Reading Data and Drawing Fair Conclusions

Read the greatest, least, totals and differences from tables and charts, draw a dual bar chart, and know what the data can and cannot prove.

In the exam for Edexcel IGCSE Maths 4MA1, Cambridge IGCSE Maths 0580 · 14 real past-paper questions below

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What the Question Wants

Most data questions give you a table or a chart and ask you to read it. The key word tells you what to look for.

Word	Look for
greatest, most, highest	the biggest value
least, fewest, lowest	the smallest value
total	add the values
difference, how many more	take the smaller from the bigger

Key idea

"Which city" or "which day" wants a name, not a number. Write the name.

Greatest or Least

The 1-mark question: "Which of these cities has the lowest temperature?" These are the coldest night temperatures, in degrees Celsius.

City	Temperature
Oslo	$- 7$
Moscow	$- 12$
Ottawa	$- 9$
Cairo	$9$
Tokyo	$2$

Worked example

1
$- 12 < - 9 < - 7 < 2 < 9$ — Put the five temperatures in order, smallest first. Below zero, the bigger the number after the minus, the colder it is.
2
$lowest = - 12$ — The lowest is the first in the order: the most negative number.
3
$Moscow$ — The question asks which city, so write the name from the same row, not the number.

Common mistake

Choosing $- 7$ because 7 is smaller than 12. Below zero, the bigger the number after the minus sign, the colder it is.

Key idea

Big numbers: count the digits first. $98400$ is less than $102000$ because it has fewer digits.

Totals and Differences

The 1-mark question: "Work out the total" or "Work out the difference". These are visitors to four museums in one year.

Museum	Visitors
A	$184250$
B	$97600$
C	$126480$
D	$73900$

Worked example

1
$184250 + 73900$ — “Total of A and D” means add. Find A and D in the table and add their visitor numbers.
2
$= 258150$ — Line up the digits by place value and add. So A and D had 258 150 visitors together.
3
$126480 - 97600$ — “Difference of C and B” means take away. Put the bigger number, C, first and take away B.
4
$= 28880$ — So C had 28 880 more visitors than B.
5
$97600 + 28880 = 126480$ — Check by adding back: the smaller number plus the difference gives the bigger number. It does, so the answer is right.

Common mistake

Adding when the question says "difference". Difference and "how many more" both mean take away.

Differences Below Zero

Temperature questions often ask for a difference when one value is below zero. Here is how to handle the minus sign.

Work out the difference between 9 °C and −12 °C.

Worked example

1
$9 - (- 12)$ — Difference means bigger take away smaller. 9 is bigger than −12, so it goes first. Put −12 in brackets so its minus is not lost.
2
$= 9 + 12$ — Taking away a negative is the same as adding: $- (- 12) = + 12$ .
3
$= 21$ — 9 + 12 = 21. The difference is 21 degrees.
4
$12 + 9 = 21$ — Check on a number line: from −12 up to 0 is 12 degrees, then from 0 up to 9 is 9 more. Together that is 21.

Common mistake

Writing 9 − 12 = −3. That ignores the minus on −12. One value is above 0 and one is below, so add the two distances from 0.

Key idea

A difference is a distance between two values, so give it as a positive number: 21, not −21.

Drawing a Dual Bar Chart

The 4-mark question: "Show this information by drawing a suitable diagram." Two places, the same months: draw a dual bar chart.

Month	Amman, Dubai
January	8, 19
April	16, 27
July	25, 35
October	19, 30

These are average temperatures, in degrees Celsius.

Worked example

1
$biggest value = 35$ — Find the biggest number in the table: Dubai in July. The scale must reach it, or that bar will not fit.
2
$0, 5, 10, \dots, 40$ — Count up in equal steps of 5, starting at 0, until you pass 35. Equal steps keep every bar's height fair.

Steps

1
Label both axes: months along the bottom, temperature up the side.
2
Draw two bars for each month, side by side, the same width.
3
Add a key to show which bar is which city.

Common mistake

No key, or a scale with uneven steps like 0, 5, 10, 20. Each one costs a mark.

Bar chart

Shows the actual number for each group, so you can read values and see which is bigger.

Pie chart

Shows each group as a share of the whole, so you can see what fraction each one is.

Key idea

“Give an advantage of a bar chart over a pie chart”: you can read the actual numbers from a bar chart. A pie chart shows only the share of the whole.

Which Method? Read the Question

Find the key word, then find the right row or bar.

You see	You do
Greatest or least	biggest or smallest value, give the name
Lowest temperature	the most negative number
Total	add
Difference, how many more	bigger take away smaller
Draw a suitable diagram	dual bar chart with a key
Symbols with a key	Pictograms
Compare two groups	Comparing Two Sets of Data
Two things rising together	Scatter Diagrams and Correlation

Key idea

Data only tells you about the data. One year of visitors does not prove a museum is always the busiest. Two things rising together does not prove one causes the other.

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