Bar chart (II): Comparison

Foundation

Compare two sets side by side.

For:Primary 4 Mathematics · Unit:Data Handling · Lesson 24 of 24 in the learning path

After this lesson, you can:
  • A double bar chart pairs two bars per category to compare sets
  • The legend names each colour's set — it is essential
  • Read the scale first: lines × scale
數學Mathematics

1Summary 重點摘要

Compare two sets side by side.

2Vocabulary cards Vocabulary

d
double bar chart雙棒形圖

Two bars side by side per category, comparing two data sets.

c
compare比較

Seeing which set is bigger and by how much.

l
legend / key圖例

The key saying which colour stands for which set.

p
paired bars成對棒

The two bars of one category sit together for direct comparison.

s
scale刻度

How much each gridline stands for, e.g. one square = 5.

d
difference相差

Subtracting the two values, e.g. 12 − 8 = 4.

t
total總和

Both sets (or everything) added together.

s
survey調查

Collecting data, e.g. asking the class their favourite sport.

3Step by step Steps

  1. Part 1: What a double bar chart looks likeA double bar chart compares two sets of data. To compare the sports Class A and Class B like best, every sport on the horizontal axis has two bars side by side: one for Class A, one for Class B, drawn touching each other. The side-by-side design lets the two groups be compared directly within the same category, without flipping between two separate charts — quick and accurate.
  2. Part 2: The legend is the keyThe legend, usually in a corner, uses colour squares and words: blue means Class A and orange means Class B. The legend is the key to the whole chart — without it nobody can tell which bar belongs to which class, and no comparison is possible. So the first step in reading is always to check the legend; when drawing your own chart, never forget to add one, or readers will mix up the two sets.
  3. Part 3: Check the scale, then readBefore reading any bar, confirm the vertical scale: what each grid line is worth. If each line means 5 people, then in the football pair the blue bar reaches line 2, so 2 × 5 = 10 people, while the orange bar reaches line 3, so 3 × 5 = 15 people. Mistake the grid for 1 and every reading is only a fifth of the truth. The safe order is: check the scale, count the lines, then multiply.
  4. Part 4: Compare side by sideComparing the two bars within one category gives the gap between the classes. In football the orange bar is taller, so Class B has more fans: 15 − 10 = 5 people. The height difference between the two bar tops equals the difference between the two groups, so differences are found by subtraction: larger minus smaller. The design shows the gap at a glance, but written answers still need the subtraction and the unit.
  5. Part 5: Biggest gap and totalsWork out each gap in turn and the biggest one stands out: football differs by 5, basketball by 10, while swimming is 9 in both classes — a difference of 0 — so basketball shows the largest contrast. If the question asks for a total instead, such as how many in both classes like football, switch to addition: 10 + 15 = 25. Always check whether the question wants a difference (subtract) or a total (add).
  6. Part 6: Drawing one wellTo draw your own double bar chart: first list the categories on the horizontal axis; second choose a vertical scale that still fits the largest value; third draw two equal-width, touching bars for every category at the correct heights; fourth colour the two sets differently; fifth write the legend in a corner and add a title. Without a legend or with an unclear scale the chart loses its value, so check every part after drawing.

4Diagrams Diagrams

棒形圖:比較多少 Bar chart0246810本數 books6小明4小紅9小剛2小美看圖答題:最多——小剛 9 本;小明比小紅多 2 本;小美最少棒形圖專門做比較——棒越長,數越大,一眼排序 all bars share the same scale
Fig. 1: Bar chart comparison

5Worked example Example

Example: the scale is 5 people per grid line. In basketball, Class A's bar reaches line 2 and Class B's reaches line 4. (1) Which class has more? (2) How many more?

  1. Class A: 2 grid lines at 5 people each, so 2 × 5 = 10 people.
  2. Class B: 4 × 5 = 20 people; the orange bar is clearly taller.
  3. (1) Compare the two bars: 20 > 10, so Class B has more people.
  4. (2) Find the gap: 20 − 10 = 10, so Class B has 10 more.
  5. Answer: Answer: (1) Class B has more; (2) by 10 people. To read a double bar chart, confirm the scale first, read each bar's height, then subtract to find the gap, and the comparison cannot go wrong.

6Common mistakes Mistakes

✗ Assuming blue is always Class A without the legend
✓ Always confirm with the legend which colour is which set
✗ Adding the two bars when asked for the difference
✓ Difference is subtraction: 20 − 10 = 10; adding gives the total
✗ Reading each gridline as 1
✓ Check the scale first: this chart counts by 5
✗ Comparing bars from different categories
✓ Only compare the pair within one category

7Quick check Quick check

Q1How many bars per category in a double bar chart?

Q2What does the legend do?

Q3Class A 8, Class B 12 — the difference?

Q4Scale is 5 per line; the bar reaches line 3. The value?

Q5Both classes have 9 liking swimming — the total?

8Recap Recap

  • A double bar chart pairs two bars per category to compare sets
  • The legend names each colour's set — it is essential
  • Read the scale first: lines × scale
  • Difference: subtract; total: add
  • Compare only within the same category

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