IB MYP 4-5 Maths- Data manipulation and misinterpretation- Study Notes - New Syllabus
IB MYP 4-5 Maths- Data manipulation and misinterpretation – Study Notes
Standard
- Data manipulation and misinterpretation
IB MYP 4-5 Maths- Data manipulation and misinterpretation – Study Notes – All topics
Data Manipulation and Misinterpretation
Data manipulation and misinterpretation happen when data is presented or summarized in a way that gives a false or misleading impression. This can occur intentionally (to persuade) or unintentionally (due to poor design or lack of understanding).
Why Misinterpretation Happens:
- Truncated or inconsistent scales: Axis does not start at zero or uses uneven intervals, making small changes look significant.
- Using wrong type of graph: For example, a pie chart to show change over time.
- 3D effects and distortions: Can make some data sections appear larger than they are.
- Missing context: Lack of information about sample size, source, or time period.
- Biased sampling: Non-representative samples leading to incorrect conclusions.
Other Common Issues:
- Selective reporting: Showing only part of the data that supports a claim.
- Misleading averages: Using mean instead of median when data is skewed.
- Percentage tricks: Presenting percentage increases without base values (e.g., “100% increase” from 1 to 2).
How to Avoid Misinterpretation:
- Always check scales and labels on graphs.
- Ask for the sample size and sampling method.
- Choose graphs that correctly represent the data type (e.g., line graph for trends, bar graph for categories).
- Beware of 3D effects or exaggerated colors that draw attention unnecessarily.
Example:
A bar chart compares two sales figures: Year 1 = $\$98,000$ and Year 2 = $\$102,000$. The vertical axis starts at $\$95,000$, making the bars look very different. Why is this misleading?
▶️Answer/Explanation
Step 1: The actual difference is $\$4,000$, which is small compared to $\$98,000$.
Step 2: Starting the axis at $\$95,000$ exaggerates this difference visually.
Answer: The graph misleads by truncating the axis, making a small increase seem large.
Example 2:
A company advertises “Sales increased by 200%!” without revealing that sales went from 5 units to 15 units. Why is this misleading?
▶️Answer/Explanation
Step 1: Percentage looks large but actual increase is small (10 units).
Step 2: Without original values, the statement can mislead customers into thinking growth is huge.
Answer: Always check both percentage and absolute values before interpreting growth.
Example:
Look at the pie chart below showing favorite fruits of 20 students. The chart shows $50\%$ for apples, $40\%$ for oranges, and $15\%$ for grapes. What is wrong?
▶️Answer/Explanation
Step 1: Add percentages: \(50 + 40 + 15 = 105\%\).
Step 2: Percentages must total 100%, so data is incorrect or misrepresented.
Answer: The chart is misleading because the total percentage exceeds 100%.
Example:
A graph compares two schools’ average test scores. School A $= 68\%$ School B $= 72\%$. The bars are drawn with a big gap, and the scale starts at $60\%$. What impression does this give?
▶️Answer/Explanation
Step 1: Actual difference is 4%, very small.
Step 2: Because the axis starts at 60%, the gap looks very large.
Answer: The graph is misleading because of a truncated scale exaggerating a small difference.
Important Notes:
- Percentages in a pie chart must add up to 100%.
- Always look for axis starting points and scale increments.
- Ask for actual numbers, not just percentages.
- Beware of terms like “doubles,” “triples,” or “huge increase” without context.