OCR GCSE Maths · OCR 12

Statistics

50 maths questions with worked answers with answers for OCR 12 Statistics in OCR GCSE Maths (spec J560). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official OCR material.

All 50 questions and answers

Question 1 · Sampling · OCR 12.01a
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 · OCR 12.01a
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 · OCR 12.01a
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 · Data types · OCR 12.01a
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 5 · Sampling · OCR 12.01a
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 6 · Inference · OCR 12.01a
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 7 · Sampling · OCR 12.01a
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 8 · Sampling · OCR 12.01a
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 9 · Sampling · OCR 12.01a
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 10 · Sampling · OCR 12.01a
What is a population in statistics?
Answer:
Identify the group the investigation aims to describe.
That whole group is the population.
Question 11 · Charts · OCR 12.02a
When should a pie chart be used?
Answer:
To show how a whole is split into categories.
It shows proportions, not exact frequencies.
Question 12 · Pie charts · OCR 12.02a
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 13 · Pie charts · OCR 12.02a
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 14 · Time series · OCR 12.02a
What does a time series graph show?
Answer:
How data changes over time.
For example, trends and seasonal patterns.
Question 15 · Bar charts · OCR 12.02a
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 16 · Two-way tables · OCR 12.02a
A two-way table shows 45 boys, 20 of whom walk to school. How many boys do not walk?
Answer:
45 − 20.
25.
Question 17 · Pictograms · OCR 12.02a
In a pictogram one symbol represents 8 cars. How many symbols show 28 cars?
Answer:
28 ÷ 8.
3.5 symbols.
Question 18 · Charts · OCR 12.02a
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 19 · Charts · OCR 12.02a
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 20 · Charts · OCR 12.02a
A category has frequency 12 out of 40. Find its percentage.
Answer:
Fraction in the category = 1240 = 0.3.
0.3 × 100% = 30%.
Question 21 · Charts · OCR 12.02a
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 22 · Charts · OCR 12.02a
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 23 · Frequency polygons · OCR 12.02b
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 24 · Histograms · OCR 12.02b · Higher only
What does the vertical axis of a histogram show?
Answer:
Frequency density.
Frequency density = frequency ÷ class width.
Question 25 · Histograms · OCR 12.02b · Higher only
A class 10 < x ≤ 25 has frequency 30. Find the frequency density.
Answer:
Class width = 15.
30 ÷ 15 = 2.
Question 26 · Histograms · OCR 12.02b · 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 27 · Cumulative frequency · OCR 12.02b · 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 28 · Cumulative frequency · OCR 12.02b · 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 29 · Box plots · OCR 12.02b · 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 30 · Interquartile range · OCR 12.02b · Higher only
LQ = 23 and UQ = 41. Find the interquartile range.
Answer:
IQR = UQ − LQ.
41 − 23 = 18.
Question 31 · Averages · OCR 12.02b
Find the mean of 4, 7, 9, 10 and 15.
Answer:
Total = 45.
45 ÷ 5 = 9.
Question 32 · Averages · OCR 12.02b
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 33 · Averages · OCR 12.02b
Find the mode of 3, 6, 6, 2, 8, 6, 3.
Answer:
6 appears 3 times.
Mode = 6.
Question 34 · Range · OCR 12.02b
Find the range of 14, 3, 22, 9, 17.
Answer:
Largest − smallest.
22 − 3 = 19.
Question 35 · Mean from a table · OCR 12.02b
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 36 · Grouped data · OCR 12.02b
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 37 · Grouped data · OCR 12.02b
Why is the mean from grouped data only an estimate?
Answer:
The exact values are not known.
Midpoints are used instead.
Question 38 · Grouped data · OCR 12.02b
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 39 · Populations · OCR 12.03a
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 40 · Interpreting · OCR 12.03a
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 41 · Scatter graphs · OCR 12.03c
What does positive correlation mean?
Answer:
As one variable increases, so does the other.
The points slope upwards.
Question 42 · Line of best fit · OCR 12.03c
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 43 · Interpolation · OCR 12.03c
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 44 · Correlation · OCR 12.03c
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 45 · Outliers · OCR 12.03c
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 46 · Scatter graphs · OCR 12.03c
Ice cream sales rise as temperature rises. What type of correlation is this?
Answer:
Both increase together.
Positive correlation.
Question 47 · Scatter graphs · OCR 12.03c
What does no correlation look like?
Answer:
The points are scattered randomly.
There is no relationship.
Question 48 · Scatter graphs · OCR 12.03c
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 49 · Scatter graphs · OCR 12.03c
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 50 · Outliers · OCR 12.03d
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.

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