AQA GCSE Maths · 3.6

Statistics

50 maths questions with worked answers with answers for 3.6 Statistics in AQA GCSE Maths (spec 8300). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official AQA material.

All 50 questions and answers

Question 1 · Data types · S4
Is the number of siblings discrete or continuous data?
Answer:
Count siblings in whole numbers: 0, 1, 2 and so on.
These separate possible values make the data discrete.
Question 2 · Data types · S4
Is a person's height discrete or continuous data?
Answer:
Height can take values throughout a range, including values between measurements.
It is continuous data.
Question 3 · Data types · S4
What is primary data?
Answer:
Identify who collected the data and why.
Data collected first-hand for the investigation is primary data.
Question 4 · Data types · S4
What is secondary data?
Answer:
Identify who collected the data and why.
Data previously collected by someone else or for another purpose is secondary data.
Question 5 · Sampling · S1
Why might surveying only a football club bias an estimate of favourite sports across a school?
Answer:
The sample consists only of football club members.
They may favour football more than the school as a whole, so the sample may be biased.
Question 6 · Sampling · S1
A school has 600 students. A sample of 60 contains 15 cyclists. Estimate the number of cyclists in the school.
Answer:
The sample fraction is 1560 = 14.
Estimate 14 × 600 = 150 cyclists, assuming the sample is representative.
Question 7 · Sampling · S1
Why does a random sample not guarantee a perfect representation of a population?
Answer:
A random sample is selected by chance.
Chance variation can make its characteristics differ from the whole population.
Question 8 · Sampling · S1
What is a population in statistics?
Answer:
Identify the group the investigation aims to describe.
That whole group is the population.
Question 9 · Mean · S4
Find the mean of 3, 5, 7 and 9.
Answer:
Add the values: 3 + 5 + 7 + 9 = 24.
Divide by 4: mean = 24 ÷ 4 = 6.
Question 10 · Mean · S4
Find the mean of 4, 4, 7 and 13.
Answer:
Add the values: 4 + 4 + 7 + 13 = 28.
Divide by 4: mean = 28 ÷ 4 = 7.
Question 11 · Mean · S4
Five numbers have mean 8. What is their total?
Answer:
Total = mean × number of values.
8 × 5 = 40.
Question 12 · Mean · S4
Four numbers have mean 6. Three are 2, 5 and 8. Find the fourth.
Answer:
The total of four numbers is 4 × 6 = 24.
The known numbers sum to 2 + 5 + 8 = 15.
The missing number is 24 − 15 = 9.
Question 13 · Mean · S4
A score of 2 occurs three times and a score of 5 occurs twice. Find the mean.
Answer:
Total score = 2 × 3 + 5 × 2 = 16.
There are 3 + 2 = 5 scores.
Mean = 16 ÷ 5 = 3.2.
Question 14 · Mean · S4
Find the mean of 1, 2, 2, 3, 7.
Answer:
Add the values: 1 + 2 + 2 + 3 + 7 = 15.
Divide by 5: mean = 15 ÷ 5 = 3.
Question 15 · Median · S4
Find the median of 3, 8, 5, 2, 7.
Answer:
Order the values: 2, 3, 5, 7, 8.
The middle value is 5.
Question 16 · Median · S4
Find the median of 2, 4, 6, 8.
Answer:
The ordered values are 2, 4, 6, 8.
Average the middle two: (4 + 6) ÷ 2 = 5.
Question 17 · Median · S4
Find the median of 1, 1, 2, 4, 9, 10, 12.
Answer:
There are 7 ordered values.
The fourth, or middle, value is 4.
Question 18 · Mode · S4
Find the mode of 2, 3, 3, 4, 5.
Answer:
Count how often each value occurs.
3 occurs twice and the others once, so the mode is 3.
Question 19 · Mode · S4
Find the modes of 1, 1, 2, 2, 3.
Answer:
Both 1 and 2 occur twice; 3 occurs once.
The modes are 1 and 2.
Question 20 · Mode · S4
A frequency table has 5 for value A, 9 for B and 3 for C. Give the modal value.
Answer:
Compare frequencies: A has 5, B has 9 and C has 3.
The largest frequency is 9, so the modal value is B.
Question 21 · Range · S4
Find the range of 4, 7, 10 and 15.
Answer:
Range = largest value − smallest value.
15 − 4 = 11.
Question 22 · Range · S4
Two sets have ranges 6 and 12. Which has greater spread by the range measure?
Answer:
Compare the two ranges: 12 > 6.
The second set has the larger spread as measured by range.
Question 23 · Range · S4
Find the range of −3, 2, 5 and 9.
Answer:
Largest value = 9 and smallest = −3.
Range = 9 − (−3) = 12.
Question 24 · Grouped data · S4
For 0 < x ≤ 10 there are 4 values, and for 10 < x ≤ 20 there are 6. What is the modal class?
Answer:
Compare frequencies: 4 in the first class and 6 in the second.
The larger frequency is 6, so the modal class is 10 < x ≤ 20.
Question 25 · Grouped data · S4
Classes 0 < x ≤ 10 and 10 < x ≤ 20 have frequencies 2 and 3. Estimate the mean using midpoints.
Answer:
The class midpoints are 5 and 15.
Estimated total = 5 × 2 + 15 × 3 = 55; total frequency = 5.
Estimated mean = 55 ÷ 5 = 11.
Question 26 · Grouped data · S4
Why is a mean calculated from grouped data an estimate?
Answer:
Individual values within each class are unknown.
The calculation substitutes the class midpoint for each value, so the mean is an estimate.
Question 27 · Charts · S2
A pie chart has a 90° sector. What fraction of the whole does it represent?
Answer:
The complete circle is 360°.
Fraction represented = 90360 = 14.
Question 28 · Charts · S2
In a pie chart of 60 people, 15 prefer cycling. Find the sector angle.
Answer:
The fraction preferring cycling is 1560 = 14.
Sector angle = 14 × 360° = 90°.
Question 29 · Charts · S2
A pictogram uses one symbol for 4 people. How many people do 5 symbols represent?
Answer:
Each symbol represents 4 people.
5 × 4 = 20 people.
Question 30 · Charts · S2
A category has frequency 12 out of 40. Find its percentage.
Answer:
Fraction in the category = 1240 = 0.3.
0.3 × 100% = 30%.
Question 31 · Charts · S2
A time series has values 12, 15, 13 and 18 in consecutive years. What is the overall change?
Answer:
Overall change = final value − initial value.
18 − 12 = 6, so it is an increase of 6.
Question 32 · Charts · S2
Which chart is suitable for comparing counts of separate categories?
Answer:
Separate categories need separate bars to compare their frequencies.
A bar chart is suitable.
Question 33 · Scatter graphs · S6
As x rises, y generally rises. What correlation is suggested?
Answer:
As x increases, the general trend is for y to increase.
This suggests positive correlation.
Question 34 · Scatter graphs · S6
As x rises, y generally falls. What correlation is suggested?
Answer:
As x increases, the general trend is for y to decrease.
This suggests negative correlation.
Question 35 · Scatter graphs · S6
Does correlation by itself prove causation?
Answer:
Correlation describes an association between variables.
Another factor or chance could explain it, so correlation alone does not prove causation.
Question 36 · Scatter graphs · S6
Why can a prediction outside the range of observed data be unreliable?
Answer:
A prediction beyond the observed range is extrapolation.
The observed pattern might change outside that range, making the prediction unreliable.
Question 37 · Scatter graphs · S6
A line of best fit is y = 2x + 1. Predict y when x = 5.
Answer:
Substitute x = 5 into y = 2x + 1.
y = 2 × 5 + 1 = 11.
Question 38 · Scatter graphs · S6
A line of best fit is y = 20 − 3x. Predict y when x = 4.
Answer:
Substitute x = 4 into y = 20 − 3x.
y = 20 − 3 × 4 = 8.
Question 39 · Quartiles · S4 · Higher only
The lower quartile is 12 and the upper quartile is 27. Find the interquartile range.
Answer:
Interquartile range = upper quartile − lower quartile.
27 − 12 = 15.
Question 40 · Quartiles · S4 · Higher only
The ordered data are 1, 2, 3, 4, 5, 6, 7. Excluding the median, find Q₁, Q₃ and the interquartile range.
Answer:
The median is 4; excluding it leaves lower half 1, 2, 3 and upper half 5, 6, 7.
Q₁ = 2 and Q₃ = 6.
Interquartile range = 6 − 2 = 4.
Question 41 · Quartiles · S4 · Higher only
A data set has Q₁ = 8 and Q₃ = 19. If 5 is added to each value, what is the new interquartile range?
Answer:
Adding 5 gives Q₁ = 13 and Q₃ = 24.
New interquartile range = 24 − 13 = 11.
Question 42 · Histograms · S3 · Higher only
A histogram class has frequency 18 and class width 3. Find its frequency density.
Answer:
Frequency density = frequency ÷ class width.
18 ÷ 3 = 6.
Question 43 · Histograms · S3 · Higher only
A class width is 5 and its frequency density is 4. Find the frequency.
Answer:
Frequency = frequency density × class width.
4 × 5 = 20.
Question 44 · Histograms · S3 · Higher only
Two histogram classes have equal widths but densities 3 and 6. Compare their frequencies.
Answer:
Frequency = density × width.
The widths are equal and 6 is twice 3, so the second frequency is twice the first.
Question 45 · Cumulative frequency · S3 · Higher only
A cumulative frequency is 28 up to 10 and 45 up to 20. How many values lie between those boundaries?
Answer:
Subtract the cumulative count at 10 from the count at 20.
45 − 28 = 17 values.
Question 46 · Cumulative frequency · S3 · Higher only
A cumulative frequency graph represents 80 values. At what cumulative frequency is the median estimated?
Answer:
The median is halfway through the 80 values.
80 ÷ 2 = 40, so read the graph at cumulative frequency 40.
Question 47 · Comparison · S4
Set A has mean 20 and range 3; set B has mean 15 and range 8. Compare them.
Answer:
Compare means: 20 > 15, so A has the higher mean.
Compare ranges: 3 < 8, so A is less spread by the range measure.
Question 48 · Comparison · S4
Every value in a list increases by 4. What happens to the mean and range?
Answer:
Adding 4 to each value increases the mean by 4.
Both maximum and minimum increase by 4, so their difference, the range, stays the same.
Question 49 · Comparison · S4 · Higher only
Every value in a list is multiplied by 3. What happens to the interquartile range?
Answer:
Multiplying every value by 3 multiplies both quartiles by 3.
New interquartile range = 3Q₃ − 3Q₁ = 3(Q₃ − Q₁), so it triples.
Question 50 · Error check · S4
A student finds the median of 7, 1, 9, 3, 5 as 9. Correct the mistake.
Answer:
Order the values: 1, 3, 5, 7, 9.
The middle value is 5, so the median is 5.

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