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GRADE 6 · MATHEMATICS

Data and Graphs

Data is information we collect to answer questions. Learn how to organise data in tables, read simple graphs and describe a set of numbers using the mean, median, mode and range.

Learning time: approximately 30 minutes · Beginner level

What You Will Learn

1. What Is Data?

Data is a collection of facts or measurements. It can be numbers, categories or observations.

A survey is one way to collect data. Always think about who was asked and whether the results fairly represent the group you want to understand.

2. Organise Data in a Frequency Table

Frequency means how many times a value or category appears.

Suppose students choose their favourite fruit:

FruitFrequency (students)
Apples6
Bananas4
Oranges5
Grapes3
Total18

The total frequency is 6 + 4 + 5 + 3 = 18 students.

3. Read a Bar Chart

A bar chart compares categories. Each bar represents a category, and its height or length shows the frequency or value. The scale should be clear and the bars should be separated.

Favourite fruit survey
Apples
6
Bananas
4
Oranges
5
Grapes
3

Apples are the most popular choice in this survey.

Always read the category labels and the scale before interpreting a chart.

4. Read a Line Graph

A line graph is often used to show how something changes over time. Points are plotted and joined in order. Look at the horizontal axis for time and the vertical axis for the measured value.

Example: A line graph of daily temperature can show whether the temperature rose, fell or stayed the same during the week.

Do not assume a line graph proves why a change happened. It shows a pattern, not necessarily the cause.

5. Find the Mean (Average)

The mean is found by adding all the values and dividing by how many values there are.

Mean = total of values ÷ number of values

Worked example: 4, 6, 8 and 10

  1. Add the values: 4 + 6 + 8 + 10 = 28.
  2. There are 4 values.
  3. Divide: 28 ÷ 4 = 7.

Mean = 7.

6. Find the Median

The median is the middle value when the data is arranged in order from smallest to largest.

Example 1: 3, 5, 7, 9, 11. The middle value is 7, so the median is 7.
Example 2: 2, 4, 6, 8. The middle values are 4 and 6. Their mean is (4 + 6) ÷ 2 = 5, so the median is 5.

7. Find the Mode and Range

Mode is the value that appears most often. A data set can have one mode, more than one mode or no mode.

Range is the difference between the largest and smallest values.

Example: In 2, 3, 3, 5, 7, the mode is 3. The range is 7 − 2 = 5.

8. Choose the Right Measure

MeasureWhat it tells youHow to find it
MeanAverage valueAdd values, divide by count
MedianMiddle valueOrder data, find the middle
ModeMost frequent valueFind the value appearing most
RangeSpread from lowest to highestLargest minus smallest

The mean can be affected by unusually high or low values. The median can sometimes describe the centre better when the data has an extreme value.

9. Common Mistakes to Avoid

Finding the median before ordering: Always arrange the numbers from smallest to largest first.
Dividing the mean by the wrong number: Count every data value, not the number of different values.
Confusing mode and median: Mode is most frequent; median is the middle value.
Forgetting the range calculation: Subtract the smallest value from the largest value.
Reading a graph without its scale: Check the axis labels and intervals before interpreting it.

10. Practice Exercises

Try these before revealing the answers.

  1. Find the mean of 3, 5, 7 and 9.
  2. Find the median of 2, 8, 4, 6 and 10.
  3. Find the mode of 1, 3, 3, 4, 5, 3 and 6.
  4. Find the range of 12, 5, 8, 15 and 9.
  5. A frequency table shows 4 students chose cats, 7 chose dogs and 3 chose fish. How many students answered?
  6. Find the median of 3, 5, 7 and 11.
  7. Explain one difference between a bar chart and a line graph.
Show practice answers and explanations
  1. (3 + 5 + 7 + 9) ÷ 4 = 24 ÷ 4 = 6.
  2. Order: 2, 4, 6, 8, 10. Median = 6.
  3. Mode = 3 because it appears most often.
  4. 15 − 5 = 10.
  5. 4 + 7 + 3 = 14 students.
  6. The middle values are 5 and 7. Median = (5 + 7) ÷ 2 = 6.
  7. A bar chart compares categories; a line graph often shows change over time.

11. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. What is the mean of 2, 4 and 6?
2. What is the median of 1, 3, 5, 7 and 9?
3. What is the mode of 2, 4, 4, 5 and 7?
4. What is the range of 3, 8, 10 and 12?
5. Which graph is commonly used to show change over time?

12. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Data and Graphs Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working and write answers clearly.

  1. Find the mean of 5, 7, 9 and 11.
  2. Find the median of 4, 8, 2, 10 and 6.
  3. Find the mode of 3, 4, 4, 5, 6, 4 and 7.
  4. Find the range of 14, 8, 19, 11 and 6.
  5. A survey records 8 votes for blue, 5 for green and 7 for red. Find the total number of votes.
  6. Find the median of 2, 4, 8 and 10.
  7. Explain when a line graph is useful.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. (5 + 7 + 9 + 11) ÷ 4 = 8.
  2. Ordered: 2, 4, 6, 8, 10. Median = 6.
  3. Mode = 4.
  4. 19 − 6 = 13.
  5. 8 + 5 + 7 = 20 votes.
  6. Middle values 4 and 8; median = (4 + 8) ÷ 2 = 6.
  7. A line graph is useful for showing how a value changes over time.

13. Lesson Summary

Next learning goal: Explore probability and how to describe the chance of an event.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.