Bar Graphs

Read values, differences, totals and percentages from a bar graph, choose a scale and draw one, see why the value axis starts at 0, and read dual and composite bar graphs.

Before you start

A bar graph shows data with bars. The length of each bar stands for a value, read off the scale along one axis. You read and drew simple bar graphs in Primary school.
A percentage of a whole is $\frac{\text{part}}{\text{whole}} \times 100\%$ . For example, 9 out of 36 is $\frac{9}{36} \times 100\% = 25\%$ .
A ratio is given in its simplest form by dividing both numbers by their HCF: $35 : 50 = 7 : 10$ .

The Parts of a Bar Graph

A bar graph uses bars of equal width to show how many, or how much, there is in each category. The bars can go up the page (a vertical bar graph) or across it (a horizontal bar graph). One axis names the categories. The other, the value axis, carries a scale, and the length of each bar is read off that scale.

A survey asked 50 students which of four fruits they liked best. The table shows the results, and the bar graph below it is drawn from the table.

Favourite fruit of 50 students
Fruit	Number of students
Apple	18
Orange	15
Banana	12
Grapes	5
Total	50

What a bar graph has

A title that says what the data are.

A category axis, with the name of each category under (or beside) its bar, and a label for the axis.

A value axis with a label (and the unit, if there is one) and a scale that starts at 0 and goes up in equal steps.

Bars of equal width with equal gaps between them. Only the length of a bar shows its value.

Reading a Bar Graph

To read a bar, go from the end of the bar straight across to the value axis and read the scale there. First find what one step of the scale stands for: on the fruit graph the numbers go 0, 2, 4, 6, …, so each step is 2.

A bar that ends halfway between two gridlines stands for the number halfway between them. The Orange bar ends halfway between 14 and 16, so 15 students chose orange.

Once the values are read, a bar graph answers the same questions as a table: the greatest and the least, a difference, a total, a fraction, a percentage or a ratio.

Example 1: Reading the fruit bar graph

Use the bar graph of the favourite fruit of 50 students above.

(a) How many students chose banana?

(b) How many more students chose apple than grapes?

(d) What fraction of the students chose orange? Give it in its simplest form.

Solution

Each step of the scale is 2.

(a) The Banana bar ends on the gridline for 12.

(b) The Apple bar ends on the gridline for 18. The Grapes bar ends halfway between 4 and 6, at 5.

Difference $= 18 - 5 = 13$

(d) The Orange bar ends halfway between 14 and 16, at 15.

Fraction that chose orange $= \frac{15}{50} = \frac{3}{10}$ (divide the numerator and the denominator by 5)

(a) 12 students chose banana. (b) 13 more students chose apple than grapes. (c) 24% of the students chose banana. (d) $\frac{3}{10}$ of the students chose orange.

Example 2: Library loans in one week

The bar graph shows the number of books borrowed from a school library on each day of one week.

(a) How many books were borrowed on Wednesday?

(b) On which two days was the same number of books borrowed?

(d) What percentage of the week's books were borrowed on Thursday?

(e) Find the ratio of the number of books borrowed on Monday to the number borrowed on Tuesday, in its simplest form.

Solution

Each step of the scale is 10, so a bar that ends halfway between two gridlines stands for a number ending in 5.

(a) The Wednesday bar ends halfway between 40 and 50, at 45.

(b) The Tuesday and Friday bars are the same length: both end on the gridline for 50.

Total $= 35 + 50 + 45 + 20 + 50 = 200$

(d) Percentage borrowed on Thursday $= \frac{20}{200} \times 100\% = 10\%$

(e) Monday : Tuesday $= 35 : 50 = 7 : 10$ (divide both by 5)

(a) 45 books were borrowed on Wednesday. (b) Tuesday and Friday, 50 books each. (c) 200 books were borrowed in the week. (d) 10% of them were borrowed on Thursday. (e) The ratio is $7 : 10$ .

Drawing a Bar Graph: Choosing a Scale

Before you draw a bar graph, choose the scale of the value axis. Find the greatest value in the data. Then choose a step of 1, 2, 5, 10, 20, 25, 50, 100, … so that the axis reaches the greatest value, or just past it, in about 5 to 10 equal steps.

Too large a step leaves most bars ending between gridlines, where they are hard to read. Too small a step crowds the axis with numbers and makes the graph too tall for the page. For a greatest value of 25, steps of 5 up to 25 or 30 give 5 or 6 steps; steps of 1 would need 25 of them, and steps of 10 only 3.

Drawing a bar graph

1. Find the greatest value. Choose a step of 1, 2, 5, 10, 20, 25, 50, … that reaches it, or just past it, in about 5 to 10 equal steps.

2. Draw the two axes. Mark the value axis from 0 in equal steps, and label it, with the unit if there is one.

3. Mark the categories along the other axis, equally spaced, and label that axis.

4. Draw a bar for each category: all the same width, with equal gaps, each as long as its value on the scale.

5. Give the graph a title.

Example 3: Drawing a vertical bar graph

Students voted for their favourite lunch at the school canteen. The table shows the votes.

Favourite lunch of 70 students
Lunch	Number of votes
Chicken rice	25
Nasi lemak	20
Pasta	15
Sandwiches	10
Total	70

(a) What is a suitable greatest value on the axis for the number of votes, and what step would you use?

(b) Draw a vertical bar graph of the data.

Solution

(a) The greatest value is 25 (chicken rice). Steps of 5 from 0 to 30 give 6 equal steps, the axis reaches just past 25, and every value in the table ends on a gridline. (0 to 25 in steps of 5, with 5 steps, would also do: it reaches 25 exactly.)

(b) Draw the axes. Mark the value axis 0, 5, 10, 15, 20, 25, 30 and label it "Number of votes". Mark the four lunches along the bottom, equally spaced, and label that axis "Lunch".

Draw four bars of the same width, with equal gaps, to 25, 20, 15 and 10. Give the graph a title.

(a) A greatest value of 30, in steps of 5 (or 25, in steps of 5). (b) The bar graph is drawn above.

Horizontal Bar Graphs

In a horizontal bar graph the bars go across the page. The categories are written down the vertical axis, and the scale runs along the horizontal axis, starting at 0 on the left. It shows exactly the same information as a vertical bar graph of the same data.

A horizontal bar graph is a good choice when the names of the categories are long, since each can be written in full on one line beside its bar instead of being squeezed under it, or when there are many categories.

Example 4: Drawing a horizontal bar graph

The table shows the number of Secondary 1 students in five CCAs at a school.

Secondary 1 students in five CCAs
CCA	Number of students
Chinese Orchestra	45
National Cadet Corps	40
Basketball	30
Robotics Club	35
Choir	25
Total	175

(a) Give one reason for drawing the bars horizontally.

(b) Choose a scale and draw a horizontal bar graph of the data.

Solution

(a) Names such as "National Cadet Corps" and "Chinese Orchestra" are long. Written down the vertical axis, each fits on one line beside its bar.

(b) The greatest value is 45. Steps of 10 from 0 to 50 give 5 equal steps; the bars for 45, 35 and 25 end halfway between two gridlines. (Steps of 5, with 10 steps, would also do.)

Draw the horizontal axis from 0 to 50 and label it "Number of students". Write the CCAs down the vertical axis and draw a bar across for each, all the same width.

Fraction in the Robotics Club $= \frac{35}{175} = \frac{1}{5}$ (divide the numerator and the denominator by 35)

(a) The CCA names are long, and each fits on one line beside a horizontal bar. (b) The bar graph is drawn above, with a scale from 0 to 50 in steps of 10. (c) $\frac{1}{5}$ of the students are in the Robotics Club.

Why the Value Axis Starts at 0

In a bar graph the length of a bar shows its value. When the value axis starts at 0, a bar for 50 is twice as long as a bar for 25, so the eye compares the numbers correctly just by comparing the bars.

Suppose the axis started at 40 instead. A bar for 45 would show only the 5 above 40, and a bar for 50 only the 10 above 40. The second bar would look twice as long as the first, although 50 is only a little more than 45. The lengths of the bars would no longer be in proportion to the values.

The value axis of a bar graph

The value axis of a bar graph starts at 0 and goes up in equal steps. Then the length of each bar is in proportion to its value: a bar twice as long stands for twice as much.

Example 5: An axis that does not start at 0

Two drink stalls at a hawker centre, stall A and stall B, sold 45 and 50 cups of sugar cane juice on Saturday. Ravi draws the bar graph below of these numbers. His graph is drawn wrongly: he starts his value axis at 40, not at 0, and draws no break, so the lengths of his bars are not in proportion to the values.

(a) On Ravi's graph, how much of each value does each bar show?

(b) How many times as long as stall A's bar does stall B's bar look?

(d) How should the graph be drawn?

Solution

(a) The axis starts at 40, so each bar shows only the part of its value above 40.

Stall A: $45 - 40 = 5$ . Stall B: $50 - 40 = 10$ .

(b) $10 \div 5 = 2$ , so stall B's bar looks twice as long as stall A's.

Stall B sold $50 - 45 = 5$ more cups. As a percentage of stall A's sales, $\frac{5}{45} \times 100\% \approx 11\%$ more.

(d) Start the value axis at 0, with equal steps. Then stall B's bar is only a little longer than stall A's, as it should be. Here is the graph drawn correctly, to set beside Ravi's:

(a) Stall A's bar shows 5 and stall B's shows 10. (b) Stall B's bar looks twice as long. (c) Stall B sold only about 1.1 times as many cups, about 11% more. (d) With the value axis starting at 0, as drawn above.

Dual Bar Graphs

A dual bar graph shows two sets of data on one graph, drawn to the same scale. For each category, the two bars are drawn side by side in two colours, and a key says which colour is which set.

It lets you compare in two ways: the two bars of one category (the boys against the girls in Sports), and the bars of one colour across the categories (which CCA group most boys chose).

Example 6: Reading a dual bar graph

Each of the 100 boys and 100 girls in Secondary 1 at a school belongs to one CCA group. The dual bar graph shows how many boys and how many girls are in each group.

(a) How many girls are in Performing arts?

(b) In which CCA group are there as many boys as girls?

(c) In which CCA group is the difference between the number of boys and the number of girls the greatest? What is the difference?

(d) What percentage of the girls are in Sports?

(e) Find the ratio of boys to girls in Performing arts, in its simplest form.

Solution

Each step of the scale is 10.

(a) The girls' bar for Performing arts ends halfway between 30 and 40, at 35.

(b) In Uniformed groups both bars end on the gridline for 30.

(c) The differences: Sports $40 - 20 = 20$ ; Uniformed groups $30 - 30 = 0$ ; Performing arts $35 - 10 = 25$ ; Clubs and societies $20 - 15 = 5$ .

The greatest is 25, in Performing arts, where there are 25 more girls than boys.

(d) There are 20 girls in Sports, out of 100 girls: $\frac{20}{100} \times 100\% = 20\%$

(e) Boys : girls $= 10 : 35 = 2 : 7$ (divide both by 5)

(a) 35 girls are in Performing arts. (b) Uniformed groups, with 30 boys and 30 girls. (c) Performing arts, with a difference of 25. (d) 20% of the girls are in Sports. (e) The ratio is $2 : 7$ .

Composite Bar Graphs

In a composite bar graph each bar is divided into parts, stacked one on top of another, with a key for the parts. The whole bar shows the total for its category, and each part shows one share of that total.

The bottom part starts at 0 and is read like an ordinary bar. A part higher up does not start at 0: read the scale at its top and at its bottom, and subtract.

Example 7: Reading a composite bar graph

The composite bar graph shows the numbers of boys and girls in four Secondary 1 classes.

(a) How many students are in 1B?

(b) How many girls are in 1A?

(d) What percentage of the students in 1C are girls?

(e) How many boys are there in the four classes altogether?

Solution

Each step of the scale is 5. The boys' part of each bar starts at 0; the girls' part sits on top of it.

(a) The whole bar for 1B ends at 35.

(b) In 1A, the boys' part goes from 0 to 15 and the girls' part from 15 to 40.

Girls in 1A $= 40 - 15 = 25$

(d) In 1C, the girls' part goes from 25 to 40: $40 - 25 = 15$ girls out of 40 students.

Percentage of girls $= \frac{15}{40} \times 100\% = 37.5\%$

(e) Boys $= 15 + 20 + 25 + 20 = 80$

(a) There are 35 students in 1B. (b) There are 25 girls in 1A. (c) 1C has the most boys (25). (d) 37.5% of the students in 1C are girls. (e) There are 80 boys altogether.

Advantages and Disadvantages of a Bar Graph

Advantages

The lengths of the bars make it easy to compare the categories at a glance and to see the greatest and the least.

Values are read from a scale, more exactly than from the symbols of a pictogram.

A dual bar graph compares two sets of data on one graph; a composite bar graph shows each total and its parts together.

It suits categorical data (fruits, CCAs) and discrete data with only a few values (such as the number of siblings), with a count or amount for each.

Disadvantages

A value that ends between gridlines can only be estimated, so exact numbers are better given in a table.

It does not show at once what fraction of the whole each category is; a pie chart shows parts of a whole more clearly.

With many categories, or more than two sets of data, it becomes crowded.

Its value axis must start at 0, so small differences between large values (such as 45 and 50) are hard to see.

Common mistakes

Misreading the scale. Work out what one step stands for before reading a bar. On an axis marked 0, 10, 20, …, a bar ending halfway between 40 and 50 stands for 45, not 41 or 4.5.
Reading the top of a part as its value in a composite bar graph. A part that starts at 15 and ends at 40 stands for $40 - 15 = 25$ , not 40.
Starting the value axis above 0. The bars are then no longer in proportion to the values, and small differences look large.
Unequal steps on the scale (0, 5, 10, 20, 40), or bars of different widths. The steps must be equal, and only the length of a bar may change.
Using the wrong whole for a percentage. In a dual bar graph of 100 boys and 100 girls, the percentage of the girls in Sports is out of the 100 girls, not out of all 200 students.
Choosing a scale with too many or too few steps. Aim for about 5 to 10 steps from 0 to the greatest value or just past it.
Leaving out the labels. A bar graph needs a title, a label on each axis and the unit of the values.

Practice

The questions get harder as you go. Try each one before you open its solution.

Practice 1: Ice-cream cones sold

The bar graph shows the number of ice-cream cones sold at a stall on five days.

(a) How many cones were sold on Wednesday?

(b) On which day were the most cones sold?

(d) How many cones were sold in the five days altogether?

ShowHide solution

Each step of the scale is 10.

(a) The Wednesday bar ends halfway between 70 and 80, at 75.

(b) The longest bar is Friday's, ending on the gridline for 90.

(d) $45 + 60 + 75 + 30 + 90 = 300$

(a) 75 cones (b) Friday, with 90 cones (c) 60 more cones (d) 300 cones

Practice 2: Bubble tea flavours

Mei Ling asked 100 students for their favourite bubble tea flavour. The horizontal bar graph shows the results.

(a) How many students chose taro?

(b) Which two flavours were chosen by the same number of students?

(d) Find the ratio of the number who chose brown sugar to the number who chose mango, in its simplest form.

ShowHide solution

Each step of the scale is 10.

(a) The Taro bar ends halfway between 20 and 30, at 25.

(b) The Original milk tea and Matcha bars are the same length, both ending halfway between 10 and 20, at 15.

(d) Brown sugar : mango $= 35 : 10 = 7 : 2$ (divide both by 5)

Check: $35 + 15 + 25 + 15 + 10 = 100$ students, as the question says.

(a) 25 students (b) Original milk tea and matcha, 15 students each (c) 35% (d) $7 : 2$

Practice 3: Drawing a bar graph of canteen drinks

Hui Min counted the drinks bought at one canteen drinks stall during recess.

Drinks bought at one stall during recess
Drink	Number of cups
Soya bean milk	14
Lime juice	9
Barley	11
Green tea	6
Water	4
Total	44

(a) Choose a suitable scale for the number of cups, and give a reason.

(b) Draw a vertical bar graph of the data.

ShowHide solution

(a) The greatest value is 14. Steps of 2 from 0 to 16 give 8 equal steps, reaching just past 14; every value ends on a gridline or halfway between two. (0 to 14 in steps of 2, with 7 steps reaching 14 exactly, would also do. Steps of 5 would leave most bars hard to read; steps of 1 would need 14 or more.)

(b) Mark the value axis 0, 2, 4, …, 16 and label it "Number of cups". Mark the five drinks along the bottom and label that axis "Drink". Draw five bars of equal width with equal gaps, and give the graph a title.

Fraction that were barley $= \frac{11}{44} = \frac{1}{4}$

(a) 0 to 16 in steps of 2 (8 steps, just past the greatest value 14); 0 to 14 in steps of 2 would also do. (b) The bar graph is drawn above. (c) $\frac{1}{4}$ of the drinks were barley.

Practice 4: Drawing a horizontal bar graph of library loans

The school library recorded its loans in one term by type of book.

Library loans in one term, by type of book
Type of book	Number of loans
Adventure stories	150
Mystery and detective	225
Science fiction	175
Comics and graphic novels	250
Non-fiction	200
Total	1000

(a) Give one reason for drawing the bars horizontally.

(b) Choose a scale and draw a horizontal bar graph of the data.

ShowHide solution

(a) The names of the types, such as "Comics and graphic novels", are long; down the vertical axis each fits on one line beside its bar.

(b) The greatest value is 250. Steps of 50 from 0 to 250 give 5 equal steps; 225 and 175 end halfway between two gridlines. (Steps of 25, with 10 steps, would also do.)

Percentage $= \frac{250}{1000} \times 100\% = 25\%$

(a) The names of the types of book are long. (b) The bar graph is drawn above, with a scale from 0 to 250 in steps of 50. (c) 25% of the loans were comics and graphic novels.

Practice 5: Twice as many?

There are 60 students in the badminton CCA and 65 in the table tennis CCA. Siti draws a bar graph of these numbers with her value axis starting at 55. She says, "Table tennis has twice as many students as badminton."

(a) On Siti's graph, how much of each value does each bar show?

(b) Why does Siti think that table tennis has twice as many students?

(d) How should the value axis be drawn?

ShowHide solution

(a) Her axis starts at 55, so each bar shows only the part above 55: badminton $60 - 55 = 5$ , table tennis $65 - 55 = 10$ .

(b) $10 \div 5 = 2$ : the table tennis bar is twice as long as the badminton bar, and she has compared the lengths.

(d) From 0, in equal steps. Then the bars are 60 and 65 long, and the table tennis bar is only a little longer:

(a) 5 for badminton and 10 for table tennis. (b) The bar for table tennis looks twice as long because the axis does not start at 0. (c) Only $8\frac{1}{3}\%$ more, so Siti is wrong. (d) Starting at 0, in equal steps.

Practice 6: Books borrowed by two classes

The dual bar graph shows the number of books borrowed by Class 1A and Class 1B on each day of one week.

(a) How many books did Class 1B borrow on Wednesday?

(b) On which days did Class 1B borrow more books than Class 1A?

(d) Which class borrowed more books in the week, and how many more?

ShowHide solution

Each step of the scale is 2. Read each pair of bars:

Day	Class 1A	Class 1B	Difference
Monday	12	10	2
Tuesday	15	17	2
Wednesday	9	14	5
Thursday	18	11	7
Friday	20	16	4
Total	74	68	6

(a) Class 1B's bar for Wednesday ends on the gridline for 14.

(b) Class 1B's bar is longer on Tuesday (17 against 15) and Wednesday (14 against 9).

(d) Class 1A: $12 + 15 + 9 + 18 + 20 = 74$ . Class 1B: $10 + 17 + 14 + 11 + 16 = 68$ .

$74 - 68 = 6$

(a) 14 books (b) Tuesday and Wednesday (c) Thursday, a difference of 7 books (d) Class 1A, by 6 books

Practice 7: Household spending

The composite bar graph shows how much Mr Tan's household spent on food and on transport in each of four months.

(a) How much did the household spend on food and transport altogether in January?

(b) How much was spent on transport in April?

(d) What percentage of February's total was spent on transport?

ShowHide solution

Each step of the scale is 100. The food part of each bar starts at 0; the transport part sits on top of it.

(a) The whole January bar ends on the gridline for 1100, so the total is $1100.

(b) In April the food part ends halfway between 800 and 900, at 850, and the whole bar ends at 1200.

Transport $= 1200 - 850 = 350$ , so $350 was spent on transport.

(d) In February the food part ends at 750 and the whole bar at 1000.

Transport $= 1000 - 750 = 250$

Percentage $= \frac{250}{1000} \times 100\% = 25\%$

(a) $1100 (b) $350 (c) March and April ($1200 each) (d) 25%

Practice 8: Drawing a dual bar graph

The table shows the points won by the four houses of a school at Sports Day.

Sports Day points won by each house
House	Track events	Field events
Red	45	30
Blue	60	20
Green	35	40
Yellow	50	35

(a) Choose a scale and draw a dual bar graph of the data, with the track and field points of each house side by side.

(b) Which house won the most points altogether?

ShowHide solution

(a) The greatest value is 60. Steps of 10 from 0 to 60 give 6 equal steps. Draw two bars for each house, side by side and touching, in two colours, with a key: one colour for track events, the other for field events.

(b) Red $45 + 30 = 75$ ; Blue $60 + 20 = 80$ ; Green $35 + 40 = 75$ ; Yellow $50 + 35 = 85$ .

(a) The dual bar graph is drawn above, with a scale from 0 to 60 in steps of 10. (b) Yellow, with 85 points. (c) Green (40 field points against 35 track points).

Practice 9: A missing bar

The bar graph shows how the 40 students of Class 1C travel to school. The bar for "Walk" has not been drawn.

(a) How many students walk to school?

(b) What percentage of the class travel by MRT or by bus?

(d) Complete the bar graph.

ShowHide solution

Each step of the scale is 2. MRT 15 (halfway between 14 and 16), Bus 12, Car 6, Bicycle 2.

(a) Walk $= 40 - (15 + 12 + 6 + 2) = 40 - 35 = 5$

(b) MRT or bus $= 15 + 12 = 27$ . Percentage $= \frac{27}{40} \times 100\% = 67.5\%$

(d) Draw the Walk bar to 5, halfway between 4 and 6, the same width as the others:

(a) 5 students walk. (b) 67.5% travel by MRT or by bus. (c) $2 : 1$ (d) The Walk bar is drawn to 5, as above.

Practice 10: Advantages and disadvantages

Use the canteen drinks of Practice 3 (Soya bean milk 14, Lime juice 9, Barley 11, Green tea 6, Water 4).

(a) Give one advantage of showing these data as a bar graph rather than as a table.

(b) Give one disadvantage of the bar graph compared with the table.

(c) Hui Min wants to show what fraction of all the drinks each kind of drink was. Would a bar graph or a pie chart show this more clearly?

(d) The stall also recorded the drinks bought on a second day. Why is a dual bar graph better than two separate bar graphs for comparing the two days?

ShowHide solution

(a) The lengths of the bars show at a glance that soya bean milk was bought most and water least, and how the drinks compare, without reading every number.

(b) A value can only be read from the scale, and between gridlines it must be estimated; the table gives every number exactly, and the total too.

(c) A pie chart: its sectors are parts of one whole circle, so the share of each drink is seen at once. From a bar graph the total must first be worked out.

(d) In a dual bar graph the two days are drawn to the same scale, with the two bars for each drink side by side, so each pair can be compared directly. Two separate graphs might have different scales and must be compared across the page.

(a) It makes comparisons easy at a glance. (b) Exact values are harder to read than in a table. (c) A pie chart. (d) Same scale, with each pair of bars side by side.

Practice 11: Sports Day entries in two years

The dual bar graph shows the number of students who entered four Sports Day events in 2025 and in 2026.

(a) In which event did the number of entries fall from 2025 to 2026, and by how many?

(b) Ali says, "The entries for the 100 m went up by 10%." Explain his mistake, and find the correct percentage increase.

ShowHide solution

Each step of the scale is 10. 2025: 40, 25, 20, 35. 2026: 50, 30, 15, 35.

(a) Long jump: from 20 to 15, a fall of $20 - 15 = 5$ .

(b) The 100 m entries went up from 40 to 50, an increase of 10 students, not 10%. A percentage increase is worked out of the 2025 number:

Percentage increase $= \frac{10}{40} \times 100\% = 25\%$

Increase $= 130 - 120 = 10$

Percentage increase $= \frac{10}{120} \times 100\% = 8.333\ldots\% \approx 8.3\%$

(a) Long jump, by 5 entries. (b) The increase was 10 students, which is 25% of 40, not 10%. (c) About 8.3%.

Practice 12: Boys and girls in three CCAs

The composite bar graph shows the numbers of boys and girls in three CCAs.

(a) Which CCA has the most members?

(b) In which CCA do girls make up the greatest fraction of the members? Give that fraction in its simplest form.

(d) The Robotics CCA wants equal numbers of boys and girls, and keeps all its boys. How many more girls must join, and where would the top of the Robotics bar then be?

ShowHide solution

Each step of the scale is 5. Read each part as its top minus its bottom:

Choir: boys 0 to 10, so 10; girls 10 to 40, so 30; 40 members.

Football: boys 0 to 30, so 30; girls 30 to 40, so 10; 40 members.

Robotics: boys 0 to 25, so 25; girls 25 to 45, so 20; 45 members.

(a) The tallest whole bar is Robotics, at 45.

(b) Fraction of girls: Choir $\frac{30}{40} = \frac{3}{4}$ ; Football $\frac{10}{40} = \frac{1}{4}$ ; Robotics $\frac{20}{45} = \frac{4}{9}$ . The greatest is $\frac{3}{4}$ , in the Choir.

Percentage of girls $= \frac{60}{125} \times 100\% = 48\%$

(d) Robotics has 25 boys, so it needs 25 girls: $25 - 20 = 5$ more girls.

Members then $= 25 + 25 = 50$ , so the top of the bar would be on the gridline for 50.

(a) Robotics, with 45 members. (b) The Choir, where $\frac{3}{4}$ of the members are girls. (c) 48% (d) 5 more girls; the bar would then reach 50.

Key Points

A bar graph shows the value of each category by the length of a bar; the bars have equal widths and equal gaps.
A bar graph has a title, a label on each axis (with the unit of the values), and a scale on the value axis.
The value axis starts at 0 and goes up in equal steps, so that a bar twice as long stands for twice as much.
To read a bar, first find what one step of the scale stands for. A bar ending halfway between two gridlines stands for the number halfway between them.
Differences, totals, fractions, percentages and ratios are worked out from the values read off the graph; a percentage of a group is out of that group's total.
To choose a scale, take a step of 1, 2, 5, 10, 20, 25, 50, … that reaches the greatest value, or just past it, in about 5 to 10 steps.
Draw the bars horizontally when the names of the categories are long or there are many categories; the information is the same.
A dual bar graph puts two sets of data side by side on one scale, with a key, so that they can be compared category by category.
A composite bar graph stacks the parts of each total in one bar; the whole bar is the total, and a part is the value at its top minus the value at its bottom.
A bar graph makes comparisons easy, but gives exact values less exactly than a table and shows parts of a whole less clearly than a pie chart.