A line graph of a barangay's water use runs from January to June. The line rises steeply from January to March, then falls gently to June. In which month was use highest?
The line climbs until March and falls afterwards, so the peak is at March. The commonest error is answering June because it is last, or February because the climb looks steepest there — but steepness is how fast it changed, not how high it got. Height on the graph is the amount; slope is the rate.
1
Match the display to the question.
Display
Best for
Example
Bar graph
comparing separate categories
learners per grade level
Line graph
change over time
monthly water use
Pie chart
parts of one whole
how a budget is divided
Histogram
how continuous data is spread
heights grouped into intervals
Scatter plot
whether two things move together
study hours against test score
Bars versus histograms
A bar graph has gaps between its bars because the categories are
separate things. A histogram's bars touch, because the intervals
run continuously into one another. Grade level is a category; height is not.
2
Read the axes and the scale first.
A graph that does not start at zero exaggerates every difference.
Both graphs show the same three numbers — 92, 94 and 95. Only the scale changed.
Neither is a lie, but only one gives an honest first impression.
When a graph shows two sets side by side — a double bar graph of boys and girls, or two lines for two towns — read its legend (the key) next. The legend says which colour or pattern belongs to which set; without it the two sets cannot be told apart.
3
Primary and secondary graphs fail in different ways.
Primary — your own data
Secondary — someone else's
You control
the question, the sample, the scale
nothing
Watch for
a small or biased sample
who made it and why
Always check
that you asked enough people
the source, the date, the scale
With secondary data, ask who published it. A graph of soft-drink sales released by a soft-drink company is not automatically false, but it was drawn by someone who wanted a particular impression.
4
Pull real numbers out of a graph.
Most questions want a difference, a total or a fraction of a whole.
Grade
7
8
9
10
Learners
200
250
190
160
total = 800
200 + 250 + 190 + 160
Grade 7 share = 200800
= 0.25
= 25%
or 90° on a pie chart
A pie-chart angle is that fraction of 360°: 0.25 × 360 = 90°. The whole circle is
always the total, which is why a pie chart cannot show two different groups at once.
5
Four questions to ask any published graph.
Where does the axis start?not at 0?differences are exaggerated
Are the intervals equal?1990, 2000, 2005, 2006the time axis is distorted
How many were asked?"80% preferred it" — of 10 people?that is 8 people
Who published it?and what did they want?check before quoting
Remember the flow
Read the title · Read both axes · Find the scale's starting point · Then read the shape
Height is the amount. Slope is how fast it changed. They answer different questions.
6
How big is the change really? Percent change from a graph.
Percent change = change ÷ starting value × 100. Read it from the numbers, not from the bar heights.
A bar graph shows a household's electricity bill: ₱2,000 in May and ₱2,150 in June. Its vertical axis starts at ₱1,900. How big is the rise?
change = 2,150 − 2,000 = ₱150
from the axis labels
150 ÷ 2,000 = 0.075
divide by the starting value
= 7.5% rise
Comparing bar heights above a cut axis
Above ₱1,900 the May bar is 100 tall and the June bar 250 tall, so June looks two and a half times bigger. The bill went up by only 7.5%. Always compute from the labelled values.
7
Variations: an amount from a pie angle, a percent decrease, a missing sector.
Graph reading again, but with the question turned round.
In a pie chart of 600 learners' favourite sports, volleyball takes 54°. How many learners chose volleyball?
54 ÷ 360 = 0.15
the fraction of the circle
0.15 × 600 = 90 learners
the same fraction of the total
Going backwards from an angle: divide by 360, then multiply by the total.
A line graph shows a kilo of tomatoes falling from ₱80 to ₱60. What is the percent decrease?
change = 80 − 60 = ₱20
20 ÷ 80 = 0.25 = 25% decrease
divide by the START, ₱80
Dividing by ₱60 gives 33%, which is the wrong base. The starting value goes on the bottom whether the change is up or down.
A pie chart has four sectors. Three measure 120°, 90° and 75°. What is the fourth, and what percent is it?
360 − (120 + 90 + 75) = 75°
the angles fill the circle
75 ÷ 360 ≈ 0.208 ≈ 20.8%
Every pie chart's angles add to exactly 360°, and its percents to 100% — a quick test of any pie chart you are given.
On the exam
Items ask which display suits a data set, ask you to read a peak, a difference or a total off a graph, to convert between pie-chart angles and amounts, or to say why a graph misleads. The fastest route is to read the title and both axes before the shape, and to use fraction × 360° for pie charts. For a 10-second check, pie angles must add to 360°, and a percent change always divides by the starting value.
Now you try
Practice problem
Choose the display
A student has measured the heights of 120 learners and wants to show how those heights are spread out. Which display fits best?
Height is continuous data, and the question is about how it is spread, so group it into intervals and draw a histogram — bars touching, because the intervals run into one another. A pie chart shows parts of a whole, not a spread. A line graph needs something changing over time. A scatter plot needs two variables, and there is only one here.
Hint: ask two things — is the data continuous, and how many
variables are there? Those two answers eliminate three of the four options.
