Edexcel IGCSE Math A 6.1 graphical representation of data

Use this data-graphs page to draw, complete and interpret statistical displays, including grouped data, histograms and cumulative frequency diagrams.

Exam points

Complete or draw bar charts, pictograms, two-way tables and other data displays.
Interpret histograms using class width, frequency density and bar area.
Use cumulative frequency graphs to estimate medians, quartiles or counts.

Covered syllabus points

6.1.A Different methods of presenting data Pictograms, bar 6.1.B Tabulating data for statistical diagrams 6.1.C Statistical diagrams 6.1.HA Histograms 6.1.HB Cumulative frequency diagrams from tabulated data 6.1.HC Cumulative frequency diagrams

[Maximum number: 5]

All the students in year 10 and all the students in year 11 named their favourite science subject from Biology, Chemistry and Physics.

The pie chart shows information about the results for the year 10 students.
The table shows information about the results for the year 11 students.

Pie chart for year 10

Table for year 11

There are 300 students in year 10
There are 320 students in year 11
More students in year 10 than in year 11 said Biology was their favourite science subject.

How many more?

ABCDE is a regular pentagon.
DEFGHI is a regular hexagon.
AF is a straight line.
Work out the size of angle EAF

3x+6+5x+8+7x-9=320

15x+5=320\quad\Rightarrow\quad x=21

Year 11 Biology:

3x+6=3(21)+6=69

Year 10 Biology:

\frac{126}{360}\times300=105

Difference:

105-69=36

Final answer:

M1 for a correct equation or method to find x for year 11.
A1 for x=21 or 3x=63.
M1ft for finding the number for year 11 Biology.
M1 independent for finding the number for year 10 Biology.
A1 cao, dependent on the previous A1.

[Maximum number: 3]

The histogram gives information about the times, in minutes, that some customers spent in a supermarket.

Figure for Question 6.1 Graphical representation of data question 2 — Edexcel IGCSE Math A Higher

Work out an estimate for the proportion of these customers who spent between 17 minutes and 35 minutes in the supermarket.

One of the customers is selected at random.
Given that this customer had spent more than 30 minutes in the supermarket,

Total area/frequency:
$(0.7\times10)+(3.4\times5)+(1\times9)+(2.5\times6)+(4.8\times15) = 120$

Area from 17 minutes to 35 minutes:
$(1\times7)+(2.5\times6)+(5\times4.8) = 46$

Estimated proportion:
$\frac{46}{120}$

Final answer:
$\frac{46}{120}$

Accept $0.3833\ldots$ or $38\%$ or better.
M1 for a correct method to find total area/frequency.
M1 for a correct method to find the area between 17 and 35 minutes.
A1.

[Maximum number: 5]

The frequency table gives information about the times, in minutes, that 60 people took to complete a puzzle.

Table for Question 6.1 Graphical representation of data question 3 — Edexcel IGCSE Math A Higher

(a)

Complete the cumulative frequency table.

Table for Question (a) — Edexcel IGCSE Math A Higher

[ 1 ]

(b)

On the grid opposite, draw a cumulative frequency graph for your table.

Figure for Question (b) — Edexcel IGCSE Math A Higher

[ 2 ]

(c)

Use your graph to find an estimate for the number of these people who took more than 45 minutes to complete the puzzle.

[ 2 ]

Reading from the graph at 45 minutes:
(60-)54

Final answer:
$5,\ 6,\ \text{or }7$

Marking guidance:
- M1 ft for a line from x=45 to the graph and across to the y-axis, or for a correct mark/reading from the vertical scale, e.g. 54 or 53.5
- Correct answer scores full marks unless from obvious incorrect working
- A1 accept an integer value 5, 6, or 7
- Or ft from their ascending graph for an integer value

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Covered syllabus points

6.1 Graphical representation of data question 1

6.1 Graphical representation of data question 2

6.1 Graphical representation of data question 3

Question (a)

Question (b)

Question (c)