Graphs and Data

Key Concepts

• Graphs and data are ways of showing information clearly so we can:

  • read values
  • compare results
  • spot patterns
  • describe changes
  • draw conclusions

• In PSLE Mathematics, graphs and tables are often used to show:

  • data collected from surveys or measurements
  • changes over time
  • comparisons between groups
  • relationships between quantities

• When reading any graph or table, always look at:

  • the title
  • the labels
  • the units
  • the scale
  • the key or legend, if any

• A title tells you what the graph or table is about.

• A label tells you what each axis, row, column, or section represents.

• A unit tells you how the measurement is recorded, such as:

  • cm
  • g
  • °C
  • minutes
  • %

• A scale shows the value of each division or marking on an axis.

  • Example: each small square may represent 1 unit, 2 units, 5 units, or 10 units.
  • You must read the scale carefully before giving an answer.

• A variable is something that can change in an experiment.

  • Example: time, temperature, height of plant, amount of water

• The x-axis is the horizontal axis.

  • It usually shows the independent variable, often time or categories.

• The y-axis is the vertical axis.

  • It usually shows the dependent variable, which is what is measured.

• The independent variable is the factor that is changed on purpose.

  • Example: number of days, amount of light, type of material

• The dependent variable is the factor that is measured or observed.

  • Example: plant height, temperature, distance moved

• Data analysis means studying the information shown to:

  • identify highest and lowest values
  • compare data
  • describe increases or decreases
  • find patterns or relationships
  • support conclusions with evidence

Reading and Interpreting Bar Graphs

• A bar graph uses rectangular bars to show and compare values in different groups or categories.

• In a bar graph:

  • each bar represents one category
  • all bars should have the same width
  • bars are separated by spaces
  • the height or length of each bar shows the value

• Bar graphs are useful for comparing:

  • number of students
  • types of animals
  • amounts of rainfall in different months
  • number of seeds germinated under different conditions

• To read a bar graph:

  1. Read the title.
  2. Check what the x-axis and y-axis represent.
  3. Look at the unit on the y-axis.
  4. Read the scale carefully.
  5. Match the top of the bar to the correct value.

• When comparing bars, use scientific language such as:

  • “A has the highest value.”
  • “B is lower than C.”
  • “The difference between A and D is 5 units.”

• If asked to find the difference, subtract:

  • larger value − smaller value

• If asked to find the total, add all relevant values.

Line Graphs and Trends

• A line graph uses plotted points joined by lines to show how something changes, usually over time.

• Line graphs are useful for showing:

  • temperature changes during the day
  • plant growth over weeks
  • water level changes over time
  • speed changes during motion

• In a line graph:

  • the x-axis usually shows time or another continuous variable
  • the y-axis shows the measured value
  • each point represents one reading
  • points are connected to show change or trend

• A trend is the general pattern in the data.

• Common trends:

  • increase: values go up
  • decrease: values go down
  • constant: values stay the same
  • fluctuate: values go up and down

• When describing a line graph, use words like:

  • increases gradually
  • increases sharply
  • decreases slowly
  • remains constant
  • reaches a maximum
  • reaches a minimum

• A maximum is the highest value.

• A minimum is the lowest value.

• If a line rises from left to right:

  • the measured value is increasing

• If a line falls from left to right:

  • the measured value is decreasing

• If the line is horizontal:

  • the measured value remains constant

• To interpret trends in Science:

  • do not just describe the graph
  • connect it to the scientific idea if the question asks for it
  • Example: “The plant grew taller over 5 days, showing that growth increased with time.”

Pie Charts

• A pie chart is a circle divided into sectors to show parts of a whole.

• The whole circle represents:

  • the total amount
  • 100%
  • 360°

• Each sector represents a category.

• The larger the sector:

  • the greater the amount or percentage

• Pie charts are useful for showing:

  • fractions
  • percentages
  • proportions

• To read a pie chart:

  1. Read the title.
  2. Check the labels or legend.
  3. Find the fraction, percentage, or angle for each sector.
  4. Compare sector sizes.

• Important facts:

  • full circle = 360°
  • half circle = 180°
  • quarter circle = 90°
  • total percentage = 100%

• If you know the angle of a sector:

  • fraction of whole = angle ÷ 360
  • percentage = (angle ÷ 360) × 100%

• If you know the percentage:

  • angle = (percentage ÷ 100) × 360°

• If you know the total number:

  • category value = fraction × total
  • or category value = percentage × total

• Example:

  • If 25% of a pie chart represents 40 pupils, then total number of pupils is:
    • 40 ÷ 25 × 100 = 160 pupils
  • A quicker method:
    • 25% = 1/4
    • total = 40 × 4 = 160

Tables and Diagrams

• A table organises data into rows and columns.

• Tables help us:

  • read values quickly
  • compare observations
  • identify patterns
  • record experiment results neatly

• A table usually includes:

  • a title
  • row headings
  • column headings
  • units

• To read a table:

  1. Read the title.
  2. Look at the headings.
  3. Check the units.
  4. Read values carefully from the correct row and column.

• In Mathematics, tables often record:

  • quantities and amounts
  • scores and frequencies
  • measurements and lengths
  • costs and totals
  • time and distance values

• A diagram is a labelled drawing used to show information clearly.

• In data questions, diagrams may include:

  • pictures with labels
  • symbols
  • simple visual comparisons
  • comparison tables, frequency tables, or schedule diagrams

• Sometimes a pictogram is used.

  • A pictogram uses pictures or symbols to represent data.
  • A key tells how much each symbol represents.
  • Example: 1 picture = 2 animals

• Always check the key carefully.

  • A half-symbol may represent half the value of one full symbol.

Data Analysis and Comparison

• Data analysis means examining data carefully to understand what it shows.

• In PSLE Mathematics data questions, you may need to:

  • compare two sets of data
  • identify trends or patterns
  • state similarities and differences
  • read values accurately from graphs or tables
  • calculate totals, averages, or percentages from data

• A comparison tells how two or more things are alike or different.

• Good comparison answers should:

  • mention both items
  • use correct values
  • include units where needed
  • state whether one is greater, smaller, faster, slower, more, less, same, or different

• Useful comparison phrases:

  • “___ is greater than ___.”
  • “Both ___ and ___ increased over time.”
  • “___ showed the largest change.”
  • “The difference between ___ and ___ is ___.”
  • “___ remained constant while ___ increased.”

• A conclusion is a statement that sums up what the data shows.

• A good scientific conclusion:

  • is based only on the data given
  • uses evidence from the graph or table
  • does not include guesses not supported by data

• Example:

  • Weak conclusion: “Plant A is better.”
  • Better conclusion: “Plant A grew the tallest, reaching 18 cm after 4 weeks.”

• If asked to give evidence:

  • quote actual values from the data
  • Example: “Group B had 12 seeds germinate, while Group A had 8.”

Important Definitions

• Bar graph: a graph that uses rectangular bars to show and compare values in different categories.

• Line graph: a graph that uses points joined by lines to show changes over time or across continuous data.

• Pie chart: a circle divided into sectors to show parts of a whole.

• Table: a chart that organises information into rows and columns.

• Diagram: a labelled drawing or visual representation used to show information clearly.

• Pictogram: a chart that uses pictures or symbols to represent data.

• Title: the heading that tells what the graph, table, or chart is about.

• Axis: a reference line on a graph used for plotting data.

• X-axis: the horizontal axis on a graph.

• Y-axis: the vertical axis on a graph.

• Scale: the value represented by each division on an axis.

• Unit: the standard measurement used, such as cm, g, min, or °C.

• Variable: a factor that can change in an experiment.

• Independent variable: the factor that is changed on purpose.

• Dependent variable: the factor that is measured or observed.

• Trend: the general pattern shown by data.

• Increase: to become greater in value.

• Decrease: to become smaller in value.

• Constant: staying the same without change.

• Maximum: the highest value in a set of data.

• Minimum: the lowest value in a set of data.

• Sector: a section of a pie chart.

• Percentage: a value out of 100.

• Fraction: a way of showing part of a whole.

• Data analysis: studying data to identify patterns, compare results, and draw conclusions.

• Conclusion: a statement that explains what the results show.

• Evidence: information from the data used to support an answer or conclusion.

Worked Examples

Example 1: Reading a Bar Graph

A bar graph shows the number of beans that germinated in 4 trays.

• Tray A: 6
• Tray B: 10
• Tray C: 8
• Tray D: 4

Question:

Which tray has the highest number of germinated beans, and how many more beans germinated in Tray B than in Tray D?

Step-by-step solution:

1. Find the highest bar.

   • Tray A = 6
   • Tray B = 10
   • Tray C = 8
   • Tray D = 4
   • Highest value = 10

2. State the tray with the highest number.

   • Tray B has the highest number of germinated beans.

3. Find the difference between Tray B and Tray D.

   • Tray B = 10
   • Tray D = 4
   • Difference = 10 − 4 = 6

Answer:

• Tray B has the highest number of germinated beans.
• 6 more beans germinated in Tray B than in Tray D.

Example 2: Interpreting a Line Graph

A line graph shows the height of a plant over 5 weeks.

• Week 1: 4 cm
• Week 2: 6 cm
• Week 3: 9 cm
• Week 4: 9 cm
• Week 5: 12 cm

Question:

Describe the trend in the plant’s growth.

Step-by-step solution:

1. Read the values in order.

   • 4 cm → 6 cm → 9 cm → 9 cm → 12 cm

2. Look for changes.

   • From Week 1 to Week 3, the height increased.
   • From Week 3 to Week 4, the height remained constant.
   • From Week 4 to Week 5, the height increased again.

3. Write the trend clearly.

   • The plant grew taller overall from Week 1 to Week 5.
   • Its height increased from 4 cm to 9 cm in the first 3 weeks, remained constant at 9 cm from Week 3 to Week 4, then increased to 12 cm by Week 5.

Answer:

The plant’s height increased overall. It increased from Week 1 to Week 3, remained constant from Week 3 to Week 4, and increased again from Week 4 to Week 5.

Example 3: Reading and Calculating from a Pie Chart

A pie chart shows how 40 pupils travel to school.

• Bus: 50%
• Car: 25%
• Walk: 15%
• Bicycle: 10%

Question:

How many pupils travel to school by car and by bicycle altogether?

Step-by-step solution:

1. Find the percentage for car and bicycle.

   • Car = 25%
   • Bicycle = 10%
   • Total percentage = 25% + 10% = 35%

2. Calculate 35% of 40 pupils.

   • 35% of 40
   • = 35/100 × 40
   • = 14

3. State the answer.

   • 14 pupils travel by car and bicycle altogether.

Answer:

14 pupils

Common Mistakes to Avoid

• Not reading the title of the graph or table.
• Ignoring the units and giving answers without units when needed.
• Reading the scale wrongly.
  • Example: each division may represent 2 or 5, not 1.
• Confusing the x-axis and y-axis.
• Saying a value is increasing when the line is actually decreasing.
• Forgetting that a horizontal line means the value is constant.
• Giving a comparison without using actual data values.
• Writing conclusions that are not supported by the data.
• Forgetting to add all parts when finding a total.
• Subtracting in the wrong order when finding a difference.
• In pie charts, forgetting that:
  • total angle = 360°
  • total percentage = 100%
• Misreading the key in a pictogram.
• Forgetting that a half-symbol represents half the value.
• Copying data wrongly from the wrong row or column in a table.
• Describing only one item when the question asks to compare two items.

Exam Tips

• Always start by reading:

  • the title
  • labels
  • units
  • scale
  • key

• Underline command words such as:

  • state
  • compare
  • describe
  • calculate
  • conclude

• For compare questions:

  • mention both sets of data
  • use words like “higher than”, “lower than”, “same as”
  • include values if possible

• For describe the trend questions:

  • use phrases like:
    • “increases”
    • “decreases”
    • “remains constant”
    • “increases at first, then remains constant”

• For calculate questions:

  • show the working clearly
  • write the correct unit in the final answer

• For conclusion questions:

  • base your answer only on the data given
  • support your answer with evidence

• Useful mark-earning phrases:

  • “The highest value is…”
  • “The lowest value is…”
  • “The difference is…”
  • “This shows that…”
  • “Based on the data…”
  • “___ increased from ___ to ___.”

• If the graph is about an experiment:

  • think about the scientific meaning of the trend
  • link the data to the experiment result if asked

• Check your final answer:

  • Is the number correct?
  • Did you include the unit?
  • Did you answer exactly what was asked?

Quick Summary

• Read the title, labels, units, scale, and key before answering.
• A bar graph compares values in different categories.
• A line graph shows changes and trends, often over time.
• A pie chart shows parts of a whole; whole circle = 360° = 100%.
• A table organises data into rows and columns for easy reading.
• A pictogram uses symbols, so always check the key.
• The x-axis is horizontal; the y-axis is vertical.
• A trend may show an increase, decrease, constant value, or fluctuation.
• To compare data, use actual values and words like higher, lower, same, or difference.
• To find a difference, subtract the smaller value from the larger value.
• To find a total, add the values correctly.
• A good conclusion must be based on the data and supported with evidence.