Bar chart: travel to school
Bus
Walk
Car
Cycle
Most pupils travel by bus. The difference between bus and cycle is 18 - 6 = 12 pupils.
Back to National 4
Topic
Statistics and Data
Statistics is about collecting, summarising, graphing and interpreting data. You will use averages, range, bar charts, pie charts, line graphs, scattergraphs and comparisons.
Topic explanation
Bar charts, pie charts and line graphs each answer different questions. Read titles, labels, scales and units before calculating.
A scattergraph plots paired values such as study time and test score, temperature and ice cream sales, or age of car and value.
Positive correlation means both values tend to increase together. Negative correlation means one tends to decrease as the other increases. No correlation means there is no clear pattern.
A line of best fit is a sensible straight line through the middle of the points. Use it to estimate, but avoid claiming that correlation proves cause.
Graph and data examples
Pie chart: screen time
- Video: 40%
- Games: 25%
- Messages: 20%
- Other: 15%
A pie chart shows parts of a whole. 25% is one quarter, so its angle is 90 degrees.
Frequency table: test scores
| Score | Frequency |
|---|---|
| 4 | 2 |
| 5 | 5 |
| 6 | 8 |
| 7 | 4 |
| 8 | 1 |
The most common score is 6 because it has the highest frequency. The total frequency is 20.
Line graph: savings over weeks
The values increase each week, so the trend is upward over time.
Positive correlation
Study time and test score
The line slopes up, so this shows positive correlation.
Negative correlation
Age of car and value
The line slopes down, so this shows negative correlation.
No correlation
Shoe size and favourite subject
The points have no clear upward or downward pattern.
What to look for
Read the title, labels and scale first. For scattergraphs, judge the overall direction of the points and line.
Watch out
Describe the whole trend rather than one unusual point, and remember correlation does not prove cause.
Practise
Find the most common value, compare two bars, estimate from a line of best fit and explain the trend in context.
Quick methods
- Choose a graph
- Use bar charts for categories, line graphs for time, and scattergraphs for two linked measurements.
- Correlation
- Positive rises, negative falls, and no correlation has no clear pattern.
- Line of best fit
- Draw or choose a line through the middle of the points and use it to estimate.
- Compare data
- Use averages, range and graph trends to make a clear comparison.
Worked examples
Example 1
A bar chart has values 4, 7, 9, 10 and 12. Find the range.
- The largest value is 12.
- The smallest value is 4.
- Range = largest − smallest = 12 − 4
So: The range is 8.
Example 2
A line graph shows sales of 6, 8, 10 and 12 over four weeks. Find the mean weekly sales.
- Add the values: 6 + 8 + 10 + 12 = 36
- There are 4 values.
- Divide by 4: 36 divided by 4 = 9
So: The mean is 9.
Example 3
A scattergraph compares hours worked and pay. The points rise from left to right. Describe the correlation.
- Look at the overall pattern, not one point.
- The points rise as hours worked increases.
- This means both values tend to increase together.
So: There is positive correlation.