Mathematics • Year 7 • Unit 4 • Lesson 12
Interpreting Graphs
Build fluency with the six graph features: trend, peak, trough, cluster, gap and outlier. A complete description always quotes specific values from the scale.
1. I do — fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. A line graph shows monthly rainfall (mm) for a town: Jan 15, Feb 18, Mar 80, Apr 45, May 30, Jun 25, Jul 20, Aug 20, Sep 22, Oct 28, Nov 35, Dec 12. Describe all features.
Step 1 — Overall trend.
Overall: rainfall is generally decreasing from the March peak (80 mm) to December (12 mm).
Reason: state the direction first, with start and end values from the y-axis.
Step 2 — Peak and trough.
Peak: March at 80 mm. Trough: December at 12 mm.
Reason: peak = maximum, trough = minimum — always include value AND position.
Step 3 — Cluster, gap, outlier.
Cluster: July–September, all values around 20–22 mm. Outlier: March (80 mm) sits far above the other 11 months.
Reason: cluster = concentrated; outlier = a value far from the rest.
Step 4 — Interpret in context.
March's peak suggests a late-summer storm; the dry cluster (Jul–Sep) suggests a dry winter.
Answer: Peak March (80 mm); trough December (12 mm); cluster Jul–Sep (~20 mm); March is an outlier; overall decreasing trend after March.
2. We do — fill in the missing description
A dot plot shows quiz scores (out of 20) for 10 students: 5, 12, 13, 14, 14, 15, 15, 16, 17, 18. Fill in each blank. 5 marks
Step 1 — Peak (most common value):
The most common scores are _______ and _______ (each appearing twice).
Step 2 — Trough (lowest value):
The lowest value is _______.
Step 3 — Cluster:
The main cluster of scores lies between _______ and _______.
Step 4 — Gap:
There is a gap between scores _______ and _______ (no scores in that range).
Step 5 — Outlier:
The score _______ is the outlier because it sits far below the main cluster.
3. You do — independent practice
Use the data values provided. Read carefully and quote specific values in your answer.
Foundation — quick reads
3.1 A line graph shows temperatures: 18, 21, 25, 28, 30, 27, 22, 18 °C across an 8-hour day. What is the peak temperature and at what hour? 1 mark
3.2 A dot plot shows house numbers visited: 8, 10, 12, 14, 16, 18, 20. State the trend (increasing, decreasing, stable, or fluctuating). 1 mark
3.3 A class survey records pet counts: 1, 1, 2, 2, 2, 3, 3, 8. Identify the outlier. 1 mark
3.4 A line graph shows sales: 100, 100, 102, 99, 101 per week. Describe the trend in one word. 1 mark
Standard — describe with values
3.5 A bar chart shows weekly screen time (hours) for 7 students: 8, 12, 14, 14, 15, 18, 28. (i) Identify the outlier and state its value. (ii) Identify the cluster and the range it covers. 2 marks
3.6 A line graph shows a city's daily max temperature for one week (°C): Mon 22, Tue 24, Wed 25, Thu 38, Fri 26, Sat 25, Sun 24. Describe the peak with its value and day, and state whether Thursday is an outlier. Justify. 2 marks
Extension — push your thinking
3.7 A line graph shows monthly profit ($k): Jan 50, Feb 55, Mar 60, Apr 65, May 70, Jun 75, Jul 80, Aug 80, Sep 80, Oct 82, Nov 90, Dec 100. (i) Describe the overall trend in one sentence with start and end values. (ii) Identify a plateau and state the months it covers. 3 marks
3.8 Invent a data set of 10 values that contains: an obvious peak, a cluster of 4 values, a gap of at least 5 units, and one outlier. List the 10 values, then label each feature. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Quiz scores dot plot (We do)
Step 1: most common scores are 14 and 15 (each appears twice).
Step 2: lowest value is 5.
Step 3: main cluster lies between 12 and 18.
Step 4: gap between 5 and 12 (no scores in that range).
Step 5: the score 5 is the outlier — far below the main cluster.
3.1 — Peak temperature
Peak temperature = 30 °C, at hour 5 (the fifth value in the sequence).
3.2 — Trend
Increasing — values climb steadily from 8 to 20.
3.3 — Outlier
8 is the outlier — far from the cluster of 1–3 pets.
3.4 — Trend in one word
Stable (or constant) — values fluctuate only slightly around 100.
3.5 — Screen time
(i) Outlier = 28 hours — far above the rest.
(ii) Cluster covers approximately 8 to 18 hours (the other 6 values bunch in this range).
3.6 — Daily max temperature
Peak = 38 °C on Thursday. Thursday IS an outlier — every other day sits between 22 and 26 °C, but Thursday jumps to 38 °C, far above the surrounding cluster.
3.7 — Monthly profit
(i) Overall trend: profit increases steadily from $50k in January to $100k in December.
(ii) Plateau: July, August and September — all three months sit at $80k with no change.
3.8 — Invented data set (sample)
Values: 2, 5, 6, 7, 8, 18, 25, 25, 26, 50.
Cluster: 5, 6, 7, 8 (between 5 and 8).
Gap: between 8 and 18 (no values).
Peak: 50 (highest value).
Outlier: 50 (far above all other values).
Marking: 1 for valid data set; 1 for each feature clearly identified; 1 for spotting the gap.