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GCSE Statistics study materials
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GCSE Statistics practice questions

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Question 1Data collection

Which of these is an example of secondary data?

  1. Measurements recorded in a laboratory
  2. Existing hospital patient records Correct answer.
  3. Responses to a new researcher survey
  4. Sensor readings taken in an experiment

Explanation

Secondary data are data collected by someone else for a different purpose. Existing hospital records were not gathered by this researcher, so they are secondary. Laboratory measurements, survey responses and sensor readings collected for the current study are primary data.

Question 2Data collection

What is a census?

  1. A survey of every population member Correct answer.
  2. A survey repeated every month
  3. A survey of volunteers only
  4. A survey of a small selected group

Explanation

A census attempts to collect data from every member of the population. It gives complete coverage but is expensive and time-consuming.

Question 3Data collection

Which of these gives qualitative data?

  1. The masses of 20 apples in grams
  2. The colours of cars in a car park Correct answer.
  3. The heights of 30 students in cm
  4. The number of cars in a car park

Explanation

Qualitative data describe qualities or categories rather than numerical amounts. Colours are labels, so they are qualitative. Heights, counts and masses are numerical.

Question 4Data collection

Which variable is continuous?

  1. The number of goals scored in a match
  2. The number of pages in a book
  3. The time taken to run 100 m Correct answer.
  4. The number of siblings a student has

Explanation

Continuous data can take any value in a range and are usually measured. Time can be measured to increasing precision, so it is continuous. Counts are discrete.

Question 5Data collection

What is a sampling frame?

  1. A diagram showing the sample
  2. The person who collects the data
  3. The questionnaire used in a survey
  4. A list of all population members Correct answer.

Explanation

A sampling frame is the list or register from which a sample is drawn. It should ideally include every member of the population exactly once.

Question 6Data collection

In a simple random sample, every member of the population...

  1. is chosen deliberately by the researcher
  2. must volunteer to take part
  3. has an equal chance of being selected Correct answer.
  4. is selected in a fixed pattern

Explanation

Simple random sampling gives every member of the population an equal probability of selection. Selection is by chance, not by the researcher's choice.

Question 7Data collection

Which sample is most likely to be biased?

  1. Numbers from a random generator
  2. People leaving a gym are surveyed Correct answer.
  3. Every tenth name on a list
  4. Names drawn from a hat

Explanation

A sample is biased if some parts of the population are more likely to be included. People leaving a gym are more likely to exercise, so the sample over-represents them.

Question 8Data collection

Why is a pilot study carried out?

  1. To test the questionnaire Correct answer.
  2. To publish results quickly
  3. To select the sample randomly
  4. To increase the sample size

Explanation

A pilot study is a small trial run of the survey. It identifies unclear questions, poor response options and practical problems before the main survey.

Question 9Data collection

A researcher selects every 20th name from an alphabetical list of 2000 employees after a random start. Which method is used?

  1. Cluster sampling
  2. Quota sampling
  3. Systematic sampling Correct answer.
  4. Stratified sampling

Explanation

Systematic sampling selects items at regular intervals from a list after a random starting point. Every 20th name follows a fixed interval, so this is systematic sampling.

Question 10Data collection

A school has 600 boys and 400 girls. A stratified sample of 50 is taken. How many girls should be included?

  1. 30
  2. 20 Correct answer.
  3. 25
  4. 40

Explanation

Stratified sampling allocates the sample size in proportion to each group's size. Girls make up 400/1000 = 0.4 of the population, so 0.4 × 50 = 20.

Question 11Data collection

Which statement describes quota sampling?

  1. The interviewer fills set numbers of people in chosen categories Correct answer.
  2. Whole clusters are selected at random and all members surveyed
  3. Each member of the population is listed and chosen at random
  4. The population is split into groups and a random sample is taken from each

Explanation

Quota sampling sets target numbers for categories, and the interviewer chooses people until each quota is filled. Selection within a quota is not random, which can introduce bias.

Question 12Data collection

Which survey question is leading?

  1. How do you travel to school?
  2. Do you own a bicycle?
  3. How many hours do you read each week?
  4. The library is great, isn't it? Correct answer.

Explanation

A leading question suggests a particular answer or makes one response seem expected. The tag question invites agreement that the library is great.

Question 13Data collection

Which is an advantage of a closed question?

  1. It cannot be answered incorrectly
  2. The responses are easy to compare and analyse Correct answer.
  3. It avoids the need for a pilot study
  4. It allows respondents to give detailed reasons

Explanation

Closed questions have fixed response options, so answers can be coded and compared easily. They are less useful when detailed explanations are needed.

Question 14Data collection

A questionnaire asks: 'How much do you spend on food each week?' Why might the answers be unreliable?

  1. The question is too long
  2. The question is leading
  3. The question has too many options
  4. Respondents may not recall amounts Correct answer.

Explanation

Self-reported figures depend on memory and may be estimates. If respondents cannot recall exact amounts, the data are unreliable even if the question is clear.

Question 15Data collection

A researcher records how many cars pass a junction between 8 am and 9 am. This is...

  1. an observation Correct answer.
  2. a census
  3. a controlled experiment
  4. a questionnaire survey

Explanation

The researcher is watching and recording behaviour without asking questions, which is observation. Experiments involve deliberately applying a treatment, and a census covers a whole population.

Question 16Data collection

Which is an advantage of a face-to-face interview over a postal questionnaire?

  1. It can reach a very large sample quickly
  2. It is cheaper to administer
  3. The interviewer can clarify questions Correct answer.
  4. Respondents feel less pressure to answer

Explanation

In a face-to-face interview the interviewer can explain questions and probe answers, improving understanding. Interviews are usually more expensive and slower than postal surveys.

Question 17Data collection

A town has 40 streets. A researcher randomly selects 5 streets and surveys every household on those streets. Which method is this?

  1. Cluster sampling Correct answer.
  2. Systematic sampling
  3. Quota sampling
  4. Stratified sampling

Explanation

Cluster sampling selects whole groups (clusters) at random and then surveys all members of the selected groups. Streets are the clusters here.

Question 18Data collection

Why is a sample often preferred to a census?

  1. It always gives more accurate results
  2. It is quicker and cheaper Correct answer.
  3. It removes all bias from the data
  4. It does not need a sampling frame

Explanation

A sample can be collected faster and at lower cost than a census. A census gives complete coverage but is often impractical for large populations.

Question 19Data collection

Why are sensitive personal questions usually placed near the end of a questionnaire?

  1. To avoid the need for a pilot study
  2. To make the questionnaire shorter
  3. To let respondents build trust first Correct answer.
  4. To make coding easier

Explanation

Placing sensitive questions later lets respondents become comfortable with the survey before answering personal items. This can improve response quality and reduce early drop-out.

Question 20Data collection

A set of bathroom scales gives readings 3 kg too high every time. The readings are...

  1. reliable but not valid Correct answer.
  2. neither reliable nor valid
  3. both reliable and valid
  4. valid but not reliable

Explanation

Reliability means repeated measurements give consistent results; validity means measuring the true value. The scales are consistent, so reliable, but always 3 kg too high, so not valid.

Question 21Data collection

In a capture-recapture study, 40 fish are caught, marked and released. Later, 50 fish are caught and 8 are marked. What is the best estimate of the population?

  1. 200
  2. 400
  3. 320
  4. 250 Correct answer.

Explanation

The proportion marked in the second sample estimates the proportion marked in the population. So 8/50 = 40/N, giving N = 40 × 50 ÷ 8 = 250.

Question 22Data collection

A researcher uses a telephone directory as a sampling frame for a survey about internet access. What is the main weakness?

  1. It is too small to sample from
  2. It lists people in alphabetical order
  3. It changes too slowly to be useful
  4. It omits people with no landline Correct answer.

Explanation

A good sampling frame should include every member of the population. A telephone directory omits people without a landline, who may differ in internet access, causing coverage bias.

Question 23Data collection

A company surveys its employees about job satisfaction by email. Only 30% reply. The results are most likely to suffer from...

  1. a leading question
  2. non-response bias Correct answer.
  3. sampling with replacement
  4. measurement error

Explanation

Non-response bias occurs when people who do not respond differ systematically from those who do. A 30% response rate means most employees are not represented.

Question 24Data collection

A drug trial gives the new drug to volunteers who ask for it and compares them with volunteers who do not. Why is this not a valid experiment?

  1. Volunteers chose their own group Correct answer.
  2. The drug is not measured in grams
  3. The sample is too small to analyse
  4. The volunteers are not paid

Explanation

In a valid experiment, treatments should be assigned randomly to comparable groups. Here volunteers choose their group, so differences may be due to the type of person rather than the drug.

Question 25Data collection

A researcher takes a random sample of 50 from a population of 5000 using random numbers. Which statement is true?

  1. Without replacement duplicates always occur
  2. Random sampling guarantees representativeness
  3. A larger sample always removes bias
  4. The same person can be chosen twice Correct answer.

Explanation

With replacement, each selected item is returned to the population, so it can be chosen again. Without replacement, each member can appear at most once.

Question 26Data collection

Which of the following is an example of continuous data?

  1. The number of pages in a paperback book
  2. The number of cars in a car park
  3. The number of goals in a match
  4. The mass of a parcel in kilograms Correct answer.

Explanation

Continuous data can take any value within a range and are usually measured, such as mass. Counts such as pages, goals and cars are whole numbers, so they are discrete.

Question 27Data collection

Which of the following is an example of secondary data?

  1. Answers collected in a survey run by the researcher
  2. Readings recorded by a sensor set up for the study
  3. Figures taken from a government website Correct answer.
  4. Measurements made by a student during an experiment

Explanation

Secondary data are data that were collected by someone else and then used by the researcher. Figures from a government website already exist, whereas the other options are collected first-hand for the study.

Question 28Data collection

Which of the following best describes a sampling frame?

  1. A method of selecting every tenth item
  2. A small trial run carried out before a questionnaire
  3. A graph showing the spread of the data
  4. A list of all the members of the population Correct answer.

Explanation

A sampling frame is the list or register from which a sample is actually selected, such as a list of names or addresses. It should ideally match the population of interest.

Question 29Data collection

A questionnaire asks: 'Do you agree that the library should stay open later and that more books should be bought?' What is the main problem with this question?

  1. It uses vague wording
  2. It asks about two issues at once Correct answer.
  3. It asks for sensitive information
  4. It is a leading question

Explanation

The question combines two separate opinions-opening hours and book purchases-so a single answer cannot show which part the respondent agrees with. Such questions are called double-barrelled.

Question 30Data collection

A reporter asks readers of a magazine to send in their views by post. What type of sample is this?

  1. Simple random sample
  2. Self-selecting sample Correct answer.
  3. Stratified sample
  4. Systematic sample

Explanation

People choose whether to respond, so only those with strong views or an interest in the magazine are likely to reply. This is a self-selecting, or volunteer, sample.

Question 31Data collection

Which of the following is a disadvantage of an open question?

  1. It cannot collect detailed responses
  2. It restricts the range of answers that respondents can give
  3. It must be answered with a number
  4. It is difficult to analyse because the answers vary Correct answer.

Explanation

Open questions allow any answer, which gives detail but produces varied responses that must be coded before analysis. This makes them harder to summarise than closed questions.

Question 32Data collection

A study finds that students who eat breakfast get higher test scores. Which of the following is a possible confounding variable?

  1. The number of students included in the study
  2. The test scores achieved by each student
  3. The amount of sleep each student gets Correct answer.
  4. The subject of the test being taken

Explanation

A confounding variable is linked to both the response and the explanatory variable, so its effect cannot be separated. Sleep may affect test scores and may also differ between breakfast eaters and non-eaters.

Question 33Data collection

A scientist wants to test whether a new fertiliser increases plant growth. Which design gives the fairest comparison?

  1. Compare fertilised plants with plants of a different species
  2. Give fertiliser only to the plants that look healthiest
  3. Give fertiliser to all the plants in the experiment
  4. Randomly allocate plants to fertiliser or no fertiliser Correct answer.

Explanation

A fair test needs a control group and random allocation, so any difference in growth can be attributed to the fertiliser. Without a comparison group or random assignment, confounding factors remain.

Question 34Data collection

Two independent random samples of size 100 are taken from the same population. The sample means are different. What is the main reason for this?

  1. Non-response error
  2. Bias in the sampling frame
  3. Sampling variation Correct answer.
  4. Measurement error

Explanation

Even with the same sampling method, different random samples contain different individuals, so sample statistics vary. This natural variability is called sampling variation.

Question 35Processing, representing and analysing data

A researcher records the exact time, in seconds, that each of 40 runners takes to complete a race. What type of data is this?

  1. Continuous Correct answer.
  2. Ordinal
  3. Categorical
  4. Discrete

Explanation

Time is measured on a numerical scale and can take any value within a range, including decimals. Numerical data that can take any value in an interval are continuous.

Question 36Processing, representing and analysing data

A frequency table shows the scores 1, 2 and 3 with frequencies 3, 5 and 2 respectively. What is the mean score?

  1. 2.0
  2. 1.9 Correct answer.
  3. 1.8
  4. 2.1

Explanation

The mean from a frequency table is the total of score times frequency divided by the total frequency. Here the total is 1×3 + 2×5 + 3×2 = 19 and there are 10 values, giving 1.9.

Question 37Processing, representing and analysing data

Which statement describes a histogram for continuous data?

  1. It has gaps between all bars
  2. It uses a circle divided into sectors
  3. It has no gaps between bars Correct answer.
  4. It shows categories in any order

Explanation

A histogram represents continuous numerical classes, so adjacent bars touch to show that the classes are continuous. Gaps would suggest separate categories rather than a continuous scale.

Question 38Processing, representing and analysing data

The daily number of texts sent by a student over seven days is 3, 5, 5, 7, 8, 5 and 9. What is the mode?

  1. 7
  2. 6
  3. 5 Correct answer.
  4. 8

Explanation

The mode is the value that occurs most often. The value 5 appears three times, more than any other value.

Question 39Processing, representing and analysing data

The temperatures recorded on six days were 12 °C, 15 °C, 9 °C, 18 °C, 22 °C and 7 °C. What is the range?

  1. 13 °C
  2. 15 °C Correct answer.
  3. 14 °C
  4. 16 °C

Explanation

The range is the largest value minus the smallest value. Here 22 − 7 = 15, so the range is 15 °C.

Question 40Processing, representing and analysing data

On a scatter graph, the points rise from left to right closely around a straight line. Which description fits?

  1. Negative and strong
  2. Positive and weak
  3. No correlation
  4. Positive and strong Correct answer.

Explanation

A rising pattern means that as one variable increases, the other tends to increase, which is positive correlation. Points close to a straight line indicate a strong relationship.

Question 41Processing, representing and analysing data

The ordered values in a data set are 12, 14, 15, 21, 23, 27, 31 and 35. What is the median?

  1. 24
  2. 22 Correct answer.
  3. 23
  4. 21

Explanation

There are eight values, so the median is the mean of the fourth and fifth values. The fourth and fifth values are 21 and 23, giving (21 + 23) ÷ 2 = 22.

Question 42Processing, representing and analysing data

A two-way table shows that 18 students play a sport and 12 do not. Of the 18 who play a sport, 7 are girls. How many of the students who play a sport are boys?

  1. 11 Correct answer.
  2. 7
  3. 5
  4. 12

Explanation

The total number of students who play a sport is 18, and 7 of these are girls. Subtracting gives 18 − 7 = 11 boys who play a sport.

Question 43Processing, representing and analysing data

A grouped frequency table has classes 0–10, 10–20 and 20–30 with frequencies 4, 6 and 10. Using midpoints, what is the estimated mean?

  1. 20
  2. 17
  3. 18 Correct answer.
  4. 19

Explanation

The midpoints are 5, 15 and 25, giving a total of 5×4 + 15×6 + 25×10 = 360. Dividing by the total frequency 20 gives an estimated mean of 18.

Question 44Processing, representing and analysing data

A frequency table gives values 1, 2, 3 and 4 with frequencies 4, 8, 6 and 3. What is the median?

  1. 2.5
  2. 1
  3. 3
  4. 2 Correct answer.

Explanation

The total frequency is 21, so the median is the 11th value. The cumulative frequency reaches 4 after value 1 and 12 after value 2, so the 11th value lies in the group for value 2.

Question 45Processing, representing and analysing data

In a survey of 240 people, 60 chose bus as their main transport. What angle should represent bus in a pie chart?

  1. 60°
  2. 120°
  3. 90° Correct answer.
  4. 45°

Explanation

The angle for a category is found by dividing its frequency by the total and multiplying by 360°. Here 60/240 × 360° = 90°.

Question 46Processing, representing and analysing data

A box plot has lower quartile 12, median 18 and upper quartile 27. What is the interquartile range?

  1. 9
  2. 15 Correct answer.
  3. 27
  4. 6

Explanation

The interquartile range is the upper quartile minus the lower quartile. Here 27 − 12 = 15.

Question 47Processing, representing and analysing data

A data set of 10 values contains one value that is much larger than all the others. Which average is most affected by this value?

  1. Mode
  2. Range
  3. Median
  4. Mean Correct answer.

Explanation

The mean uses the size of every value, so a very large outlier increases the total and pulls the mean upwards. The median and mode depend on position or frequency rather than the size of the outlier.

Question 48Processing, representing and analysing data

Two classes have the same mean test score. Class A has standard deviation 4.2 and Class B has standard deviation 8.6. What can be concluded?

  1. Class B is more spread out Correct answer.
  2. Class A is more spread out
  3. Class A has the higher mean score
  4. Class B has the lower mean score

Explanation

Standard deviation measures the spread of values around the mean. A larger standard deviation means the values are more spread out, and 8.6 is greater than 4.2.

Question 49Processing, representing and analysing data

A line of best fit on a scatter graph passes through the points (10, 25) and (30, 45). Using this line, what is the estimated y-value when x = 20?

  1. 35 Correct answer.
  2. 40
  3. 30
  4. 45

Explanation

The line rises by 20 in y as x rises by 20, so its gradient is 1. At x = 20, which is halfway between 10 and 30, y is halfway between 25 and 45, giving 35.

Question 50Processing, representing and analysing data

Quarterly sales are 20, 24, 28, 32 and 36. What is the 3-point moving average centred on the third quarter?

  1. 28 Correct answer.
  2. 26
  3. 32
  4. 30

Explanation

A 3-point moving average centred on the third value uses the second, third and fourth values. The average is (24 + 28 + 32) ÷ 3 = 28.