temperatures in degrees Fahrenheit.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The 100 m times, in seconds, of 12 athletes are: 10.8, 11.0, 11.0, 11.2, 11.2, 11.4, 11.4, 11.6, 11.6, 11.8, 12.0, 12.0. Treat the 12 athletes as the whole population. Use your GDC.

   (a)

   Use your GDC to find the mean, the median, the lower quartile, the upper quartile, the interquartile range and the standard deviation of the times.

   [6 marks]

   (b)

   (i) After a training programme, every time is reduced by $0.3$ s. Write down the new mean, standard deviation and IQR.
   (ii) The reduced times are then each multiplied by $4$. Find the mean, standard deviation and IQR of these new values.

   [6 marks]

   Total for question 4: 12 marks

End of questions