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From Lists: Error Analysis & Misconceptions

Mathematics

GCSE Higher

14 questions

~28 mins

1 views0 downloads

About This Worksheet

A worksheet focusing on understanding and applying the concept of mean from lists, with emphasis on common errors and misconceptions. Suitable for GCSE Higher students.

Topics covered:

#Mathematics

#Probability & Statistics

#Mean (Average)

#From Lists

#GCSE Higher

Worksheet Preview

Full preview • 14 questions

From Lists: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Higher

Name:

Date:

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Untitled Worksheet

Grade GCSE Higher

Fluency & Practice

Calculate the mean for each list of numbers. Show your working in the grid spaces provided.

Find the mean of the data set: 5, 8, 12, 7, 10.

[2 marks]

Calculate the mean of the list: 15, 20, 25, 30.

[2 marks]

Determine the mean of: 3, 7, 9, 11, 13.

[2 marks]

List the steps to find the mean of 10, 20, 30, 40.

[3 marks]

Problem Solving & Reasoning

Answer the following questions that involve multiple steps or explanations.

A list of five test scores is: 70, 85, 90, 75, 80. A student claims the mean is 80. Is this correct? Show your working and explain.

[4 marks]

A data set is: 4, 8, 12, 16, 20. Another student calculates the mean as 12, but this is incorrect. Identify the mistake and correct it.

[3 marks]

Given the list: 2, 4, 6, 8, 10, find the mean and interpret its significance in this context.

[3 marks]

Real-world Applications

Solve these problems based on practical scenarios involving lists of data.

A class has test scores: 65, 70, 75, 80, 85. What is the average score? If the teacher wants an average of at least 75, what is the minimum score the next student must get?

[4 marks]

Challenge & Extension

Tackle these more advanced problems to extend your understanding.

A list contains 10 numbers. The mean is 50. If one number is removed and the new mean becomes 55, what was the removed number?

[4 marks]

Construct a list of 6 numbers with a mean of 20, where the sum of the first three numbers is 45, and the last three is 75. Fill in the list and verify the mean.

[4 marks]

Mixed Review

Answer these questions to review various aspects of calculating from lists.

Is the following statement true or false? 'Adding the maximum and minimum values and dividing by two gives the mean.'

[1 mark]

Calculate the mean of the list: 3, 3, 3, 3, 3.

[2 marks]

Error Analysis & Misconceptions

Identify and correct the common mistakes in the following scenarios.

A student calculates the mean of 4, 8, 12 as 8 by adding 4+8 and dividing by 2. What mistake did they make? Correct it.

[3 marks]

A list has numbers: 10, 20, 30, 40, 50. A student claims the mean is 25 because they averaged the max and min. Is this correct? Explain.

[3 marks]

Answer Key

Fluency & Practice

Question 1: Find the mean of the data set: 5, 8, 12, 7, 10.

Answer: 8.4

Question 2: Calculate the mean of the list: 15, 20, 25, 30.

Answer: 22.5

Question 3: Determine the mean of: 3, 7, 9, 11, 13.

Answer: 8.6

Question 4: List the steps to find the mean of 10, 20, 30, 40.

Answer: Add all numbers (10+20+30+40=100), then divide by 4 (100/4=25).

Problem Solving & Reasoning

Question 1: A list of five test scores is: 70, 85, 90, 75, 80. A student claims the mean is 80. Is this correct? Show your working and explain.

Answer: Sum = 70+85+90+75+80=400; Mean=400/5=80; Claim is correct.

Question 2: A data set is: 4, 8, 12, 16, 20. Another student calculates the mean as 12, but this is incorrect. Identify the mistake and correct it.

Answer: Incorrectly added the numbers or divided incorrectly. Correct sum: 60; Correct mean: 12.

Question 3: Given the list: 2, 4, 6, 8, 10, find the mean and interpret its significance in this context.

Answer: Sum=30; Number of data points=5; Mean=6. Represents the average value of the data set.

Real-world Applications

Question 1: A class has test scores: 65, 70, 75, 80, 85. What is the average score? If the teacher wants an average of at least 75, what is the minimum score the next student must get?

Answer: Current total=375; To reach at least 75, total should be 6×75=450; Next score=450-375=75.

Challenge & Extension

Question 1: A list contains 10 numbers. The mean is 50. If one number is removed and the new mean becomes 55, what was the removed number?

Answer: Original sum=10×50=500; New sum=9×55=495; Removed number=500-495=5.

Question 2: Construct a list of 6 numbers with a mean of 20, where the sum of the first three numbers is 45, and the last three is 75. Fill in the list and verify the mean.

Answer: Sum=6×20=120; First three sum=45; Last three sum=75; List could be: 10, 15, 20, 25, 25, 25.

Mixed Review

Question 1: Is the following statement true or false? 'Adding the maximum and minimum values and dividing by two gives the mean.'

Answer: False

Question 2: Calculate the mean of the list: 3, 3, 3, 3, 3.

Answer: 3

Error Analysis & Misconceptions

Question 1: A student calculates the mean of 4, 8, 12 as 8 by adding 4+8 and dividing by 2. What mistake did they make? Correct it.

Answer: Incorrectly summed only two numbers. Correct sum=4+8+12=24; Correct mean=24/3=8.

Question 2: A list has numbers: 10, 20, 30, 40, 50. A student claims the mean is 25 because they averaged the max and min. Is this correct? Explain.

Answer: Incorrect approach. Actual mean: (10+20+30+40+50)/5=30. Averaging max and min gives 30, but it is not the mean.

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Details

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

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Related Worksheets

From Lists: Error Analysis & Misconceptions

About This Worksheet

Topics covered:

Worksheet Preview

From Lists: Error Analysis & Misconceptions

Untitled Worksheet

Fluency & Practice

Problem Solving & Reasoning

Real-world Applications

Challenge & Extension

Mixed Review

Error Analysis & Misconceptions

Quick Actions

What is Remix?

Details

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