SkillrHub • Year 7 Maths

AC9M7ST01 • Homework

Descriptive Statistics and Numerical Data

Calculate accurately, identify anomalies, and justify which statistics best describe the data rather than reporting numbers without interpretation.

5 × 2 marks
Short response
5 × 5 marks
Extended reasoning
1 enrichment
AI/data application

Part A — Short response

  1. Calculate the mean and median of 12, 14, 15, 15, 18. (2)
  2. Find the mode and range of 3, 5, 5, 7, 10. (2)
  3. Which is usually more affected by an extreme outlier: mean or median? Explain. (2)
  4. A data set has mean 20 and median 12. What might this suggest about the distribution? (2)
  5. Classify reaction times 0.45, 0.48, 0.50, 0.52 seconds as discrete or continuous data and justify. (2)

Part B — Extended response

  1. Reading times are 10,12,12,15,18,20,45 minutes. Calculate mean, median, mode and range; identify the outlier; explain its effect on the mean and range. (5)
  2. Class A screen times: 1.5,2,2,2.5,3 hours. Class B: 1.5,2,2,2.5,10 hours. Calculate mean and median for both, explain the outlier effect, and identify the more consistent class. (5)
  3. Create two different data sets with mean 10 and median 10. Compare their ranges and explain why equal centre does not mean equal distribution. (5)
  4. Temperatures are 22.1,22.3,22.4,22.5,22.4,22.3,30.0°C. Calculate mean, median and range; identify the anomaly and explain what should be checked before removing it. (5)
  5. A data set has mean 50, median 50 and range 120. Explain how this can happen and why mean/median alone do not describe variability. (5)

Part C — Enrichment

11. Recommendation-system data. Viewing times are 10,12,15,15,20,22,25,200 minutes. Calculate mean, median, mode and range; identify the outlier; explain why median may better represent typical viewing; and explain how an AI system could use both robust summaries and anomaly detection without automatically deleting unusual behaviour.

Answers

1

Mean = 74÷5 = 14.8; median = 15.

2

Mode = 5; range = 10−3 = 7.

3

Mean, because every value contributes its full magnitude to the arithmetic average.

4

It is evidence consistent with right skew or high extreme values pulling the mean above the median; it is not by itself absolute proof of shape.

5

Continuous: reaction time is measured and can take values throughout an interval.

6

Sum=132; mean≈18.86, median=15, mode=12, range=35. Outlier 45 raises mean and range.

7

A mean=2.2, median=2. B mean=3.6, median=2. The 10-hour value raises B's mean and range; A is more consistent.

8

Example: 8,10,12 and 1,10,19. Both mean/median 10; ranges 4 and 18, so spread differs substantially.

9

Mean≈23.71°C, median=22.4°C, range=7.9°C; anomaly 30.0°C. Check measurement, recording, equipment and experimental context before deciding whether it should be excluded.

10

Values can balance around 50 while extremes are 120 apart. Centre and spread describe different features.

11

Mean=39.875, median=17.5, mode=15, range=190. The 200-minute session heavily inflates mean. Median better reflects the central cluster, while the unusual session can still be flagged and investigated because it may represent genuine behaviour.