Statistics: data collection and presentation — KCSE Mathematics

KCSE Mathematics · 114 practice questions · 4 syllabus objectives

38 easy38 medium38 hard

What You'll Learn

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

Collect and organise data into frequency tables; draw and interpret bar charts, histograms, frequency polygons and pie charts

Construct and interpret cumulative frequency tables and curves (ogives); estimate the median from a cumulative frequency curve

Distinguish between grouped and ungrouped data; choose appropriate class intervals and construct frequency tables

Statistics: data collection and presentation

Sample Questions

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1
easySHORT ANSWER4 marks

Define grouped data and ungrouped data in the context of statistics. (4 marks)

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Part (a) — 2 marks
Grouped data: data that is organized into classes or intervals for easier analysis (1 mk)
Grouped data often summarizes large sets of observations into manageable categories (1 mk)
Part (b) — 2 marks
Ungrouped data: individual data points that are not organized into classes (1 mk)
Ungrouped data presents raw data without any summarization or categorization (1 mk)
2
easySHORT ANSWER4 marks

Explain how to construct a cumulative frequency table from the following data on the ages of participants in a community event: 20, 22, 25, 25, 27, 28, 30, 30, 30, 32, 35. (4 marks)

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Part (a) — 4 marks
List the ages in ascending order to identify the intervals (1 mk)
Count the frequency of participants within defined intervals (1 mk)
Calculate the cumulative frequency by adding the frequencies progressively (1 mk)
Present the cumulative frequency alongside the age intervals in a table format (1 mk)
3
easySHORT ANSWER4 marks

In a survey of 50 households, the number of pets owned was recorded as follows: 0 pets: 20 households, 1 pet: 15 households, 2 pets: 10 households, 3 pets: 5 households. (a) State the total number of households surveyed. [1 mark] (b) Describe how you would represent this data using a pie chart. [3 marks]

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Part (a) — 1 mark
Total number of households is 50 (1 mk)
Part (b) — 3 marks
Calculate the angle for each category based on its frequency (1 mk)
Use the total angle of 360 degrees for the pie chart (1 mk)
Label each section with the number of pets and percentage of households (1 mk)
4

A class of 30 students was surveyed to find out how many hours they spent on homework each week. The data collected is as follows: 0-2 hours: 5 students, 3-5 hours: 10 students, 6-8 hours: 8 students, 9-11 hours: 7 students. (a) Construct a frequency distribution table for the data. [2 marks] (b) Identify the modal class from the frequency distribution. [2 marks]

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