Match the chart to the data. A pictogram uses a repeated symbol with a key. A bar chart shows separate categories, with gaps between the bars. A pie chart shows how a whole splits into parts, and each sector angle is fraction × 360°. A line graph shows how one quantity changes over time. A dot diagram suits small sets of discrete data. A histogram shows grouped numerical data with no gaps, because the groups are continuous. A stem-and-leaf diagram keeps every original value visible. The commonest lost mark is drawing a histogram with gaps, or a bar chart without them.
These are among the easiest marks in the paper and among the most frequently dropped. The reason is almost never the calculation. It is presentation: an unlabelled axis, a missing title, bars drawn touching when they should have gaps, or a pie chart whose angles do not add to 360 degrees.
Every one of those is avoidable with a habit rather than with understanding, so it is worth building the habit deliberately.
Pictogram
repeated symbol, needs a key
Bar chart
separate categories, gaps between bars
Pie chart
parts of a whole, angle = fraction × 360°
Line graph
change over time, points joined
Dot diagram
small discrete data sets
Histogram
grouped numerical data, no gaps
Stem-and-leaf
keeps every original value
Always
label both axes and add a title
The gap rule is the one examiners test most. Bar charts have gaps because the categories are genuinely separate: there is nothing between "football" and "netball". Histograms have no gaps because the groups are continuous: 10 to 20 runs straight into 20 to 30 with nothing missing in between.
Forty students chose a favourite sport: football 16, netball 10, swimming 8, athletics 6. Find the angle of each sector.
Solution
16 + 10 + 8 + 6 = 40 students.16/40 × 360 = 0.4 × 360 = 144°.10/40 × 360 = 0.25 × 360 = 90°.8/40 × 360 = 0.2 × 360 = 72°.6/40 × 360 = 0.15 × 360 = 54°.144 + 90 + 72 + 54 = 360°. Correct.Always add your angles. If they do not total exactly 360 degrees, you have made an arithmetic slip and you can find it before you draw anything. This ten-second check has saved more marks than any other habit in this topic.
In a pie chart showing how 180 people travel to work, the sector for "bus" has an angle of 100°. How many people travel by bus?
Solution
100/360.100/360 × 180.= 100 × 0.5 = 50.The step students get wrong
Treating the angle as a percentage. An angle of 100° is not 100% and it is not 10% either; it is 100/360, which is about 27.8%. Always divide by 360 first, then apply the fraction to the total the question gives you.
A pictogram represents data with a repeated symbol, and every pictogram must carry a key saying what one symbol is worth. Without the key the diagram means nothing, and that is where the marks go. Part-symbols are used for values that are not exact multiples, so half a symbol means half the key value.
Worked example: reading a pictogram
one symbol = 8 books.3 × 8 = 24 books.½ × 8 = 4 books.= (2 × 8) + 4 = 20 books.The step students get wrong
Counting symbols instead of reading the key. Three symbols is not three books, it is three lots of whatever the key says. Write the key value beside your working before you start counting, and the whole question becomes multiplication.
A line graph plots a quantity against time and joins the points, so the slope between points carries the meaning. Rising means increasing, falling means decreasing, and a flat section means no change. Use a line graph only when the horizontal axis is continuous, normally time. Joining the tops of unrelated categories is wrong: that is bar chart data.
Worked example: reading a line graph
$4200 in March and $5100 in April, the increase is 5100 - 4200 = $900.Highest point is not the same as biggest rise. A graph can peak in June while its steepest climb happened in February. Read the question carefully: "greatest increase" is about steepness between two points, "highest" is about a single value.
A dot diagram stacks one dot per value above a number line. It suits small sets of whole-number data and makes the mode obvious at a glance, because the mode is simply the tallest column. Because every individual value is still visible, you can read the median and range straight off the diagram, the same advantage a stem-and-leaf diagram has.
These test marks were recorded: 34, 41, 28, 45, 33, 39, 42, 27, 36, 48. Draw a stem-and-leaf diagram and use it to find the median.
Solution
2: leaves 7, 8. Stem 3: leaves 3, 4, 6, 9. Stem 4: leaves 1, 2, 5, 8.2 | 7 means 27 marks. Without a key the diagram scores nothing.27, 28, 33, 34, 36, 39, … The 5th is 36 and the 6th is 39.= (36 + 39) / 2 = 37.5 marks.The advantage of a stem-and-leaf diagram is that no information is lost: every original value can still be read back out, which is why you can find an exact median from it. A histogram cannot do that, because once values are grouped the individual readings are gone.
If the horizontal axis has words on it, you are drawing a bar chart. If it has a continuous number scale, you are drawing a histogram. That single test resolves nearly every case you will meet at O-Level.
How do I find a pie chart angle?
Divide the category value by the total, then multiply by 360. Always check that all your angles add to exactly 360 degrees before drawing, because that catches arithmetic errors early.
Why do histograms have no gaps?
Because the groups are continuous and run into each other. The interval 20 to 30 begins exactly where 10 to 20 ends, so there is no gap in the data and there should be none in the diagram.
What must a stem-and-leaf diagram always include?
A key, such as 3 | 4 means 34. Without a key the numbers are ambiguous and the diagram cannot be marked. The leaves should also be ordered within each row.
Which chart should I use if the question does not say?
Let the data decide. Categories with names go in a bar chart. Parts of a single whole go in a pie chart. Something changing over time goes in a line graph. Grouped measurements go in a histogram. A small set of whole numbers suits a dot diagram.
What must a pictogram always include?
A key stating what one symbol represents. Part-symbols are then read as that fraction of the key value, so half a symbol with a key of 8 means 4. Without a key the pictogram cannot be marked.
When should I use a line graph rather than a bar chart?
Use a line graph when the horizontal axis is continuous, almost always time, and you want to show a trend. Use a bar chart for separate named categories. Joining the tops of category bars with a line is a common error, because there is nothing meaningful between two categories.
How does this connect to the rest of E-Maths?
Charts are how the data arrives before you calculate anything, so reading them correctly feeds directly into mean, median and mode from frequency tables. Pie chart angles are also a straight application of ratio.
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