Edexcel GCSE Maths · S1–S6

Statistics

50 maths questions with worked answers with answers for S1–S6 Statistics in Edexcel GCSE Maths (spec 1MA1). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official Pearson material.

All 50 questions and answers

Question 1 · Sampling · S1
Why might a sample be used instead of a whole population?
Answer:
Any two from:
It is quicker. It is cheaper. Testing may destroy the items. The population may be too large.
Question 2 · Sampling · S1
What is a random sample?
Answer:
A sample where every member of the population has an equal chance of being picked.
It reduces bias.
Question 3 · Sampling · S1
Give one reason a sample may be biased.
Answer:
Any one from:
It is too small. It is taken from one place or group only. People choose whether to take part.
Question 4 · Charts · S2
When should a pie chart be used?
Answer:
To show how a whole is split into categories.
It shows proportions, not exact frequencies.
Question 5 · Pie charts · S2
In a pie chart of 60 people, 15 chose tea. Find the angle for tea.
Answer:
Each person is 360 ÷ 60 = 6°.
15 × 6 = 90°.
Question 6 · Pie charts · S2
A pie chart sector is 72°. It represents 18 people. How many people does the whole chart represent?
Answer:
72° is 72360 = 15 of the chart.
18 × 5 = 90 people.
Question 7 · Time series · S2
What does a time series graph show?
Answer:
How data changes over time.
For example, trends and seasonal patterns.
Question 8 · Frequency polygons · S4
How do you draw a frequency polygon from grouped data?
Answer:
Plot each frequency at the midpoint of its class.
Join the points with straight lines.
Question 9 · Histograms · S3 · Higher only
What does the vertical axis of a histogram show?
Answer:
Frequency density.
Frequency density = frequency ÷ class width.
Question 10 · Histograms · S3 · Higher only
A class 10 < x ≤ 25 has frequency 30. Find the frequency density.
Answer:
Class width = 15.
30 ÷ 15 = 2.
Question 11 · Histograms · S3 · Higher only
A bar has frequency density 4 and class width 5. Find the frequency.
Answer:
Frequency = frequency density × class width.
4 × 5 = 20.
Question 12 · Cumulative frequency · S3 · Higher only
How do you plot a cumulative frequency graph?
Answer:
Add up the frequencies as you go.
Plot each total at the upper class boundary and join with a smooth curve.
Question 13 · Cumulative frequency · S3 · Higher only
How do you find the median from a cumulative frequency graph of 80 values?
Answer:
Find half of the total: 40.
Read across from 40 to the curve, then down to the x-axis.
Question 14 · Box plots · S3 · Higher only
What five values does a box plot show?
Answer:
Minimum, lower quartile, median, upper quartile and maximum.
The box spans the interquartile range.
Question 15 · Interquartile range · S3 · Higher only
LQ = 23 and UQ = 41. Find the interquartile range.
Answer:
IQR = UQ − LQ.
41 − 23 = 18.
Question 16 · Averages · S4
Find the mean of 4, 7, 9, 10 and 15.
Answer:
Total = 45.
45 ÷ 5 = 9.
Question 17 · Averages · S4
Find the median of 12, 5, 9, 3, 15, 8.
Answer:
Order: 3, 5, 8, 9, 12, 15. The middle two are 8 and 9.
Median = 8.5.
Question 18 · Averages · S4
Find the mode of 3, 6, 6, 2, 8, 6, 3.
Answer:
6 appears 3 times.
Mode = 6.
Question 19 · Range · S4
Find the range of 14, 3, 22, 9, 17.
Answer:
Largest − smallest.
22 − 3 = 19.
Question 20 · Mean from a table · S4
Goals: 0 goals ×4 matches, 1 ×6, 2 ×7, 3 ×3. Find the mean.
Answer:
Total goals = 0 + 6 + 14 + 9 = 29. Matches = 20.
29 ÷ 20 = 1.45.
Question 21 · Grouped data · S4
How do you estimate the mean from grouped data?
Answer:
Multiply each class midpoint by its frequency and add.
Divide by the total frequency.
Question 22 · Grouped data · S4
Why is the mean from grouped data only an estimate?
Answer:
The exact values are not known.
Midpoints are used instead.
Question 23 · Grouped data · S4
Times: 0–10 min (f = 4), 10–20 (f = 10), 20–30 (f = 6). Estimate the mean.
Answer:
Midpoints 5, 15, 25: 20 + 150 + 150 = 320.
320 ÷ 20 = 16 minutes.
Question 24 · Modal class · S4
What is the modal class?
Answer:
The class with the highest frequency.
For grouped data.
Question 25 · Missing value · S4
The mean of 5 numbers is 8. Four of them are 6, 7, 9 and 10. Find the fifth.
Answer:
Total = 5 × 8 = 40.
40 − 32 = 8.
Question 26 · Outliers · S4
What effect does an outlier have on the mean and the median?
Answer:
The mean is pulled towards the outlier.
The median is hardly affected.
Question 27 · Choosing averages · S4
When is the median better than the mean?
Answer:
When there are outliers or the data is skewed.
For example, house prices or salaries.
Question 28 · Comparing · S4
Class A: mean 62, range 30. Class B: mean 58, range 12. Compare the classes.
Answer:
On average Class A scored higher.
Class B's scores were more consistent (smaller range).
Question 29 · Comparing · S4 · Higher only
Why is the interquartile range often better than the range for comparing spread?
Answer:
It uses the middle 50% of the data.
It is not affected by extreme values.
Question 30 · Averages · S4
The mean of 6 numbers is 15. A seventh number, 22, is added. Find the new mean.
Answer:
Old total = 90. New total = 112.
112 ÷ 7 = 16.
Question 31 · Populations · S5
What is the difference between a sample and a population?
Answer:
The population is every member of the group being studied.
A sample is part of the population.
Question 32 · Interpreting · S5
Why can a sample give a misleading conclusion about a population?
Answer:
It may not represent the population.
For example, it is small or biased.
Question 33 · Scatter graphs · S6
What does positive correlation mean?
Answer:
As one variable increases, so does the other.
The points slope upwards.
Question 34 · Scatter graphs · S6
What does negative correlation mean?
Answer:
As one variable increases, the other decreases.
The points slope downwards.
Question 35 · Line of best fit · S6
How do you draw a line of best fit?
Answer:
A straight line following the trend of the points.
Roughly equal numbers of points on each side; it need not pass through the origin.
Question 36 · Interpolation · S6
Why is it unreliable to use a line of best fit outside the data range?
Answer:
This is extrapolation.
The pattern may not continue beyond the data.
Question 37 · Correlation · S6
Does correlation prove that one variable causes the other?
Answer:
No.
Both may be linked to a third factor, or it may be coincidence.
Question 38 · Outliers · S6
What is an outlier on a scatter graph?
Answer:
A point that does not fit the general pattern.
It should be ignored when drawing a line of best fit.
Question 39 · Scatter graphs · S6
Ice cream sales rise as temperature rises. What type of correlation is this?
Answer:
Both increase together.
Positive correlation.
Question 40 · Scatter graphs · S6
What does no correlation look like?
Answer:
The points are scattered randomly.
There is no relationship.
Question 41 · Bar charts · S2
What is a composite (stacked) bar chart?
Answer:
Each bar is split into sections for sub-categories.
It shows totals and how they are made up.
Question 42 · Two-way tables · S2
A two-way table shows 45 boys, 20 of whom walk to school. How many boys do not walk?
Answer:
45 − 20.
25.
Question 43 · Cumulative frequency · S3 · Higher only
How do you find the upper quartile from a cumulative frequency graph of 80 values?
Answer:
Find 34 of 80: 60.
Read across from 60 to the curve and down.
Question 44 · Box plots · S3 · Higher only
Two box plots have medians 40 and 52 and IQRs 15 and 8. Compare them.
Answer:
The second set has a higher median, so higher on average.
It also has a smaller IQR, so it is more consistent.
Question 45 · Averages · S4
Find the mean of 2.4, 3.1, 2.8 and 3.7.
Answer:
Total = 12.
12 ÷ 4 = 3.
Question 46 · Data types · S1
What is the difference between discrete and continuous data?
Answer:
Discrete data can only take certain values (e.g. shoe size).
Continuous data can take any value in a range (e.g. height).
Question 47 · Data types · S1
What is the difference between primary and secondary data?
Answer:
Primary data is collected by you.
Secondary data is collected by someone else.
Question 48 · Sampling · S1
Why should a sample be as large as practical?
Answer:
Small samples are more affected by chance.
Larger samples give more reliable conclusions about the population.
Question 49 · Inference · S1
In a random sample of 50 pupils, 12 cycle to school. Estimate how many of the 900 pupils cycle.
Answer:
1250 = 0.24 of the sample.
0.24 × 900 = 216.
Question 50 · Pictograms · S2
In a pictogram one symbol represents 8 cars. How many symbols show 28 cars?
Answer:
28 ÷ 8.
3.5 symbols.

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