Statistics: measures of central tendency — KCSE Mathematics

KCSE Mathematics · 105 practice questions · 4 syllabus objectives

32 easy37 medium36 hard

What You'll Learn

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

Calculate the mean, median and mode for ungrouped data; state which measure is most appropriate in a given context

Calculate the mean of grouped data using the mid-class value; estimate the mode and median from a frequency table or histogram

Compare data sets using their means and medians; explain the effect of outliers on the mean

Statistics: measures of central tendency

Sample Questions

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1
easySHORT ANSWER4 marks

Explain how an outlier of 100 affects the mean and median of the following data set: {10, 20, 30, 40, 50}. (4 marks)

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Part (a) — 2 marks
New sum = 10 + 20 + 30 + 40 + 50 + 100 = 250 (1 mk)
New mean = 250 / 6 = 41.67 (1 mk)
Part (b) — 2 marks
New data set arranged: {10, 20, 30, 40, 50, 100} (1 mk)
Median = (30 + 40) / 2 = 35 (1 mk)
2
easySHORT ANSWER4 marks

Identify the mean and median of the following set of scores: {12, 15, 22, 30, 45}. (4 marks)

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Part (a) — 2 marks
Sum of scores is 124 (1 mk)
Mean = 124 / 5 = 24.8 (1 mk)
Part (b) — 2 marks
Scores arranged in ascending order: {12, 15, 22, 30, 45} (1 mk)
Median = 22 (middle value) (1 mk)
3
easySHORT ANSWER2 marks

From the frequency distribution of daily temperatures recorded over a week: 20°C (2), 21°C (3), 22°C (5), 23°C (4), determine the mode. (2 marks)

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Part (a) — 2 marks
Identified the temperature with the highest frequency: 22°C (1 mk)
Mode stated as 22°C (1 mk)
4

From the following set of daily temperatures (°C): 15, 18, 20, 18, 22, 23, 18, state the mean and explain which measure of central tendency is most informative in this context. (4 marks)

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Why Practise Statistics: measures of central tendency?

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