Statistics: measures of dispersion — KCSE Mathematics

KCSE Mathematics · 104 practice questions · 4 syllabus objectives

30 easy36 medium38 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Calculate the range and interquartile range (IQR = Q₃ – Q₁) for ungrouped and grouped data

Calculate the variance and standard deviation for ungrouped data and interpret the spread of a data set

Construct a box-and-whisker plot using the five-number summary (min, Q₁, median, Q₃, max) and interpret the shape of the distribution

Statistics: measures of dispersion

Sample Questions

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1
easySHORT ANSWER4 marks

In a school sports day, the times (in seconds) for six athletes to complete a race are: 12, 15, 11, 14, 13, 16. Explain how to calculate the five-number summary and state what the box-and-whisker plot reveals about the athletes' performance. (4 marks)

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Part (a) — 2 marks
Identify the minimum time (11 seconds) (1 mk)
Identify Q₁ (12.5 seconds), median (13.5 seconds), Q₃ (15 seconds), and maximum (16 seconds) (1 mk)
Part (b) — 2 marks
Shows the range of athletes' times (1 mk)
Highlights variability in performance among athletes (1 mk)
2
easySHORT ANSWER4 marks

The monthly temperatures (in °C) recorded for a city over six months are: 22, 25, 27, 23, 30, 28. Describe how to determine the five-number summary and interpret what the box-and-whisker plot indicates about the temperature distribution. (4 marks)

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Part (a) — 2 marks
Identify the minimum temperature (22°C) (1 mk)
Identify Q₁ (23°C), median (26°C), Q₃ (28.5°C), and maximum (30°C) (1 mk)
Part (b) — 2 marks
The plot shows the spread of temperatures (1 mk)
Indicates potential skewness or symmetry in temperature distribution (1 mk)
3
easySHORT ANSWER4 marks

The weights (in kg) of seven parcels are: 10, 12, 14, 9, 11, 13, 15. (a) Calculate the variance of the weights. (2 marks) (b) Calculate the standard deviation of the weights. (2 marks)

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Part (a) — 2 marks
Find the mean of the weights (1 mk)
Calculate variance using the formula Σ(weights - mean)² / 7 (1 mk)
Part (b) — 2 marks
Standard deviation = √variance (1 mk)
Provide final answer rounded to 2 decimal places (1 mk)
4

The ages of a group of five friends are: 22, 25, 19, 21, 23. Calculate the variance and standard deviation of their ages. (4 marks)

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