- Define and explain Interpreting data honestly in your own words
- Use key terms such as Median accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
This lesson focuses on Interpreting data honestly: reading claims critically and spotting misleading scales and cherry-picked averages.
Reading claims critically and spotting misleading scales and cherry-picked averages.
Key ideas
Reading charts carefully
Check the axes first: a bar chart that starts above zero can exaggerate small differences, and a pie chart must show sectors proportional to the data. Frequency diagrams need equal class widths, or frequencies must be scaled by width.
Choosing an average
Use the mean for symmetric data with no extremes, the median when a few extreme values would distort the mean (such as salaries), and the mode for categories (such as favourite colours). Always consider the range too, since identical averages can hide very different spreads.
Key term — Median: The middle value when data is ordered from smallest to largest; a robust average unaffected by extreme values.
Why might a bar chart with a y-axis starting at 50 be misleading?
Bars look far more different than the values are, because the truncated axis exaggerates small differences.
Answer: Bars look far more different than the values are, because the truncated axis exaggerates small differences.
- Reading a truncated bar chart at face value If the y-axis does not start at zero, bars exaggerate differences — check the scale before comparing.
- Finding the median without ordering the data Always sort the values first; the median is the middle of the ordered list, not the middle of the original list.
Practice
The median (7.5); the mean (12.5) is distorted by the outlier 40.
Sum = 50; mean = 50 ÷ 5 = 10.
Ordered: 2, 4, 7, 9, 11; median = 7.
Mode = 6; range = 6 − 2 = 4.
Quick check
Which of these best defines "Median"?
A scatter diagram shows points rising left to right. What type of correlation is this?
- Interpreting data honestly: reading claims critically and spotting misleading scales and cherry-picked averages.
- Reading charts carefully: Check the axes first: a bar chart that starts above zero can exaggerate small differences, and a pie chart must show sectors proportional to the data.
- Range: The difference between the largest and smallest values, giving a simple measure of how spread out the data is.
- Watch out for: reading a truncated bar chart at face value