A graph can show a pattern without proving a cause

By UK GCSE Geography · independent study · myAudience

Image: illustration, not a documentary photograph. Original teaching model created for myAudience. · Original generated teaching illustration; no source textbook artwork reproduced.

A graph can show a pattern without proving a cause

Choose a display to match the question and data. Bars compare distinct categories; lines can show an ordered series such as change over time; a histogram represents numerical intervals, with frequency density needed when interval widths differ. A scatter plot shows paired measurements. Labels, units, coverage and dates are part of the evidence, not decorative details. A graph without them can suggest a pattern but cannot support a precise numerical claim.

Mean, median and range describe different properties. The mean uses every value and is sensitive to extreme observations; the median is the middle of an ordered distribution; the range describes its total spread but depends only on its endpoints. An unusual value should prompt a check, not automatic deletion. It might be an error or a genuinely important part of the phenomenon.

Combining group means requires attention to group sizes. Giving a tiny sample and a large sample equal weight can misrepresent the mean for all observations. If the aim is instead to compare places equally, a place-weighted average may answer that different question. State the unit being averaged and use the corresponding weights. A technically correct calculation can still be irrelevant to the question asked.

A scatter plot can show association, clusters and unusual cases. It cannot by itself establish causation: another variable may influence both measurements, or the direction of influence may be unclear. Interpolation estimates within the observed range, whereas extrapolation assumes a pattern continues beyond it. That assumption becomes particularly risky where a physical threshold, policy change or different population could alter the relationship.

The illustration's blank tally and unnumbered scatter plot are prompts for enquiry, not observed data. A defensible interpretation separates description from explanation: first state the pattern, then consider mechanisms and competing explanations. Inspect sample selection and measurement methods before making a population-wide claim. A smooth line, narrow axis or impressive correlation number does not repair biased observations or turn an association into a controlled experiment.

Worked example: Five invented trips at stop A have mean waiting time 4 minutes; 95 at stop B have mean 20 minutes. Calculate the mean across all 100 observed trips and explain why simply averaging the two means fails.

A contributes 5 × 4 = 20 waiting minutes; B contributes 95 × 20 = 1,900.

Combined mean = (20 + 1,900) / 100 = 19.2 minutes.

The unweighted mean (4 + 20) / 2 = 12 minutes gives each stop equal weight, not each trip.

Answer: 19.2 minutes is the mean for these observed trips. It is not necessarily the mean for all travellers: collection times and selection may be unrepresentative.

Check your understanding: For invented values 1, 2, 2, 3, 12, which centre is less affected by the high value, and does that justify removing 12?

Answer: The median is 2, while the mean is 4; this does not justify removal.

Why: The range is 11. Investigate whether 12 is valid and explain why the chosen centre answers the question instead of deleting inconvenient data.