Chapter Overview
Data becomes useful when it answers a clear question. This chapter covers collection, organisation, representative values and visual displays that help us recognise patterns without hiding variation.
This chapter belongs to Ganita Prakash, Grade 7. Focus on explaining each step, checking whether an answer is reasonable, and comparing more than one solution method.
Learning Objectives
After studying this chapter, you should be able to:
- explain and apply statistical questions;
- explain and apply mean and median;
- explain and apply data displays;
- explain and apply interpreting variation;
- communicate the reasoning behind a solution clearly;
- check answers using estimation, substitution, or a second method.
Key Concepts
| Concept | Meaning | |---|---| | Statistical questions | A statistical question expects varied data, such as the travel time of students, rather than one fixed answer. | | Mean and median | The mean is total divided by count. The median is the middle ordered value, or the mean of the two middle values. | | Data displays | Tables, dot plots and bar graphs organise values; double bar graphs compare two related datasets. | | Interpreting variation | A representative value summarises data but should be considered together with spread, clusters and unusual values. |
Detailed Explanation
Statistical questions
A statistical question expects varied data, such as the travel time of students, rather than one fixed answer.
Mean and median
The mean is total divided by count. The median is the middle ordered value, or the mean of the two middle values.
Data displays
Tables, dot plots and bar graphs organise values; double bar graphs compare two related datasets.
Interpreting variation
A representative value summarises data but should be considered together with spread, clusters and unusual values.
Do not memorise a rule without testing it on examples. Ask what each number, operation, line, or symbol represents and whether the result fits the original situation.
Important Rules and Formulae
- Order data before finding the median.
- Label axes, categories and units on every graph.
- Do not use a broken or uneven scale unless it is clearly shown.
Worked Examples
Example 1
Problem: Find the mean and median of 3, 5, 5, 7, 10.
Solution: Mean = 30÷5 = 6; median = 5.
Example 2
Problem: Find the median of 4, 8, 10, 15.
Solution: The middle values are 8 and 10, so median = 9.
Show the mathematical statement, substitution or construction step before writing the final answer. Include units wherever the quantity is measured.
Common Mistakes
- Dividing the sum by the largest value instead of the number of observations.
- Finding the median before arranging the data.
- Drawing bars of unequal width or using an inconsistent scale.
Quick Revision
- Statistical questions: A statistical question expects varied data, such as the travel time of students, rather than one fixed answer.
- Mean and median: The mean is total divided by count.
- Data displays: Tables, dot plots and bar graphs organise values; double bar graphs compare two related datasets.
- Interpreting variation: A representative value summarises data but should be considered together with spread, clusters and unusual values.
Practice Questions
- Find the mean of 6, 8, 10, 12.
- Find the median of 9, 2, 7.
- Which graph is useful for comparing two groups across categories?
- Can one extreme value strongly affect the mean?
Answers and Explanations
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-
- A double bar graph.
- Yes.
Self-Check
Explain one rule from this chapter in your own words, create a fresh example, solve it, and verify the answer. If the explanation and verification agree, the concept is understood rather than merely memorised.