# Exam-style Questions: Representing Data

1. The heights of 100 plants were measured. The results are shown in the table below.

 Height (h cm) 4 < h ≤ 5 5 < h ≤ 6 6 < h ≤ 7 7 < h ≤8 8 < h ≤ 9 9 < h ≤ 10 10 < h ≤ 11 11 < h ≤ 12 Frequency 3 7 11 28 24 17 8 2

a) Complete the cumulative frequency table for the 100 plants.

(1 mark)

 Height (h cm) h ≤ 4 h ≤ 5 h ≤ 6 h ≤ 7 h ≤ 8 h ≤ 9 h ≤ 10 h ≤ 11 h ≤ 12 Cumulative Frequency 0 3

b) Draw the cumulative frequency diagram on the grid below.

(3 marks)

c) Use your graph to estimate how many plants are less than 9.4cm high.

(1 mark)

d) Use your cumulative frequency diagram to estimate the inter-quartile range of the heights.

(2 marks)

(Marks available: 7)

Answer outline and marking scheme for question: 1

a)

 Height (h cm) h ≤ 4 h ≤ 5 h ≤ 6 h ≤ 7 h ≤ 8 h ≤ 9 h ≤ 10 h ≤ 11 h ≤ 12 Cumulative Frequency 0 3 10 21 49 73 90 98 100

(1 mark)

b) 9 points plotted correctly, curve or straight lines.

(3 marks)

c) 78 to 82

(1 mark)

d) 1.7 to 2.2

(2 marks)

(Marks available: 7)

2. a) Ian and Alex decide to conduct a survey on the use of computers.

They want to know whether boys or girls use a computer in their coursework for word-processing, spreadsheets or both.

In the space below, design an observation sheet to collect information from a group of boys and girls.

(3 marks)

b) Alex used a spell-check on her computer to find spelling mistakes in some course-work.

The table below shows the distribution of spelling mistakes

 Number of spelling mistakes on the page 0 1 2 3 4 Number of pages 10 6 1 1 2

Calculate the mean number of spelling mistakes per page.

(3 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 2

a) Two way table with boys/girls

Columns for WP, SS, both, neither.

One way table or questionnaire

Gender column or box

Columns or boxes for WP & SS

(3 marks)

b) 0.95 or 19/20

(3 marks)

(Marks available: 6)

3. The graph shows the speed of a car in kilometres per hour (km/h).

a) What is the speed of the car after 10 seconds?

(1 mark)

b) After 30 seconds, the car travels at a steady speed of 60 km/h for 1 minute. Continue the graph by drawing a line AB to show this.

(1 mark)

c) Draw a straight line from B to the point C (110, 0).

(1 mark)

d) What does the graph between B and C tell you about what the car is doing?

(1 mark)

(Marks available: 4)

Answer outline and marking scheme for question: 3

a) 20km/h

b) Horizontal straight line, ending at (90,60).

c) Straight line from (90,60) to (110,0)

d) 'Slowing down' or 'stopping'

(Marks available: 4)