Revision mat · Averages & Range

Calculator allowed8 marks

Question mix weighted by 213 real exam questions from 135 GCSE papers (2017–24), so the most common question types get the most space. Show your working.

Mean $\text{mean}=\dfrac{\text{sum of values}}{\text{how many}}$Median $\text{middle value}$Mode $\text{most common}$Range $\text{highest}-\text{lowest}$Estimated mean (grouped) $\dfrac{\sum(\text{midpoint}\times f)}{\sum f}$
From a list≈24% of real exam Qs
1Here are the cars sold per day for 9 days:
5, 2, 2, 7, 8, 10, 6, 2, 2
Write down the median.
Answer: (1 mark)
Missing value & compare≈22% of real exam Qs
2The mean of these 5 numbers is $9$.
One value is missing (shown as $?$).
Work out the missing value.
8, 4, 10, 7, ?
Answer: (3 marks)
Frequency table≈20% of real exam Qs
3The frequency table shows the number of pets of some students.
Calculate the mean number of pets.
Give your answer to 1 decimal place.
Number of petsFrequency
03
19
27
31
Answer: (3 marks)
★ Exam capstonemixed & other forms ≈22% of real exam Qs
4Ella and Beth each recorded the cars sold per day for 5 days.
Ella: 14, 12, 9, 15, 5
Beth: 7, 9, 11, 13, 10
Work out the mean for Ella.
Answer: (1 mark)

Mark scheme · Averages & Range

Total: 8 marks

Award the marks shown for each correct step, then add up the total out of 8. A method mark counts even if the final answer is wrong.

1Here are the cars sold per day for 9 days:
5, 2, 2, 7, 8, 10, 6, 2, 2
Write down the median.[1 mark]
Method
Put the values in order: $2, 2, 2, 2, 5, 6, 7, 8, 10$.
The middle value is $5$.
Answer: $5$
Marks
✔1 markmedian = 5
2The mean of these 5 numbers is $9$.
One value is missing (shown as $?$).
Work out the missing value.
8, 4, 10, 7, ?
[3 marks]
Method
Total of all $5$ values $= 5 \times 9 = 45$.
Total of the known values $= 8 + 4 + 10 + 7 = 29$.
Missing value $= 45 - 29 = 16$.
Answer: $16$
Marks
✔1 marktotal = 5 × 9 = 45
✔1 markknown total = 29
✔1 markmissing = 16
3The frequency table shows the number of pets of some students.
Calculate the mean number of pets.
Give your answer to 1 decimal place.
Number of petsFrequency
03
19
27
31
[3 marks]
Method
Multiply each value by its frequency and add: $\sum fx = 0\times3 + 1\times9 + 2\times7 + 3\times1 = 26$.
Total frequency $\sum f = 3 + 9 + 7 + 1 = 20$.
Mean $= 26 \div 20 = 1.3$.
Answer: $1.3$
Marks
✔1 markΣfx = 26
✔1 markΣf = 20
✔1 markmean = 1.3
4Ella and Beth each recorded the cars sold per day for 5 days.
Ella: 14, 12, 9, 15, 5
Beth: 7, 9, 11, 13, 10
Work out the mean for Ella.[1 mark]
Method
Mean $= (14 + 12 + 9 + 15 + 5) \div 5 = 55 \div 5 = 11$.
Answer: $11$
Marks
✔1 markElla mean = 11
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