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Temperature outside your house changes throughout the day. What kind of graph would best show this change over time — and why wouldn't a bar chart work as well?
A line graph connects data points to reveal trends — how a quantity rises, falls, or stays steady as time passes. Because the data is continuous, the line between points has meaning.
Common mistake: Using a line graph for categorical data. If your x-axis has categories like "red, blue, green" instead of ordered numbers or times, connecting the points with a line is meaningless — use a bar chart instead. Line graphs only make sense when intermediate values between points could exist.
Use a line graph when your data is continuous and measured over time. The connecting line suggests that values between recorded points are real and meaningful.
Good examples: temperature over hours, population over decades, stock price over weeks, rainfall over months.
Not suitable for: favourite sports (categorical), number of students per school (discrete categories), colours of cars (no numeric order).
A line graph must have: a descriptive title, both axes labelled with their variable and units, an even scale on each axis, and a dot at each data point.
Scale tip: if your data goes from 0 to 80, use intervals of 10 or 20 — not 7 or 13.
Monthly rainfall (mm): Jan 80, Feb 65, Mar 55, Apr 40, May 25, Jun 15.
Step 1 — Plot points: x-axis = month, y-axis = rainfall (mm), scale 0–90 in steps of 10.
Step 2 — Connect: draw straight lines between consecutive points.
Step 3 — Describe the trend: The rainfall is decreasing steadily from January to June. This suggests the data is from a region moving into its dry season.
Estimate at April 15th (interpolation): halfway between April (40) and May (25) → approximately 32–33 mm. This is reasonable because it lies within the data range.
Interpolation means estimating a value between two known data points. Since we have data on both sides of the estimate, this is generally reliable.
Example: If January = 80 mm and February = 65 mm, then mid-January ≈ 72–73 mm. ✓ Reasonable.
Extrapolation means predicting a value beyond the last data point — extending the trend into the future (or past). This is less reliable because the trend might change.
Example: If June = 15 mm, extrapolating to July might give ~5 mm. But what if the wet season starts in July and rainfall jumps to 70 mm? The trend reverses — extrapolation fails.
Rule: Always state whether an estimate is an interpolation or extrapolation, and comment on its reliability.
Line graphs show continuous data over time. Plot (time, value) pairs, connect with straight lines. Always include: title, labelled axes with units, even scale, dot at each point.
Interpolation = estimate within the data range (reliable). Extrapolation = predict beyond the data range (less reliable — trends may change).
Trend = the overall direction: increasing / decreasing / roughly constant / fluctuating.
Which of the following data sets is most suitable for a line graph?
A line graph shows temperature (°C) vs time. At 1pm the temperature is 28°C and at 5pm it is 32°C. The graph is a straight line between these points. What is the temperature at 3pm?
A student has rainfall data for January to June. She estimates the rainfall for April 10th (which lies between her recorded data points). What is this called, and how reliable is it?
Which of the following describes an incorrect feature of a line graph?
A line graph shows annual sales figures: $120k, $135k, $148k, $162k, $178k over five years. Which word best describes the trend?
Q6. A shop's monthly sales (units) for the first 6 months are: Jan 120, Feb 135, Mar 150, Apr 165, May 180, Jun 195. (a) Describe the trend. (b) Estimate the sales in July by interpolation or extrapolation — state which, and comment on reliability.
Q7. Explain why a line graph is not appropriate for displaying data about students' favourite colours (red, blue, green, yellow, other). What type of graph should be used instead?
Q8. A line graph shows a town's population at 10-year intervals: 1990: 8 000, 2000: 11 000, 2010: 15 000, 2020: 20 000. (a) Estimate the population in 2005. (b) Estimate the population in 2030. (c) Which estimate is more reliable? Explain why.
(a) The trend is increasing — sales rise by 15 units each month (linear increase).
(b) July ≈ 210 units. This is extrapolation (beyond June, the last data point). It is less reliable than interpolation because the trend might not continue — a summer slowdown is possible.
Favourite colours are categorical data — there is no numerical order or meaningful "middle value" between red and blue. A line connecting the bars would imply that intermediate values exist, which is nonsense. A bar chart (or column graph) should be used instead.
(a) 2005 is halfway between 2000 (11 000) and 2010 (15 000) → estimate ≈ 13 000. This is interpolation.
(b) 2030 is beyond the last data point (2020) → estimate ≈ 26 000 (if linear trend continues). This is extrapolation.
(c) The 2005 estimate (interpolation) is more reliable. Extrapolation to 2030 assumes the trend continues unchanged for another 10 years, which may not happen (e.g. population could plateau or decline).
Two cities' temperatures are plotted on the same line graph. City A: Jan 5°C, Jul 28°C. City B: Jan 18°C, Jul 32°C. The two lines cross in April at approximately 20°C.
(a) What does the crossing point mean in context?
(b) City A has much colder winters and warmer summers relative to City B. Suggest which city is in the southern hemisphere — and justify your reasoning using the January and July temperatures.