OCR GCSE Maths: Statistics

A courier records the mass, $m$m kg, of each of $40$40 parcels collected one morning. The results are summarised in the table.

Mass ($m$m kg)	Frequency
$0 < m \le 2$0<m≤2	$8$8
$2 < m \le 4$2<m≤4	$15$15
$4 < m \le 6$4<m≤6	$12$12
$6 < m \le 8$6<m≤8	$5$5

(a) Write down the modal class. (1 mark)

(b) Work out an estimate for the mean mass of a parcel. (3 marks)

(c) Write down the class interval that contains the median mass. (1 mark)

A secondary school has $1200$1200 students. The table shows how many are in each year group.

Year group	Number of students
Year 7	$320$320
Year 8	$280$280
Year 9	$240$240
Year 10	$200$200
Year 11	$160$160

The headteacher takes a sample of $60$60 students, stratified by year group.

(a) Work out the number of Year 7 students that should be in the sample. (2 marks)

(b) Work out the number of Year 11 students that should be in the sample. (2 marks)

An ecologist measures the lengths, in centimetres, of the fish caught at two rivers. The box plots are summarised by the values below.

	Minimum	Lower quartile	Median	Upper quartile	Maximum
River A	$8$8	$15$15	$22$22	$31$31	$46$46
River B	$12$12	$20$20	$25$25	$29$29	$40$40

(a) Work out the interquartile range of the fish lengths at River A. (2 marks)

(b) Compare the fish lengths at the two rivers. Give one comparison, using a statistic from the table. (2 marks)

A cafe owner records the midday outdoor temperature and the number of bowls of hot soup sold on $12$12 days. On the scatter graph, the days with a lower temperature tended to have more bowls of soup sold. The temperatures recorded ranged from $4\,^{\circ}\text{C}$4∘C to $19\,^{\circ}\text{C}$19∘C.

(a) Describe the type of correlation shown by the scatter graph. (1 mark)

(b) The owner draws a line of best fit. Describe how she could use it to estimate the number of bowls of soup sold on a day when the temperature was $11\,^{\circ}\text{C}$11∘C. (1 mark)

(c) The owner uses the line of best fit to estimate the soup sales on a day when the temperature is $-6\,^{\circ}\text{C}$−6∘C. Give a reason why this estimate may not be reliable. (1 mark)

Here are the numbers of emails an office worker received on each of $8$8 days: $34, \quad 28, \quad 41, \quad 19, \quad 34, \quad 52, \quad 27, \quad 45.$34,28,41,19,34,52,27,45.

(a) Find the median number of emails. (1 mark)

(b) Work out the range. (1 mark)

Here are the numbers of goals scored by a hockey player in $8$8 matches: $5, \quad 7, \quad 5, \quad 9, \quad 11, \quad 5, \quad 8, \quad 7.$5,7,5,9,11,5,8,7.

Write down the mode. (1 mark)