LF-P5-S2-L32 Composite bar chart + data analysis

Lam Fung Academy· LF Academy

Primary 5 · Lesson 32 · Student Handout

Composite bar chart + data analysis

Unit ten · statisticsanddatahandle · 65 minutes · 1-to-3 Online Lesson

Corresponding textbooks:"New Thinking in Primary School Mathematics (Second Edition)" Volume 5B Unit 10 + Modern Education 5L B Unit 19
Core Trap:🪴 T10 Statistics and Data - Confusing different groups of rods · Ignoring the legend · Unit conversion error
SSPA association:🟡 Medium and high frequency6-8 mark picture reading questions are often given in the test paper
Prerequisite knowledge:Understand compound bar graphs (including legends, scales, double classifications) ❷ Compare and analyze data ❸ Draw bar graphs based on data tables ❹ Averages and statistical reasoning
Our goals:❶ Understand compound bar graphs (including legends, scales, double classifications) ❷ Compare and analyze data ❸ Draw bar graphs based on data tables ❹ Averages and statistical reasoning

Student Name: Class: Date: Time Spent:

I.Warm-Up Questions（total 6 question，5 minutes）

📊 數據解碼員

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🔓 開始解碼 →

Question

Difficulty

Working Space（Show full working）

In a bar chart, the height of a bar represents 25 students. If the height of the rod corresponds to a scale of 4, how many students does the rod represent?

Basic

Look at the simple bar chart below:
Class 5A has 30 people, Class 5B has 28 people, Class 5C has 32 people, and Class 5D has 26 people. Which class has the largest number of people? How many more people are there in class 5A than in class 5D?

Basic

Each grid on the vertical axis of the bar chart represents 10 books. If a stick occupies 7 and a half squares, how many books does it represent?

Advanced

The following is a four-month sales data table for a store:

monthly parts	January	February	March	April
Sales (pieces)	120	150	180	140

Which month has the highest sales? How many more items than the lowest month?

Basic

The following table shows the statistics of the favorite fruits of the two classes. How many "rods" do you need to draw the data into a simple bar chart?

	Apple	Banana	Orange
5A	12	8	15
5B	10	14	9

Advanced

Xiaowen counted the number of books borrowed in four months: 120, 95, 150, 135. Find the averagenumber of books borrowed per month in these four months.Number of books borrowed per month.

Advanced

II.Core Knowledge ＋ Worked Examples

Knowledge Point 1: Reading Composite Bar Chart🟡 SSPA

❶ Composite bar chart= Displaystwo or more sets ofdata in the same chart, each group is distinguished by a different color/pattern
❷ Three key reading steps |||SEP|||: Look firstLegend(Legend)→ Then look atHorizontal axis(x-axis, classification) → Look againVertical axis(y-axis, value/scale)❸ Each classification position has multiple bars (representing different groups), you must
Check the legendto confirm what each bar represents❹ When reading the value: From the top of the
vertical axis to the pastvertical axis scale, count carefully one grid at a time.Vertical axis scale, carefully count each grid

📊 Reference chart: Stationery store quarterly sales data composite bar chart

▲ The above composite bar graph is the main reference chart in this class. Most of the examples and exercises are based on the data of this graph.

📊 Simple bar chart example: match score

▲ Each square represents 2 points. The red team has 18 points = 9 squares, and the blue team has 24 points = 12 squares. Note: Axis labels should be clear and scales should be even.

💡 Bar chart vs line chart – when to use which?

Bar charts are used to compare quantities in different categories; line charts are used to show trends in the same data over time. The following two representations of the same set of data:

▲ Left: Bar chart (emphasis on comparison of monthly values) | Right: Line chart (emphasis on upward/downward trends) - note that the two usage scenarios are different!

🪴 Trap detonation example (the most important demonstration in this class)

According to the composite bar chart above: How many pieces of “store A notebooks” were sold in January? How many pieces of “store B notebooks” were sold in January?

❌ Common mistakes (not looking at the legend)

January = only looking at the first bar = 100
But I can’t tell which store it is

Confuse store A notebook and store B notebook! There is no reference to the legend to confirm the meaning of each bar.

✅ Correct solution

Store A notebook (January) = 100 pieces
Store B Notebook (January) = 130 pieces

Look at the legend first → Confirm the direction of the twill → The first line in the first set of notebooks in store A = 100, the third line in the first set of notebooks in store B = 130

🧠 Tip: "First look at the illustration to identify the pattern, then find the correct position of the month, pull the line horizontally to read the scale, and the answer units must be written in the same order."

⚠️ The most frequent error: Reading directly without looking at the legend first, mistaking store A for store B and mistaking the notebook for a folder!

⚠️ The second most frequent error: incorrect number of vertical axis cells. Each grid = 25 pieces (50÷2), not 10 pieces or 100 pieces!

Knowledge Point - Worked Examples (first look at the legend → find the category → read the scale → write answer + unit)

#	Question	Difficulty	Working Space
Example 1	According to the composite bar chart: How many pieces of "Store B folders" were sold in February?	🌱
Example 2	According to the composite bar chart: What is the difference in the sales volume of "Store A Notebook" and "Store A Folder" in March?	🌿

Knowledge Point 1 Synchronization practice

#	Question	Difficulty
7	According to the composite bar chart: How many pieces of "store A notebook" and "store B notebook" were sold in total in January?	🌱
8	According to the composite bar chart: How many pieces of “store B notebooks” were sold in April?	🌱
9	According to the composite bar chart: In which month did "Store A folders" sell the most? How many pieces were sold?	🌿
10	According to the composite bar chart: How many units of all products (four bars) were sold in February?	🌿

Knowledge Point 2: Data Comparison and Analysis 🟡 SSPA

Four basic questions for comparing data from composite bar graphs:
❶ Find the difference |||SEP|||: The height difference of the two bars = subtract the values ("more", "less", "difference") |||SEP||：How many times one bar is the other = larger value ÷ smaller value
❷ Comparative trend：The trend of the same color bar in four months → rise/fall/first rise and then fall
❸ Find multiples: How many times one rod is the other = larger value ÷ smaller value
❹ Compare trends: The trend of the same color bar in four months → rising/falling/rising first and then falling

❶

Find the difference

Big, reduced, "difference", "how much more"

❷

Sum

Add them all up "Total" "Total"

❸

Find multiples

Big ÷ Small "How many times is..."

❹

look at trends

Month-to-month change direction for the same group

example

Example 3: According to the composite bar chart, in which month did "store A notebook" have the highest sales volume? How many times the sales volume of notebooks in store A was the sales volume of folders in store B in this month? (rounded to an integer)

example

Example 4: Based on the composite bar chart, describe the sales trend of "Store B Notebook" from January to April.

Knowledge Point 2 Synchronization practice

#	Question	Difficulty
11	According to the composite bar chart: In March, how many more notebooks did store A sell than folders in store A?	🌱
12	According to the composite bar chart: In January, how many pieces of the two types of products were sold in store B?	🌱
13	According to the composite bar chart: In April, how many times the sales of notebooks in store B were the sales of folders in store A?	🌳
14	According to the composite bar chart: Which store (store A or store B) has higher total sales volume of "notebooks" from January to April? How many pieces higher?	🌳

Knowledge point 3: Making a composite bar chart 🟡 SSPA

Steps to draw a composite bar graph from the data table:
❶ Determine the vertical axis scale |||SEP|||: Find the maximum value in the data and determine how much each cell represents (usually 2, 5, 10, 20, 25, 50, 100)Draw the coordinate axis |||SEP|||: Write the category name (such as month) on the horizontal axis, and mark the scale numbers and units on the vertical axis
❷ Drawing sticks |||SEP|||: Draw sticks with different patterns in each group in order (legend order); the height of the stick = data value ÷ Representative value of each cell × height of the cellAdd legend |||SEP|||: Mark what each pattern represents next to or below the chart
❸ Write a title |||SEP|||: Write a clear title above the chart: Draw bars with different patterns in each group in sequence (in the order of the legend); the height of the bar = data value ÷ representative value of each grid × grid height
❹ Add legend: Label next to or below the chart what each pattern represents.
❺ write title: Write a clear title above the chart

example

Example 5: The following table shows the number of extracurricular activities for two classes of students. If we want to use a composite bar chart to represent it, is it appropriate for each grid on the vertical axis to represent 5 people? Why?

	Football	Basketball	Swimming	Running
Class 5A	12	8	15	10
Class 5B	10	14	9	11

example

Example 6: Based on the data in the table above, calculate the total number of people in each activity of Class 5A and Class 5B, and determine which activity is the most popular.

⚠️ Production trap: If the vertical axis grid value is too large → the stick is too short and difficult to distinguish; if it is too small → the stick exceeds the range of the chart!

📐 Graduation formula: "Look at the maximum value, divide the number of cells, take an integer (2/5/10 times), and draw each cell clearly."

Knowledge Point 3 Synchronization practice

Question

Difficulty

Working Space

The table below shows the total sales of the two stores in four months. If each grid on the vertical axis represents 100 yuan, how many grids are needed to draw the highest value?

monthly parts	January	February	March	April
Total amount of store A ($)	300	450	520	380
Total amount of store B ($)	280	500	480	420

🌿

Continuing with the data table from the previous question: If you want to draw a composite bar chart, each grid represents 50 yuan, how many grids should be drawn for the sales volume of store B in March?

🌿

The following table shows the test scores (out of 100) for the two groups of students. What would happen if the vertical axis started at 60 minutes instead of 0?

	average Text	English	Mathematics
Group A average	72	68	75
Group B average	80	75	85

🌳

Based on the data in the composite bar chart, draw a simple data table to record the notebook sales of store A in four months. (No need to draw a picture, just write a data table)

🌿

📐 Drawing practice area — fromdatato chart

🖊️ Exercise 1: Draw a simple bar chart based on the table below

▲Data: 100 items in January, 120 items in February, 150 items in March, and 130 items in April. Each grid represents 25 pieces. Please draw a bar shape in the dotted box.

🖊️ Exercise 2: Draw a composite bar chart based on the table below

▲ For data, please refer to the composite bar chart of "Number of Extracurricular Activities for Two Classes" above. Note: Draw class 5A (blue) first, then draw class 5B (orange), with two sticks side by side in each group.

Knowledge Point 4: Statistical Applications - Averages, Estimation and Inference🟡 SSPA

Do statistical analysis from the composite bar chart:
❶ Mean= Sum ÷ Number of terms. For example: the four-month average monthly sales of laptops in store A = the sum of four months of sales ÷ 4
❷ Estimation |||SEP|||: Infer the sales of the next month based on the trend (see whether the trend is rising or falling, then give a reasonable number)Reasoning |||SEP|||: Analyze why the sales in a certain month are particularly high/low (perhaps holidays, exam seasons, weather, etc.)
❸ Comprehensive |||SEP|||: Combine picture reading + calculation + reasoning to answer more complex open-ended questions: Analyze why sales in a certain month are particularly high/low (perhaps holidays, exam season, weather, etc.)
❹ comprehensive: Combine picture reading + calculation + reasoning to answer more complex open-ended questions

example

Example 7: Based on the composite bar chart, find the average monthly sales volume of "store A notebook" from January to April.

example

Example 8: Based on the changing trend of "Laptops in Store B" from January to April in the composite bar chart, what is your estimate of the sales volume of notebooks in Store B in May? Why?

Knowledge Point Four Synchronization Practice

#	Question	Difficulty
19	Based on the composite bar chart: Find the average monthly sales volume of "Store A Folder" from January to April.	🌿
20	According to the composite bar chart: What is the total sales volume of "Store B folders" in four months? How many pieces per month on average?	🌿
21	According to the composite bar chart: Store A’s total sales (notebooks + folders, four months in total) and Store B’s total sales, which store is higher? How much difference?	🌳
22	If both stores have a "buy two, get one free" sale in May, how do you expect sales to change in May? Why? (Open question, just be reasonable)	🌳

III. Lesson Layered Synchronization Practice

Basic layer (total 3 questions, everyone must do)

#	Question	Difficulty
23	According to the composite bar chart: Which product sold the most in March? How many pieces?	🌱
24	According to the composite bar chart: What is the difference in the sales volume of the two products in store A in January?	🌱
25	According to the composite bar chart: Which of the four months had the lowest total sales of all items?	🌱

Advanced layer (total 3 questions, 🚶 🚀 choose do)

#	Question	Difficulty
26	According to the composite bar chart: Comparing the sales trends of "store A notebook" and "store B notebook" (from January to April), what are the similarities and differences between the two trends?	🌿
27	According to the composite bar chart: In which month did the notebook category (total of store A + store B) have the highest sales volume among the four months? What about the folder class?	🌿
28	According to the composite bar chart: If the data for January is accidentally obscured by the bar in the B store folder, can you infer the approximate number from the trends in other months? Give reasons.	🌳

🌳 challenge layer (total 3 questions, 🚀 choose do, SSPAKiller Questions)

Question

Difficulty

Working Space

Without the aid of charts: The following table shows the half-year sales data of stores A and B. Which store has a higher average monthly sales volume? How much difference?

monthly parts	January	February	March	April	May	June
Store A (10,000 yuan)	12	15	18	14	20	17
Store B (10,000 yuan)	14	13	19	16	18	22

🌳

The following table shows the number of members of the school's three societies, represented by a composite bar chart (each grid on the vertical axis represents 5 people).
5A: Computer 8, Music 12, Art 15 5B: Computer 14, Music 9, Art 11
(a) Draw the vertical axis label (b) Calculate the height of each bar (number of grids) (c) Draw a simple diagram (just draw the relative position and height)

🏔️

The following table shows the sales of two bookstores for three months, but some data are missing. It is known that store A’s April sales = store B’s April sales + 30, and the two stores sold a total of 720 in March.

monthly parts	February	March	April
Store A ($)	250	?	?
Store B ($)	200	380	?

Find: (a) Store A’s sales in March (b) If store A’s sales in April are 50 less than in March, what is the sales of store B in April?

🏔️

Knowledge point 5: Statistics application questions (subject to sub-test text questions) 🟡 SSPA compulsory exam

Four steps to solve the problem:❶ Circle keywords("average", "total", "difference", "several times" → choose the right calculation) ❷Extract data from the chart ❸ Column calculation ❹ Write a complete answer(Step points will be deducted if you do not write an answer!)

example

Example 9: The article counts the number of books borrowed from the library in the past four months: 270, 310, 290, 330. (a) Draw a simple bar graph (each cell represents 50 books) (b) Find the average monthly borrowing volume (c) If the borrowing volume in May is the average of the previous four months, how many more books are there in May than in January?

applicationquestionpractice (all must do, column → calculate → answer sentence)

Question

Difficulty

Working Space

The supermarket counts the monthly sales (boxes) of three types of drinks:
240 boxes of Coke, 180 boxes of orange juice, and 210 boxes of lemon tea.
If the data is drawn as a bar chart, and each grid on the vertical axis represents 30 boxes, how many grids are needed? (calculated separately for each drink)

🌿

The toy store sold 85 units in January, 95 units in February, 120 units in March, and 100 units in April.
(a) Find the average monthly sales
(b) Which month's sales are higher than the average? How much higher?

🌿

The table below shows the number of books donated by the two classes. Represented as a composite bar graph (each bar represents 10 books).

	Story book	Popular science book	Comics
5A (book)	40	30	50
5B (book)	35	45	25

(a) How many spaces are there in the comics of Class 5A? (b) Which type of books has the most total number of books in both classes? How many copies?

🌿

According to the composite bar chart data: If store A and store B are merged into a "chain store group", what is the total sales volume of the group each month from January to April? Draw a data table with a line chart of the group's total sales (no need to draw a graph, just list the data).

🌳

According to the composite bar chart data: (a) What percentage of store A’s notebook sales account for store A’s total sales? (b) What percentage of store B’s folder sales account for store B’s total sales? (The answer is expressed as a simple fraction)

🌳

IV.Class afterhomework

Basic must-do questions (total 4 questions)

Question

Difficulty

Working Space

According to the composite bar chart, which store had higher total sales (notebooks + folders) in April? How many pieces high?

🌱

According to the composite bar chart, what is the total sales volume of "store A notebooks" from January to April?

🌱

The table below shows the game scores. Draw a simple bar graph (each square represents 2 points) and find how many squares are needed for each bar.

Team	Red Team	Blue Team	Green Team	Yellow Team
Score	18	24	14	20

🌿

Based on the composite bar chart, calculate the average monthly sales volume of "B-store notebooks" from January to April.

🌿

Advanced choose doquestion (total 3 questions, 🚀 choose do)

Question

Difficulty

Working Space

The following table shows the sales data of the two stores, drawn as a composite bar chart. If each square on the vertical axis represents 20, how many squares are needed for each bar?

	Season 1	Season 2
Store X (items)	80	100
Store Y (items)	60	120

🌿

The table below shows the three-day turnover of the snack bar ($). Draw a composite bar graph, with each bar representing $100.

	Monday	Tuesday	Wednesday
Morning ($)	450	380	520
Afternoon ($)	600	550	480

(a) How many squares should be drawn on the stick on Wednesday morning? (b) Which time period (morning or afternoon) has higher total turnover?

🌳

Based on the composite bar chart, answer: If the combined total sales of the two stores in May increased by 15% compared with April, approximately how many units were sold in May? (Take an integer)

🌳

📐 Comprehensive drawing practice — full coverage of three types of charts

Must-haves for sub-tests: being able to read pictures, but also drawing pictures!

SSPA Paper 1 Frequently Asked Question Type: You are given a data table and asked to (a) draw a bar graph (b) draw a line graph (c) answer data questions.
The following three questions provide blank chart templates. Please complete the drawing according to the question data.

Paint 1

Question

chart

📊

The supermarket counts the monthly sales (boxes) of three types of drinks: 240 boxes of Coke, 180 boxes of orange juice, and 210 boxes of lemon tea. Please draw the bars in the blank bar graph below.

050100150200250300 (box) sales volume of Coke, orange juice and lemon tea. Please draw a bar chart of beverage sales (please draw a bar shape in the dotted box)

📊

The table below shows the number of donated books for the two classes. Please draw it in the blank composite bar chart below.

	Story book	Popular science book	Comics
5A (book)	40	30	50
5B (book)	35	45	25

0102030405060 (this) book quantity story book popular science book comic please accord to Q34data to draw the composite bar chart 5A class 5B class (please enter the dotted box and draw the bar shape according to data)

📈

Based on the composite bar chart data, calculate the total monthly group sales of store A + store B from one to four months after the merger, and then mark the data points and connect the lines in the line chart below.

0100200300400500600 (pieces) Sales volume January February March April Please draw the group's total sales line graph according to Q35data (please mark the points according to data and connect the lines)

📊 Circle chart (pie chart) example – stationery sales proportion

▲ Circle graphs are used to express "what fraction of a part accounts for the whole." The larger the fan shape = the higher the proportion.

🏔️Museum Admission Composite Stick Chart (🌳1 supporting template)

▲ Three patterns (adult/student/elderly) × four months. Use a pencil to sketch first, make sure the height is correct, and then add color.

V.🏔️ Ultimate challenge area

Question

Difficulty

Working Space

🏔1

Museum attendance statistics (people):

	January	February	March	April
Adults	320	280	450	380
Students	180	150	220	200
Elders	90	85	110	95

(a) Represented by a composite bar graph (three patterns) (b) Which month has the largest total number of visitors? (c) What is the average monthly student enrollment? (d) If total attendance in May is 10% greater than in April, estimate attendance in May.

🏔️

🏔2

Based on the original data of the composite bar chart, reorganize the table below and find out:
(a) Which store has the highest sales volume of which category of goods in which month?
(b) If store A earns $8 for each notebook and $5 for folders, and store B earns $7 for each notebook and $6 for folders, which store has a higher total profit?

🏔️

VI. The Lessoncorecommon errorsummary

✅ Self-examination in this hall (tick after completion)

☐ I know the pitfalls of solving each knowledge point ☐ I can complete 🌱basic questions independently ☐ I can challenge 🌿advanced questions ☐ I remember the formula

🎯 Review of Learning Objectives - After completing this lesson you should be able to:

☐ Identify all trap types in our hall ☐ Solve 🌱basic questions independently (100% correct) ☐ Challenge🌿Advanced questions (80%+ correct) ☐ Explain the lesson formula to classmates

#	common error	Correct Approach
1	Reading without looking at the legend first \|\|\|SEP\|\|\|: Treat store A as store B, treat the notebook as a folder: Treat store A as store B and treat your notebook as a folder	The first step is to look at the legend and confirm what each pattern represents.
2	Counting the wrong number of vertical axis cells \|\|\|SEP\|\|\|: Ignore the value represented by each cell and directly count the number of cells as the answer: Ignore the value represented by each cell and directly count the number of cells as the answer.	First confirm "each cell = ?", use the number of cells × the value of each cell = the actual value
3	Confusing "difference" and "multiple" \|\|\|SEP\|\|\|: use division for subtraction questions and subtraction for multiples questions: Use division for subtraction questions and subtraction for multiples questions	"How much different/more" → subtraction; "How many times is..." → division
4	Average calculation error \|\|\|SEP\|\|\|: Forgot to divide by the number of items, or add missing data: Forgot to divide by the number of items, or add missing data	First list all the data → sum → divide by the number of items → check whether the number of items is correct
5	Improper scale when making bar chart \|\|\|SEP\|\|\|: grid value is too large or too small: The grid value is too large or too small	Use the maximum value ÷ the expected number of cells → take the nearest integer (a multiple of 2/5/10)
6	Forgot to write the unit \|\|\|SEP\|\|\|: The answer only contains numbers, missing "pieces", "people", "yuan", etc.: The answer only contains numbers, leaving out "pieces", "persons", "yuan", etc.	The unit must be included in the answer for each step; the unit must also be written in the answer sentence
7	Ignore the background information provided by the chart title(such as time, location, unit)	Read the chart title → Understand the background → Then do data analysis

Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.

📚 Related topics: L16 Bar Chart Reading · L17 Bar Chart Production · L32 Composite Bar Chart