Different types of data suit different visual displays: a histogram or box plot suits numerical data with many values, a bar graph suits categorical comparisons, and a scatter plot suits examining a relationship between two numerical variables. Choosing the right display — and being able to justify why it suits the data and purpose — is as important as calculating the statistics themselves. A well-planned statistical investigation follows the full cycle: posing a genuinely investigable question, planning how to collect appropriate data, collecting it carefully, analysing it, and reporting findings honestly — including being upfront about how strong or weak the evidence actually is for any conclusion drawn.
Example
Investigating "is there a relationship between hours of study and test scores?" calls for a scatter plot (comparing two numerical variables), not a bar graph — and after collecting and plotting real data from classmates, a fair report would note not just whether a relationship appears, but how strong it looks and any obvious limitations, like a small sample size.
Key terms
Statistical investigation:
A structured process of posing a question, collecting data, analysing it and reporting findings.
Scatter plot:
A graph showing the relationship between two numerical variables using individual points.
Questions
1. A histogram or box plot suits:
Numerical data with many values
Only categorical data
Only two data points
No data at all
2. A bar graph suits:
Categorical comparisons
Only continuous numerical relationships
Only a single data point
Nothing measurable
3. A scatter plot suits examining:
A relationship between two numerical variables
A single category only
No relationship at all
Only text data
4. A statistical investigation should include:
Posing a question, collecting data, analysing and reporting
Only guessing an answer
Skipping data collection entirely
Only a title with no content
5. A fair report should be upfront about:
How strong or weak the evidence is for any conclusion
Nothing about the evidence's quality
Only the most favourable result
Only the researcher's opinion
6. Choosing the right display for data is:
As important as calculating the statistics
Completely unimportant
Only relevant for categorical data
Never required
7. Investigating hours of study versus test scores calls for a:
Scatter plot
Bar graph only
Pie chart only
No graph at all
8. Why would a scatter plot be more appropriate than a bar graph for investigating the relationship between study hours and test scores?
Both variables are numerical and continuous, and a scatter plot can show how they relate to each other
Bar graphs are always the correct choice for any two numerical variables
Study hours and test scores are categorical, not numerical, variables
The type of data has no bearing on which display is most appropriate
9. Why might a box plot be more useful than a simple bar graph for comparing the spread of two numerical data sets?
A box plot shows the distribution — median, spread and outliers — not just a single summary value per category
Bar graphs always show more detail about spread than box plots
Box plots and bar graphs display exactly the same information
Spread of data has no bearing on which display type suits it best
10. Why is it important for a statistical investigation to plan HOW data will be collected before starting, rather than deciding afterward?
Planning in advance helps ensure the data collected will actually be suitable to answer the original question fairly
Planning data collection methods in advance never affects the quality of a statistical investigation
Data collection methods should always be decided only after all the data has already been gathered
How data is collected has no bearing on whether it can answer the investigation's question
11. Why might reporting "there appears to be a weak relationship" be more honest than claiming "study hours cause higher test scores" from the same scatter plot data?
A scatter plot can show correlation, but proving causation requires much stronger evidence than a simple observed pattern
Correlation and causation always mean exactly the same thing
Any pattern seen in a scatter plot always proves a definite cause-and-effect relationship
There is no meaningful difference between these two ways of describing a result
12. Why might justifying your choice of data display (not just picking one) be an important part of a statistical investigation?
Explaining your reasoning shows the display was deliberately chosen to suit the data and purpose, not picked arbitrarily
Justifying a display choice is never actually necessary for a statistical investigation
Any display type works equally well for any type of data with no need for justification
The choice of display has no real bearing on how well an investigation communicates its findings
13. Why might acknowledging a small sample size as a limitation strengthen, rather than weaken, a statistical report's credibility?
Transparency about limitations helps readers appropriately judge how much confidence to place in the findings
Acknowledging limitations always makes a report seem completely unreliable and worthless
A statistical report should always claim complete certainty regardless of its actual limitations
Sample size limitations have no bearing on how a report should be evaluated
14. Why might a statistical investigation into "do plants grow better with more sunlight?" need to consider what OTHER display types could also be relevant if additional variables are involved?
If multiple factors are studied together, some findings might need different displays (e.g. a table for multiple variables, plus a scatter plot for the two-variable trend)
Only one single display type is ever needed regardless of how many variables are being studied
Considering multiple display types is never useful in a genuine statistical investigation
Additional variables have no bearing on which displays are appropriate for a given investigation
15. Why might a well-designed statistical investigation report include the RAW data or method used, not just the final conclusion?
It allows others to independently verify the analysis and check for any errors or alternative interpretations
Raw data and method are never relevant once a conclusion has been reached
Providing raw data or method always weakens the perceived credibility of a report
Verification of results by others has no genuine value in statistical investigation
16. A researcher has data on favourite music genre (categorical) for 200 students. Which display would be most appropriate, and why?
A bar graph, since it clearly compares counts across distinct, unordered categories
A scatter plot, since scatter plots are always the best choice regardless of data type
A box plot, since box plots work equally well for categorical and numerical data
No display is appropriate for this type of data
17. Why might comparing two histograms (rather than two single averages) give a more complete picture when investigating whether one class performed better than another on a test?
Histograms reveal the full distribution and spread of scores, not just a single central value that could hide important differences
A single average always provides exactly the same information as a full histogram
Comparing distributions never reveals anything beyond what a single average shows
Histograms and averages always lead to identical conclusions in every case
18. Why might a genuinely rigorous statistical investigation include a step where you consider what could have gone wrong with your data collection, even after you've finished collecting it?
Reflecting on possible flaws helps you fairly judge how much confidence to place in your own conclusions before reporting them
Investigations should never involve any reflection on their own possible limitations
Once data is collected, there is never any need to consider potential flaws in the process
Considering possible flaws always invalidates an entire statistical investigation
19. Why might presenting the exact same underlying data as a line graph instead of a bar graph sometimes misleadingly suggest a trend that doesn't actually exist?
A line graph implies continuity and trend even when connecting unrelated or non-sequential categories, which can create a false impression
Line graphs and bar graphs always convey identical impressions regardless of the data being categorical or continuous
Choice between line and bar graphs never has any effect on how data is interpreted
Line graphs are always the objectively correct choice for representing any type of data
20. Why might a genuinely thorough statistical investigation report also mention what further research or data collection could strengthen its conclusions?
Identifying next steps shows an honest awareness of the current investigation's limits and how understanding could be deepened further
A truly rigorous investigation should always present its findings as complete and needing no further exploration
Suggesting further research always weakens the credibility of a statistical report
Statistical investigations should never consider what additional data might be useful
21. Understanding how to choose data displays and plan investigations mainly helps you to:
Select appropriate representations for data and conduct statistical investigations rigorously and honestly
Assume any display type works equally well for any kind of data
Skip planning and go straight to collecting data without a clear question
Report only the most favourable findings from any collected data
Answer key (parent copy)
1. Numerical data with many values
2. Categorical comparisons
3. A relationship between two numerical variables
4. Posing a question, collecting data, analysing and reporting
5. How strong or weak the evidence is for any conclusion
6. As important as calculating the statistics
7. Scatter plot
8. Both variables are numerical and continuous, and a scatter plot can show how they relate to each other
9. A box plot shows the distribution — median, spread and outliers — not just a single summary value per category
10. Planning in advance helps ensure the data collected will actually be suitable to answer the original question fairly
11. A scatter plot can show correlation, but proving causation requires much stronger evidence than a simple observed pattern
12. Explaining your reasoning shows the display was deliberately chosen to suit the data and purpose, not picked arbitrarily
13. Transparency about limitations helps readers appropriately judge how much confidence to place in the findings
14. If multiple factors are studied together, some findings might need different displays (e.g. a table for multiple variables, plus a scatter plot for the two-variable trend)
15. It allows others to independently verify the analysis and check for any errors or alternative interpretations
16. A bar graph, since it clearly compares counts across distinct, unordered categories
17. Histograms reveal the full distribution and spread of scores, not just a single central value that could hide important differences
18. Reflecting on possible flaws helps you fairly judge how much confidence to place in your own conclusions before reporting them
19. A line graph implies continuity and trend even when connecting unrelated or non-sequential categories, which can create a false impression
20. Identifying next steps shows an honest awareness of the current investigation's limits and how understanding could be deepened further
21. Select appropriate representations for data and conduct statistical investigations rigorously and honestly