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This page sets out the method for bar charts in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Bar charts topic page.
When you see a finished bar chart, check the scale before you read any height.
When you see 'draw a bar chart for this data', set up the axes before drawing any bars.
The side scale may go up in 1s, 2s or 5s.
If the grid lines go up in 2s, a bar that ends halfway between the 4 line and the 6 line has height 5.
The taller bar has the higher frequency.
Subtract the heights to find how many more.
Bars for categories have gaps, because the categories are separate.
A histogram, later, has no gaps and uses area.
A scale that does not start at zero exaggerates differences.
GCSE bar charts start at zero unless a question shows otherwise and you read it carefully.
Add the heights to get the total frequency.
Do not add the labels.
A dual bar chart has two bars per category.
Read the key before you compare colours.
Put a ruler or a finger on the top of the bar and move it across to the scale. That number is the frequency. If the top sits halfway between the 10 line and the 12 line, the bar is 11. Check what each grid step is worth before you guess. If the scale goes up in fives, a bar halfway between the 10 line and the 15 line is 12.5, so read the scale with care.
The bars are separate because the categories do not form a number line. You do not join the tops. Joining them would invent values between "bus" and "car", and those words are not numbers. Leave the gaps. The gap is part of the chart, not a missing bar.
Method: 1. Read the scale, including what each grid step is worth. 2. Read the height of the bar from zero. 3. Ignore the category label when you are writing the frequency. 4. Do not join the tops. The gaps show that the categories are separate.
The total frequency is the sum of the heights. If walk is 8, bus is 5 and car is 11, the total is 8 + 5 + 11 = 24. Add every bar the question includes. Leaving one out gives a total for a smaller group than the one asked for.
A missing bar is subtraction from a given total. If the total is 46 and three bars are 12, 7 and 15, the missing bar is 46 - 12 - 7 - 15. Do all three subtractions. Stopping after one bar leaves a number that is still too big to be the missing frequency.
Method: 1. List the height of every known bar. 2. Add those heights for a total. 3. For a missing bar, subtract each known height from the given total. 4. Reject a negative height. It means a bar was read wrongly.
A dual bar chart has two bars side by side for each category. The key tells you what the two colours mean, such as Year 7 and Year 8, or boys and girls. Read the key before you compare. Subtracting a boy bar from a girl bar in a different category answers a question you were not asked.
How many more means a subtraction of the two heights you were asked about. The taller bar is the larger frequency. You can also add a pair to find how many people are in that category altogether. Addition and subtraction answer different questions. Read the last line of the question again before you choose.
Method: 1. Read the key so you know which bar is which group. 2. For a difference, subtract the two heights named in the question. 3. For a category total, add the bars that sit in that category. 4. Do not compare a bar from one category with a bar from another unless the question says so.
Bar charts and histograms both use blocks, and that is where the likeness ends. A bar chart compares separate categories. The blocks have gaps, they start at zero, and the height is the frequency. You never multiply a bar-chart height by a width. There is no class width to use.
A histogram is for continuous data sorted into classes, and the classes can have different widths. There are no gaps. The area of a block stands for the frequency, so the height is a frequency density, not the frequency itself. You do not need density here. You only need to refuse the swap: do not treat a histogram as a bar chart, and do not put gaps into a histogram just because a bar chart has them.
Method: 1. On a bar chart, read the height as the frequency. 2. Keep the gaps. They show separate categories. 3. Start the scale at zero so the heights stay honest. 4. Leave frequency density for histograms, where the class widths may differ.
A bar chart does not always count in ones. Before you read any bar, find what one small square is worth. Look at two labelled lines, subtract to find the gap, then divide by the number of equal squares between them. Labels at 0 and 10 with 5 squares between them mean each square is 10 ÷ 5 = 2. A bar that ends 4 squares above the 10 line is at 10 + 4 × 2 = 18.
A bar that stops half way between two lines needs the midpoint of those two lines. If the lines are 8 and 12, the bar is at (8 + 12) ÷ 2 = 10, not 8.5. Counting half a square as 0.5 is a classic trap. Say the scale to yourself before every reading: "each square is worth 2". Mark the value on the chart in pencil if there is more than one bar to read.
Method: 1. Find the gap between two labelled lines. 2. Divide the gap by the number of squares between them to get the value of one square. 3. Count the squares from a labelled line and multiply by the value of a square. 4. Add that to the labelled value and write down the reading with its unit.
Tip: If your reading is not a multiple of the square value, you have probably counted squares wrongly.
A composite bar chart stacks two or more parts in one bar. The bottom part starts at zero, so its top edge shows its size. The next part sits on top of it, so its top edge shows the total so far, not its own size. To find the size of the top part, read the top of the whole bar and subtract the top of the lower part.
For a bar with total height 32 and a boys part that reaches 19, the girls part is 32 - 19 = 13. Reading the girls part as 32 is an easy slip because the top of the bar is the easiest number to see. When a question says the numbers of boys and girls are equal, halve the total of that bar. A bar of height 24 gives 12 boys and 12 girls.
Method: 1. Read the top of the lower part. This is its size. 2. Read the top of the whole bar. This is the total. 3. Subtract the lower part from the total to get the upper part. 4. Check that the two parts add to the total.
Many questions give you some bars and then describe the missing ones in words: "twice as many on Thursday as on Monday" or "the total for the week was 105". Work in numbers first and only draw the bar at the end. Write each day as a number, use the clue to find the missing values, then work out how many squares each bar needs using the scale.
When a total is given, add the bars you know and subtract from the total. When a clue compares two bars, such as "half as many", use that bar as the starting point. Finish by adding every bar, including the new ones, and check you reach the stated total. A bar drawn to the wrong height loses the accuracy mark even if the working is right.
Method: 1. List every bar as a number, with a blank for the missing ones. 2. Use each clue to fill a blank, one clue at a time. 3. Subtract from the total for the last bar. 4. Divide by the scale to find how many squares to draw, then check the total.
"Make two criticisms of her bar chart" is a short question that earns marks for specific, correct points. Look for missing labels on the axes, no title, a vertical scale that does not go up evenly, bars with different widths or uneven gaps, a scale that does not start at zero, and bars that are not labelled. Give two different criticisms, each in a short sentence.
Be precise. "It is wrong" earns nothing. "The vertical scale goes 0, 5, 10, 20, 25, so the gap from 10 to 20 is twice as big as the other gaps" earns the mark. The best answers refer to something you can point to on the chart. You are not asked to draw a better chart, so do not spend time on one.
Method: 1. Check the title, both axis labels and the key. 2. Check that the scale goes up by the same step each time. 3. Check that every bar has the same width and the same gaps. 4. Write two separate, specific criticisms.
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