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Averages and range - Teacher Slides.pptx
The lesson slides with the teacher's notes on each slide, and every question and mark scheme built in. Built from the lesson script on 29 September 2026.
EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Averages and range
Interpreting and representing data
Lesson 5 of 6
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before
Interpreting and representing data
Lesson 5 of 6
Answer each one, then check.
1
Work out the mean of 2, 4 and 6.
2
Put 7, 3, 9, 1 in order.
3
What is the middle value of 1, 3, 7?
4
Last lesson: what is interpolation?
5
Round 12.46 to 1 decimal place.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before - Answers
Interpreting and representing data
Lesson 5 of 6
1
Work out the mean of 2, 4 and 6.
(2 + 4 + 6)/3 = 4
2
Put 7, 3, 9, 1 in order.
1, 3, 7, 9
3
What is the middle value of 1, 3, 7?
3
4
Last lesson: what is interpolation?
Estimating inside the range of the data.
5
Round 12.46 to 1 decimal place.
12.5
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Interpreting and representing data
Lesson 5 of 6
1
Find the mean, median, mode and range of a set of data.
2
Choose the most suitable average.
3
Find averages and the range from a frequency table.
4
Estimate the mean of grouped data, and find the modal class and the class containing the median.
5
Solve problems with missing values and combined means.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Three Averages and a Spread
Interpreting and representing data
Lesson 5 of 6
Mean
Add up all the values and divide by how many there are: mean = total/(number of values).
Median
The middle value when the data is in order. With an even number of values, the mean of the middle two.
Mode
The most common value. There can be more than one, or none.
Range
Largest value − smallest value. It measures spread, not average.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
All Four from a List
Interpreting and representing data
Lesson 5 of 6
Find the mean, median, mode and range of 4, 8, 3, 9, 8, 6, 12.
1
Mean: add them and divide by 7
50/7 = 7.14 (2 d.p.)
2
Median: put them in order
3, 4, 6, 8, 8, 9, 12: the middle (4th) value is 8
3
Mode: the most common
8 appears twice
4
Range: largest − smallest
12 − 3 = 9
ANSWER
Mean 7.14, median 8, mode 8, range 9
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Which Average?
Interpreting and representing data
Lesson 5 of 6
MEAN
• Uses every value.
• Pulled up or down by outliers.
• Best when there are no extreme values.
MEDIAN AND MODE
• The median is not affected by outliers - best for data like house prices or salaries.
• The mode is the only average for qualitative data, such as favourite colour.
• The mode can be unhelpful if every value is different.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART ONE
Frequency Tables
When each value comes up many times.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Pets Owned by 30 Students
Interpreting and representing data
Lesson 5 of 6
Add a column for frequency × value: it gives the total number of pets.
Number of pets (x)
Frequency (f)
f × x
0
8
0
1
12
12
2
6
12
3
3
9
4
1
4
Total
30
37
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Averages from a Frequency Table
Interpreting and representing data
Lesson 5 of 6
Use the pets table to find the mean, median, mode and range.
1
Mean = total of f × x ÷ total frequency
37/30 = 1.23 (2 d.p.)
2
Median: 30 values, so it is halfway between the 15th and 16th
The first 8 are 0; values 9 to 20 are 1
3
So the 15th and 16th values are both 1
Median = 1
4
Mode: the value with the highest frequency
1 (frequency 12)
5
Range: largest value − smallest value
4 − 0 = 4
ANSWER
Mean 1.23, median 1, mode 1, range 4
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART TWO
Grouped Data
When the exact values are unknown.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Journey Times of 30 Students
Interpreting and representing data
Lesson 5 of 6
Each class is represented by its midpoint.
Time, t (minutes)
Frequency (f)
Midpoint
f × midpoint
0 < t ≤ 10
5
5
25
10 < t ≤ 20
12
15
180
20 < t ≤ 30
9
25
225
30 < t ≤ 40
4
35
140
Total
30
570
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Estimating the Mean of Grouped Data
Interpreting and representing data
Lesson 5 of 6
Use the journey times table to estimate the mean, and find the modal class and the class containing the median.
1
Use the midpoint of each class
5, 15, 25, 35
2
Multiply by the frequencies and add
25 + 180 + 225 + 140 = 570
3
Divide by the total frequency
570/30 = 19
4
Modal class: the class with the highest frequency
10 < t ≤ 20
5
Median: the 15.5th value. Running total: 5, then 5 + 12 = 17
so it is in 10 < t ≤ 20
ANSWER
Estimated mean 19 minutes; modal class 10 < t ≤ 20; the median is in 10 < t ≤ 20.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Why Only an Estimate?
Interpreting and representing data
Lesson 5 of 6
With grouped data, you do not know the actual values.
The midpoint stands in
We assume every value in a class is at its midpoint.
Some are higher, some lower
The errors tend to cancel out, so the estimate is usually close.
In an exam
"Explain why your answer is an estimate" wants: "the exact values are not known, so the midpoints were used".
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Missing Values and Combined Means
Interpreting and representing data
Lesson 5 of 6
Mean × number of values = total. That one fact solves most problems.
Missing value
The mean of 5 numbers is 8, so they add up to 5 × 8 = 40. If four of them add up to 31, the fifth is 9.
Adding a value
The mean of 4 numbers is 9 (total 36). After adding one, the mean of 5 is 10 (total 50). The new number is 50 − 36 = 14.
Combined means
Class A: 20 students, mean 64 (total 1280). Class B: 25 students, mean 73 (total 1825). Mean of all 45: 3105/45 = 69.
Never average the averages
(64 + 73)/2 = 68.5 is wrong: the classes are different sizes.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Interpreting and representing data
Lesson 5 of 6
Mean
The total of the values divided by the number of values.
Median
The middle value when the data is in order.
Mode
The most common value.
Range
The difference between the largest and smallest values.
Modal class
The class with the highest frequency in grouped data.
Midpoint
The value halfway through a class, used to estimate the mean.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Interpreting and representing data
Lesson 5 of 6
YOUR TASK
Choose Your Average
12 minutes
For each data set, find the mean, median and mode, then decide which is the best average and why. (a) Salaries at a small firm: £22 000, £24 000, £24 000, £26 000, £28 000, £150 000. (b) Shoe sizes sold by a shop in one hour: 5, 6, 6, 7, 7, 7, 8, 9. (c) Favourite fruit of 10 people: apple 4, banana 3, grape 2, pear 1.
1
Work out all three averages.
2
Look for outliers and the type of data.
3
Choose and justify.
WHAT A GOOD ANSWER SHOWS
(a) Mean £45 667, median £25 000, mode £24 000 - the median, because the £150 000 outlier pulls the mean up. (b) Mean 6.875, median 7, mode 7 - the mode, because a shop orders whole shoe sizes. (c) Only the mode (apple) makes sense for qualitative data.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Interpreting and representing data
Lesson 5 of 6
Find the mean, median, mode and range of a list.
Choose the best average.
Find the mean from a frequency table.
Find the median from a frequency table.
Estimate the mean of grouped data.
Find the modal class.
Find the class containing the median.
Solve missing value and combined mean problems.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Mean = total ÷ number of values; median = middle; mode = most common; range = largest − smallest.
Frequency table: mean = Σfx/Σf.
Grouped data: use midpoints - the mean is only an estimate.
Mean × number of values = total: the key to missing values and combined means.
EXAM FOCUS
Work out an estimate for the mean weight of the 40 parcels. (4 marks)
For grouped data, add a midpoint column and an f × midpoint column to the table. Then divide by the total FREQUENCY, not by the number of classes.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Averages and Range
Interpreting and representing data
Lesson 5 of 6
Answer all questions. Show your working. Questions 1 and 5 are non-calculator. · 25 minutes
Question 1 · 2 marks · Non-calculator
Here are six numbers: 7, 3, 9, 4, 7, 12. (a) Find the median. (b) Find the range.
Question 2 · 3 marks · Calculator
The table shows the number of goals scored by a football team in 20 matches. Goals 0: 4 matches. Goals 1: 7 matches. Goals 2: 5 matches…
Question 3 · 4 marks · Calculator
The weights, w kg, of 40 parcels are recorded. 0 < w ≤ 2: 6 parcels. 2 < w ≤ 4: 15 parcels. 4 < w ≤ 6: 12 parcels. 6 < w ≤ 8: 7 parcels…
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Averages and Range (cont.)
Interpreting and representing data
Lesson 5 of 6
Question 4 · 1 mark · Calculator
For the parcels in the last question, write down the modal class.
Question 5 · 2 marks · Non-calculator
The mean of five numbers is 8. Four of the numbers are 3, 7, 9 and 12. Find the fifth number.
Question 6 · 3 marks · Calculator
Class A has 20 students. Their mean test score is 64. Class B has 25 students. Their mean test score is 73. Work out the mean score of all…
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 2 marks · Non-calculator
Interpreting and representing data
Lesson 5 of 6
“
Here are six numbers: 7, 3, 9, 4, 7, 12. (a) Find the median. (b) Find the range.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · mark scheme
Interpreting and representing data
Lesson 5 of 6
2 marks available. Award a mark for each point made.
(a) 7
B1
(b) 9
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · 3 marks · Calculator
Interpreting and representing data
Lesson 5 of 6
“
The table shows the number of goals scored by a football team in 20 matches. Goals 0: 4 matches. Goals 1: 7 matches. Goals 2: 5 matches. Goals 3: 3 matches. Goals 4: 1 match. Work out the mean number of goals per match.
HOW TO ANSWER IT
Command word: Calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · mark scheme
Interpreting and representing data
Lesson 5 of 6
3 marks available. Award a mark for each point made.
At least three products of goals × frequency correct
M1
30 ÷ 20
M1
1.5
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 4 marks · Calculator
Interpreting and representing data
Lesson 5 of 6
“
The weights, w kg, of 40 parcels are recorded. 0 < w ≤ 2: 6 parcels. 2 < w ≤ 4: 15 parcels. 4 < w ≤ 6: 12 parcels. 6 < w ≤ 8: 7 parcels. Work out an estimate for the mean weight of the parcels.
HOW TO ANSWER IT
Command word: Calculator. Worth 4 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · mark scheme
Interpreting and representing data
Lesson 5 of 6
4 marks available. Award a mark for each point made.
Midpoints used: 1, 3, 5, 7
M1
At least three products of frequency × midpoint correct
M1
160 ÷ 40
M1
4 (kg)
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 1 mark · Calculator
Interpreting and representing data
Lesson 5 of 6
“
For the parcels in the last question, write down the modal class.
HOW TO ANSWER IT
Command word: Calculator. Worth 1 mark, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Interpreting and representing data
Lesson 5 of 6
1 mark available. Award a mark for each point made.
2 < w ≤ 4
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 2 marks · Non-calculator
Interpreting and representing data
Lesson 5 of 6
“
The mean of five numbers is 8. Four of the numbers are 3, 7, 9 and 12. Find the fifth number.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · mark scheme
Interpreting and representing data
Lesson 5 of 6
2 marks available. Award a mark for each point made.
40 or 31 seen
M1
9
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 3 marks · Calculator
Interpreting and representing data
Lesson 5 of 6
“
Class A has 20 students. Their mean test score is 64. Class B has 25 students. Their mean test score is 73. Work out the mean score of all 45 students.
HOW TO ANSWER IT
Command word: Calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · mark scheme
Interpreting and representing data
Lesson 5 of 6
3 marks available. Award a mark for each point made.
1280 or 1825
P1
(1280 + 1825) ÷ 45
P1
69
A1
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