Bar Charts, Pictograms and Line Graphs
A bar chart, a pictogram and a line graph are three ways of displaying data visually so that patterns and comparisons are easy to see at a glance: a bar chart uses bars of equal width and equal gaps, with each bar's height proportional to the frequency of that category, and a pictogram uses picture symbols instead, where each full symbol represents a fixed number of items shown in a key. A line graph plots points, usually against time, and joins them with straight lines, making it the best of the three for showing how a value changes over a period.
Before you start
Make sure you're comfortable with these topics first:
Method
- Choose the right chart for the data: a bar chart or pictogram for categorical or discrete data, and a line graph when the data is recorded over a continuous sequence, such as time, and the trend matters.
- For a bar chart, draw bars of EQUAL width with EQUAL gaps between them, since the categories are separate rather than continuous, and label both axes clearly with a title.
- For a pictogram, choose a sensible key (e.g. 1 symbol = 2 units), draw a whole number of symbols for values that are exact multiples of the key, and a proportionally sized fraction of a symbol for values that are not.
- For a line graph, plot each point accurately against both axes' scales, then join consecutive points with straight lines, not curves, to show how the value changes.
- When reading any of these three charts, check the axis scale carefully first - each square or gridline might represent more than 1 unit.
- To compare two categories or find a difference, read off the two exact values first, then subtract or compare them - never judge a difference just by comparing bar heights or symbol counts by eye.
- For a pictogram, to turn a partial symbol into a value, work out what fraction of a full symbol is drawn, then multiply that fraction by the key's value.
Worked example
A pictogram shows the number of books read by four reading groups in a school library challenge, where each full book symbol represents 4 books. Group Fox has 3 full symbols, Group Owl has 2 full symbols and a half symbol, Group Hedgehog has 1 full symbol and a quarter symbol, and Group Badger has 4 full symbols. Find how many books each group read, and state which group read the most.
- Group Fox: 3 full symbols x 4 books = 12 books.
- Group Owl: 2 full symbols x 4 = 8 books, plus a half symbol worth half of 4 = 2 books, giving 8 + 2 = 10 books.
- Group Hedgehog: 1 full symbol = 4 books, plus a quarter symbol worth a quarter of 4 = 1 book, giving 4 + 1 = 5 books.
- Group Badger: 4 full symbols x 4 = 16 books.
- Comparing 12, 10, 5 and 16, Group Badger read the most books, with 16.
Practice questions
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Q1In a pictogram showing weekly bike sales at a shop, each full bike symbol represents 6 bikes. The Week 3 row shows 2 full symbols and a half symbol. How many bikes were sold in Week 3?Show answer
Answer: 15 bikes (2 x 6 = 12, plus half of 6 = 3, giving 12 + 3 = 15)
Q2A pictogram shows umbrella sales at a shop, where each full umbrella symbol represents 8 umbrellas. The Rainy Week row shows 3 full symbols and a half symbol. How many umbrellas were sold that week?Show answer
Answer: 28 umbrellas (3 x 8 = 24, plus half of 8 = 4, giving 24 + 4 = 28)
Q3A bar chart shows the number of trophies won by four running clubs at a regional athletics meet: Riverside Runners 9, Hillcrest Harriers 14, Oakwood Owls 6, Bridgeway Blazers 11. Find the difference between the club with the most trophies and the club with the fewest.Show answer
Answer: 8 trophies (Hillcrest Harriers with 14, minus Oakwood Owls with 6)
Q4A line graph shows the temperature, in degrees Celsius, recorded in a classroom every hour: 9am 15, 10am 17, 11am 19, 12pm 22, 1pm 21. Describe what happens to the temperature between 12pm and 1pm.Show answer
Answer: It falls, from 22 degrees Celsius to 21 degrees Celsius, a decrease of 1 degree, after rising steadily every hour before that
Q5A student wants to display how a company's sales changed over the 12 months of last year. State which is more suitable to show this: a bar chart or a line graph, and give a reason.Show answer
Answer: A line graph, because the data is recorded over a continuous sequence of time, and a line graph makes it easy to see the overall trend, rising or falling, between the months
Q6A pictogram shows the number of parcels delivered by a courier each day, where each full parcel symbol represents 12 parcels. Monday shows 4 full symbols, and Tuesday shows 2 full symbols and three-quarters of a symbol. Find the total number of parcels delivered over the two days.Show answer
Answer: 81 parcels (Monday = 4 x 12 = 48; Tuesday = 2 x 12 + three-quarters of 12 = 24 + 9 = 33; total = 48 + 33 = 81)
Q7A bar chart showing the number of pupils in each school club has a vertical axis where each gridline increases by 4 pupils. The bar for Chess Club reaches exactly 3 gridlines above zero. How many pupils are in Chess Club?Show answer
Answer: 12 pupils (3 x 4)
Q8A line graph tracks the number of visitors to a museum each month, from January to June: Jan 200, Feb 240, Mar 180, Apr 260, May 300, Jun 250. In which month were there the fewest visitors, and how many fewer visitors was this than in May?Show answer
Answer: March, with 180 visitors, which is 120 fewer than May's 300 visitors (300 - 180 = 120)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A pictogram shows the number of hours 5 pupils spent reading last week. Amaka's row is shown with 3 full symbols and a half symbol, and this represents 21 hours in total. (a) Work out the number of hours that one full symbol represents. (b) Zaid's row shows 2 full symbols and a quarter symbol. Work out how many hours Zaid read.
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A dual bar chart compares the number of pupils choosing Football and Netball as their favourite sport in Year 7 and Year 8. Year 7: Football 45, Netball 30. Year 8: Football 38, Netball 42. (a) Work out the total number of pupils represented in the chart. (b) A pupil claims: 'Football is more popular than Netball in this school.' Use the data to explain whether the claim is fully supported.
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A line graph shows the height of a candle, in cm, as it burns over 5 hours: 0 hours 20 cm, 1 hour 17 cm, 2 hours 15 cm, 3 hours 9 cm, 4 hours 7 cm, 5 hours 4 cm. (a) Work out the change in height of the candle between hour 2 and hour 4. (b) Between which two consecutive hours did the candle burn down fastest (fall in height the most)?
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Free printable worksheet
Want more practice on paper? Download the bar charts, pictograms and line graphs worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 31 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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