Five-number Summary: Error Analysis & Misconceptions

Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on identifying and correcting misconceptions related to the Five-number Summary and box plots, including error analysis and reasoning.

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Five-number Summary: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet

Grade GCSE Higher
A

Introduction

1.
The Five-number Summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. It provides a quick overview of the distribution of data. Ensure you understand how to calculate and interpret each component correctly.
[2 marks]
B

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the Five-number Summary for the data set: 3, 7, 8, 5, 12, 9, 10.
[3 marks]
2.
Identify the median (Q2) of the following ordered data: 2, 4, 6, 8, 10, 12.
[2 marks]
3.
A student mistakenly swaps the values of Q1 and Q3 when drawing a box plot. Explain how this error affects the interpretation of the data.
[3 marks]
4.
Find the lower quartile (Q1) of this data: 15, 20, 22, 25, 30, 35, 40.
[2 marks]
C

Problem Solving & Reasoning

Answer the questions carefully, showing detailed reasoning.
1.
A data set has a minimum of 10, Q1 of 15, median of 20, Q3 of 30, and a maximum of 50. A student notices the box plot appears skewed but has incorrectly labeled Q1 and Q3. Describe how this mistake could lead to misunderstanding the data distribution.
[4 marks]
2.
Given a data set where Q1=25, median=30, Q3=40, with minimum 15 and maximum 50, construct the box plot and explain how the outliers might affect the interpretation.
[4 marks]
D

Real-World Applications

Read the context and answer the questions based on the data provided.
1.
A teacher records students' test scores: 55, 60, 65, 70, 75, 80, 85, 90, 95. Construct the Five-number Summary and interpret what it reveals about the score distribution.
[4 marks]
E

Challenge & Extension

Attempt these advanced questions to deepen your understanding.
1.
A data set contains 100 values with Q1=20, median=50, Q3=80. The minimum is 10 and the maximum is 100. A new data point of 5 is added. Recalculate the Five-number Summary and discuss the impact.
[4 marks]
2.
Explain why the Five-number Summary might sometimes be misleading if used alone to describe the data distribution. Provide an example scenario.
[3 marks]
F

Mixed Review & Error Analysis

Review the questions carefully and correct any errors in your previous answers.
1.
A student incorrectly calculates Q3 as 45 when the ordered data is 10, 20, 30, 40, 50, 60, 70. Identify and explain the mistake.
[2 marks]
2.
The data set: 5, 7, 8, 12, 15, 20, 22. A student mistakenly records the maximum as 15. What error does this cause in the Five-number Summary, and how should it be corrected?
[3 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet