I85PREP
⌘ K
BGCSE Statistics 4040 study materials
BGCSE Statistics 4040 study resources

BGCSE Statistics 4040 practice questions

One question at a time. Build your BGCSE Statistics 4040 understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Data Collection and Sources

A researcher wants to estimate the average monthly income of households in a large town. Which of the following is a population rather than a sample?

  1. Two hundred households chosen at random from the town
  2. All households in the town Correct answer.
  3. The first fifty households on a register
  4. Households selected from one street

Explanation

The population is the complete set of all units about which information is wanted, so it includes every household in the town. Any subset drawn from that complete group is a sample, however it was selected.

Question 2Data Collection and Sources

Which of the following is an example of secondary data?

  1. Responses to a questionnaire you designed and distributed
  2. Counts you made of vehicles passing a junction
  3. A table of rainfall figures published by the national weather office Correct answer.
  4. Measurements you recorded during a laboratory practical

Explanation

Secondary data are data collected by someone else and used by a second party, such as published official records. Data you gather yourself through questionnaires, experiments or observation are primary data.

Question 3Data Collection and Sources

A survey is to be conducted on the reading habits of students in a school of 900 students. Which method is most likely to produce a representative sample of 90 students?

  1. Asking 90 volunteers from a single class to take part
  2. Choosing the first 90 students who arrive at school one morning
  3. Selecting 90 students at random from a complete list of all students Correct answer.
  4. Selecting the 90 students who use the library most often

Explanation

A simple random sample drawn from a complete list gives every student an equal chance of selection, which reduces bias. Convenience and volunteer selections favour particular groups and are unlikely to represent the whole school.

Question 4Data Collection and Sources

A factory has 600 workers divided into three shifts of 300, 200 and 100 workers. A researcher selects 60 workers by taking 30 from the first shift, 20 from the second and 10 from the third. Which sampling method is used?

  1. Simple random sampling
  2. Systematic sampling
  3. Quota sampling
  4. Stratified sampling Correct answer.

Explanation

In stratified sampling the population is divided into groups and the sample is drawn from each group in proportion to its size. Here each shift contributes one tenth of its members, matching the population proportions exactly.

Question 5Data Collection and Sources

A list of 500 names is numbered from 1 to 500. A researcher uses a random starting point and then selects every tenth name. Which sampling technique is being described?

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

Explanation

Systematic sampling involves choosing a random starting point in a list and then taking items at a fixed interval. Selecting every tenth name after a random start is the standard form of this method.

Question 6Data Collection and Sources

A researcher telephones households listed in a telephone directory to ask about internet access. Which group is most likely to be under-represented in the resulting sample?

  1. Households living in the same district as the researcher
  2. Households that are not listed in the directory Correct answer.
  3. Households with more than one telephone line
  4. Households that pay their bills monthly

Explanation

The sampling frame is the telephone directory, so households absent from it can never be selected. Any group excluded from the frame is systematically under-represented, which is frame bias.

Question 7Data Collection and Sources

Which of the following is a closed question?

  1. What improvements would you suggest for school transport?
  2. Describe how you usually travel to school.
  3. How many minutes does your journey to school take? Correct answer.
  4. Why did you choose your current school?

Explanation

A closed question offers a limited set of possible replies, often a number or fixed categories, so answers are easy to code and compare. Open questions invite free-form responses that require interpretation.

Question 8Data Collection and Sources

A questionnaire asks: "Do you agree that the new library should be open later because students need more study time?" Which problem is most evident?

  1. The question is double-barrelled
  2. The question is leading Correct answer.
  3. The question is too short
  4. The question uses technical vocabulary

Explanation

A leading question suggests the answer the researcher expects, so it pushes respondents toward agreement. The phrase justifying later opening makes agreement seem the reasonable response.

Question 9Data Collection and Sources

A student records the number of books read last month by each of 30 classmates. Which type of variable is being recorded?

  1. Quantitative continuous
  2. Quantitative discrete Correct answer.
  3. Qualitative ordinal
  4. Qualitative nominal

Explanation

A count of books can take only whole-number values, so it is quantitative and discrete. Continuous variables can take any value within a range, and qualitative variables describe categories rather than amounts.

Question 10Data Collection and Sources

Which of the following variables is measured on an ordinal scale?

  1. Number of passengers on a bus
  2. Mass of a parcel in kilograms
  3. Rating of service as poor, fair, good or excellent Correct answer.
  4. Colour of a car

Explanation

An ordinal scale has categories that can be meaningfully ranked, but the gaps between ranks need not be equal. A rating from poor to excellent has a clear order without a fixed numerical distance between levels.

Question 11Data Collection and Sources

Which source of data is most likely to be unreliable because it depends on the memory of respondents?

  1. A retrospective survey asking adults to recall how often they exercised ten years ago Correct answer.
  2. A laboratory measurement of boiling point
  3. A count of cars recorded by an automatic sensor
  4. A record of rainfall taken from a calibrated gauge

Explanation

Recall surveys rely on human memory, which fades and can be distorted over long periods, so the data may be inaccurate. Instrument-based measurements are recorded at the time and do not depend on memory.

Question 12Data Collection and Sources

A researcher wishes to compare the opinions of male and female students on a school policy. Which sampling approach best ensures both groups are adequately represented?

  1. Selecting volunteers from the football team
  2. Selecting a random sample from each gender separately Correct answer.
  3. Selecting the first students to enter the dining hall
  4. Selecting students from a single mixed class

Explanation

Sampling separately from each gender is stratified sampling, which guarantees that both groups appear in sufficient numbers for comparison. Convenience selections may over-represent one group and weaken the comparison.

Question 13Data Collection and Sources

A market researcher stands outside a supermarket on a weekday morning and interviews the first 50 shoppers who agree to talk. Which type of bias is most likely to affect this sample?

  1. The sample excludes people who shop at other times or elsewhere Correct answer.
  2. The sample size is too small to be counted
  3. The shoppers are selected by a random number generator
  4. The questionnaire has too many closed questions

Explanation

Interviewing only weekday-morning shoppers systematically excludes people who work then or shop at other times. This is a form of selection bias caused by the convenience method of choosing respondents.

Question 14Data Collection and Sources

Which of the following is the main advantage of using a pilot study before a large survey?

  1. It guarantees that the sample will be representative
  2. It identifies unclear questions and problems with the procedure before the full survey Correct answer.
  3. It removes the need for a sampling frame
  4. It increases the population size

Explanation

A pilot study is a small trial run that reveals ambiguous questions, poor instructions and practical difficulties. These can then be corrected before the main survey, improving the quality of the final data.

Question 15Data Collection and Sources

A researcher uses a random number table to choose 40 students from a numbered list of 800 students. Which sampling method is being used?

  1. Cluster sampling
  2. Quota sampling
  3. Judgement sampling
  4. Simple random sampling Correct answer.

Explanation

Using random numbers to pick individuals from a complete numbered list gives every student an equal chance of selection. This is the defining feature of simple random sampling.

Question 16Data Collection and Sources

A survey asks respondents to state their age in completed years and their occupation. Which pair correctly describes these two variables?

  1. Age is qualitative and occupation is quantitative
  2. Age is quantitative and occupation is qualitative Correct answer.
  3. Both variables are qualitative
  4. Both variables are quantitative

Explanation

Age in years is a numerical measurement, so it is quantitative. Occupation places a person into a named category, which makes it qualitative.

Question 17Data Collection and Sources

A researcher wants to estimate the proportion of defective items produced in a factory during a day. Which method gives the most reliable estimate?

  1. Inspecting items that look visibly damaged
  2. Inspecting a random sample taken at regular intervals throughout the day Correct answer.
  3. Inspecting the first ten items produced that morning
  4. Asking the machine operators for their opinion

Explanation

Sampling at regular intervals across the whole day captures variation in production conditions, giving a more representative picture. Selecting only early items or visibly damaged ones introduces systematic bias.

Question 18Data Collection and Sources

Which of the following best describes the term sampling frame?

  1. The set of all possible values a variable can take
  2. The number of people who respond to a survey
  3. A list or register of the members of the population from which a sample is drawn Correct answer.
  4. The difference between a sample estimate and the population value

Explanation

A sampling frame is the practical list of population members used to select the sample, such as a register or directory. A good frame should be complete and up to date.

Question 19Data Collection and Sources

A researcher asks students to rate their satisfaction with school meals on a scale from 1 to 5. What is the main limitation of this measurement?

  1. The data cannot be summarised in a table
  2. The scale produces qualitative nominal data
  3. The variable is continuous
  4. Different students may interpret the numbers differently Correct answer.

Explanation

Rating scales are subjective, so the meaning of each point on the scale may vary between respondents. This reduces comparability even though the numbers can still be summarised and averaged.

Question 20Data Collection and Sources

A newspaper reports that a survey of its own readers found most people support the newspaper's editorial position. Why should this result be treated with caution?

  1. Surveys can never provide useful information
  2. The sample is large, so the result must be accurate
  3. The result was published in a newspaper
  4. Readers of the newspaper are likely to share its views, so the sample is biased Correct answer.

Explanation

Readers who respond to a newspaper's own survey are self-selected and likely to be sympathetic to its viewpoint. The sample therefore over-represents one opinion and cannot be generalised to the wider public.

Question 21Data Collection and Sources

A researcher records the heights of 100 plants grown in a greenhouse. Which feature makes height a continuous variable?

  1. Height is ranked from tallest to shortest
  2. Height can take any value within a range, limited only by measurement precision Correct answer.
  3. Height is always a whole number of centimetres
  4. Height is recorded as a category

Explanation

Continuous variables can take any value in an interval, so a height could in principle be 12.3 cm or 12.31 cm depending on the instrument. Only the precision of measurement limits the recorded value.

Question 22Data Collection and Sources

A study finds that students who eat breakfast score higher in tests. A researcher concludes that eating breakfast causes higher scores. Which is the most appropriate criticism of this conclusion?

  1. Breakfast cannot be measured
  2. The conclusion is valid because the two variables are related
  3. Test scores are always unreliable
  4. Observational data cannot establish causation because other variables may explain the association Correct answer.

Explanation

Observational studies show association, not causation, because confounding factors such as income or study habits may affect both breakfast habits and test scores. A controlled experiment would be needed to support a causal claim.

Question 23Data Collection and Sources

Which of the following is the best example of data collected by direct observation?

  1. A table of population figures from a census
  2. A government report on national unemployment
  3. A student recording the number of birds visiting a feeder each hour Correct answer.
  4. A history book describing past events

Explanation

Direct observation means the researcher personally watches and records events as they occur. Counting birds at a feeder is a first-hand observation, whereas reports, books and census tables are compiled by others.

Question 24Data Collection and Sources

A researcher divides a town into 20 districts and randomly selects 4 districts, then surveys every household in those districts. Which sampling method is used?

  1. Stratified sampling
  2. Simple random sampling
  3. Cluster sampling Correct answer.
  4. Systematic sampling

Explanation

Cluster sampling selects whole groups, called clusters, and then studies all units within the chosen groups. Here the districts are clusters and every household in the selected districts is surveyed.

Question 25Data Presentation and Display

A school records the eye colour of 40 students as blue, brown, green or hazel. Which type of chart is most suitable for displaying this data?

  1. Pie chart Correct answer.
  2. Histogram
  3. Cumulative frequency curve
  4. Scatter graph

Explanation

Eye colour is categorical data, so each category occupies a sector whose angle is proportional to its frequency. A pie chart displays the proportions of a whole for named categories clearly. Histograms, scatter graphs and cumulative frequency curves all require numerical data.

Question 26Data Presentation and Display

In a bar chart, the bars for four categories have heights 12, 8, 6 and 4 units. What is the total frequency represented?

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

Explanation

The total frequency is found by adding the heights of all the bars: 12 + 8 + 6 + 4 = 30. In a bar chart each bar height equals the frequency of that category. Summing them gives the overall number of observations.

Question 27Data Presentation and Display

Which statement correctly describes a histogram?

  1. It has gaps between bars, showing separate categories
  2. It plots one point for each pair of values
  3. It has bars that touch, showing continuous grouped data Correct answer.
  4. It shows the middle half of the data as a box

Explanation

A histogram represents continuous numerical data divided into class intervals, and the bars are drawn touching to show that the variable is continuous. The area of each bar, not just its height, represents the frequency when class widths differ. Gaps between bars are characteristic of bar charts for categorical data.

Question 28Data Presentation and Display

A pie chart shows how 120 students travel to school. The sector for walking has an angle of 90 degrees. How many students walk?

  1. 40
  2. 20
  3. 30 Correct answer.
  4. 45

Explanation

A full circle is 360 degrees, so a sector of 90 degrees represents 90/360 = 1/4 of the total. One quarter of 120 students is 30 students. The angle is converted to a fraction of the whole before multiplying by the total frequency.

Question 29Data Presentation and Display

What does a scatter graph primarily show?

  1. The relationship between two numerical variables Correct answer.
  2. The cumulative total of a variable
  3. The spread of a single variable about its median
  4. The frequency of each category

Explanation

A scatter graph plots one point for each observation using two numerical variables, one on each axis. The pattern of points reveals whether a relationship or correlation exists between the variables. Frequency and cumulative totals are shown by other types of chart.

Question 30Data Presentation and Display

Which measure of average is read directly from the highest bar of a bar chart of discrete data?

  1. The median
  2. The mean
  3. The mode Correct answer.
  4. The range

Explanation

The mode is the value or category with the highest frequency, which corresponds to the tallest bar. The median requires ordering the data and locating the middle value. The mean requires calculating a total and dividing, and the range is a measure of spread rather than an average.

Question 31Data Presentation and Display

A frequency table lists the number of siblings for 20 students. Which display keeps every individual value visible while showing frequency?

  1. A cumulative frequency curve
  2. A bar chart of the frequencies Correct answer.
  3. A histogram with unequal class widths
  4. A box-and-whisker plot

Explanation

A bar chart shows each distinct value as a separate bar whose height is its frequency, so every value remains visible. A cumulative frequency curve and a box-and-whisker plot summarise the data and hide individual values. A histogram is intended for grouped continuous data.

Question 32Data Presentation and Display

On a pictogram, one symbol represents 8 books, and a row shows 3 and a half symbols. How many books does the row represent?

  1. 28 Correct answer.
  2. 20
  3. 32
  4. 24

Explanation

Each whole symbol represents 8 books, so three symbols represent 24 books. A half symbol represents 4 books, giving 24 + 4 = 28 books in total. The key must be applied to every symbol, including partial symbols.

Question 33Data Presentation and Display

A histogram has a class from 10 to 20 with frequency 15 and a class from 20 to 40 with frequency 45. Which class has the greater frequency density?

  1. The class 20 to 40, with density 2.25 Correct answer.
  2. Both classes have equal frequency density
  3. The class 10 to 20, with density 1.5
  4. The class 10 to 20, with density 0.67

Explanation

Frequency density equals frequency divided by class width. For 10 to 20 the density is 15/10 = 1.5, and for 20 to 40 it is 45/20 = 2.25. The wider class therefore has the greater frequency density, so its bar is taller.

Question 34Data Presentation and Display

A pie chart is drawn for data with frequencies 20, 30, 40 and 30. What angle represents the category with frequency 40?

  1. 144 degrees
  2. 120 degrees Correct answer.
  3. 108 degrees
  4. 90 degrees

Explanation

The total frequency is 20 + 30 + 40 + 30 = 120, so the category with frequency 40 is 40/120 = 1/3 of the data. One third of 360 degrees is 120 degrees. Each sector angle equals its fraction of the total multiplied by 360.

Question 35Data Presentation and Display

A cumulative frequency curve rises from 0 to 80. The curve passes through 20 at the value 15 and through 60 at the value 35. What is the interquartile range?

  1. 40
  2. 20 Correct answer.
  3. 25
  4. 15

Explanation

With a total frequency of 80, the lower quartile is at cumulative frequency 20 and the upper quartile at cumulative frequency 60. Reading across gives a lower quartile of 15 and an upper quartile of 35. The interquartile range is 35 minus 15, which equals 20.

Question 36Data Presentation and Display

A line graph shows a company's monthly sales over one year. Which feature is shown by the steepest downward section of the line?

  1. The lowest total sales for the year
  2. The average sales across the year
  3. The greatest decrease in sales between consecutive months Correct answer.
  4. The highest sales achieved in a single month

Explanation

On a line graph the slope between consecutive points represents the rate of change. A steep downward slope therefore indicates the largest fall between two consecutive months. The lowest point of the line, not the slope, shows the lowest sales value.

Question 37Data Presentation and Display

A scatter graph of height against weight for 20 adults shows points closely grouped around a straight line sloping upwards. What does this indicate?

  1. That height causes weight to decrease
  2. A positive correlation between height and weight Correct answer.
  3. No correlation between height and weight
  4. A negative correlation between height and weight

Explanation

An upward-sloping pattern of points indicates positive correlation: as one variable increases, the other tends to increase. The closer the points lie to a straight line, the stronger the correlation. A downward pattern would indicate negative correlation.

Question 38Data Presentation and Display

A frequency table gives the number of pets owned by 50 families. Which display would best compare the number of families owning 0, 1, 2 or 3 pets?

  1. A vertical bar chart Correct answer.
  2. A histogram
  3. A cumulative frequency curve
  4. A line graph of cumulative totals

Explanation

The number of pets is a small set of distinct discrete values, so a bar chart compares the frequencies of each value clearly. Each bar height equals the number of families for that value. Cumulative displays would hide the individual frequencies.

Question 39Data Presentation and Display

In a histogram, a bar covers the class 30 to 45 and has frequency density 4. What is the frequency of this class?

  1. 45
  2. 19
  3. 60 Correct answer.
  4. 15

Explanation

Frequency equals frequency density multiplied by class width. The class width is 45 minus 30, which is 15, and multiplying by the density 4 gives 60. This relationship follows because the area of each bar represents the frequency.

Question 40Data Presentation and Display

A pie chart of 200 responses has sectors of 150 degrees, 90 degrees, 60 degrees and 60 degrees. How many responses does the smallest sector represent?

  1. 25
  2. 50
  3. 33 Correct answer.
  4. 40

Explanation

The smallest sector is 60 degrees, which is 60/360 = 1/6 of the total. One sixth of 200 responses is approximately 33.3, which rounds to 33. The other sectors represent larger shares of the total.

Question 41Data Presentation and Display

A stem-and-leaf diagram uses stems 1, 2 and 3 with leaves 2 5 8, 0 3 3 7 and 1 4. How many values are recorded in total, and what is the median?

  1. 10 values with median 27
  2. 8 values with median 23
  3. 9 values with median 23 Correct answer.
  4. 9 values with median 22

Explanation

Counting the leaves gives 3 + 4 + 2 = 9 values, which in order are 12, 15, 18, 20, 23, 23, 27, 31, 34. With 9 values the median is the fifth value, which is 23. The stem-and-leaf diagram preserves the individual values in order.

Question 42Data Presentation and Display

A cumulative frequency curve for 60 students is used to find the median. At which cumulative frequency should the median be read?

  1. 45
  2. 30 Correct answer.
  3. 60
  4. 15

Explanation

The median corresponds to the middle value, so it is read at half the total frequency. Half of 60 is 30, so the value on the horizontal axis at cumulative frequency 30 is the median. The quartiles are read at one quarter and three quarters of the total.

Question 43Data Presentation and Display

Two data sets have box-and-whisker plots with the same median but different interquartile ranges. What does the larger interquartile range indicate?

  1. The median of that data set is higher
  2. The middle half of that data set is more spread out Correct answer.
  3. That data set contains more values
  4. The whole data set has a smaller range

Explanation

The interquartile range is the width of the box, covering the middle half of the data. A larger interquartile range therefore means the middle half is more spread out. It says nothing about the number of values or the overall range.

Question 44Data Presentation and Display

A bar chart shows sales for five shops as 40, 55, 35, 60 and 50 units. What is the mean number of units per shop?

  1. 48 Correct answer.
  2. 47
  3. 45
  4. 50

Explanation

The mean is the total of all values divided by the number of values. The total is 40 + 55 + 35 + 60 + 50 = 240, and dividing by 5 gives 48. Reading values from a bar chart and averaging them is a common use of the display.

Question 45Data Presentation and Display

A histogram has unequal class widths. Why must frequency density rather than frequency be plotted on the vertical axis?

  1. So that the tallest bar always has the highest frequency
  2. So that the area of each bar is proportional to its frequency Correct answer.
  3. So that the bars can be drawn without gaps
  4. So that the total height of all bars equals the total frequency

Explanation

When class widths differ, using raw frequencies would make wide classes appear too important. Plotting frequency density makes the area of each bar equal to its frequency. This keeps the visual area proportional to the amount of data in each class.

Question 46Data Presentation and Display

A cumulative frequency curve for 80 values gives a lower quartile of 12 and an upper quartile of 28. A value of 40 lies well beyond the upper whisker of the corresponding box plot. How is this value best described?

  1. An outlier above the upper quartile Correct answer.
  2. The maximum of the data set
  3. The upper quartile itself
  4. The median of the data set

Explanation

The interquartile range is 28 minus 12, which is 16, so the upper fence is 28 + 1.5 times 16 = 52 under the usual rule. A value far beyond the upper whisker is therefore treated as an outlier. Outliers are plotted individually rather than included in the whisker.

Question 47Data Presentation and Display

A scatter graph shows a strong negative correlation between the age of a machine and its value. Which conclusion is justified?

  1. Older machines tend to have higher values
  2. Age has no effect on value
  3. Older machines tend to have lower values Correct answer.
  4. All machines of the same age have identical values

Explanation

Negative correlation means that as one variable increases the other tends to decrease. Here, increasing age is associated with decreasing value. Correlation describes a tendency rather than an exact rule, so individual machines may still vary.

Question 48Data Presentation and Display

A pie chart is drawn using frequencies 5, 10, 15 and 20. If the sector for 5 is drawn first, what angle remains for the other three categories combined?

  1. 36 degrees
  2. 270 degrees
  3. 300 degrees
  4. 324 degrees Correct answer.

Explanation

The total frequency is 50, so the sector for 5 is 5/50 = 1/10 of the circle, which is 36 degrees. The remaining sectors therefore occupy 360 minus 36 = 324 degrees. Checking with the other frequencies, 45/50 of 360 also gives 324 degrees.

Question 49Data Presentation and Display

A histogram has two classes: 0 to 10 with frequency density 2 and 10 to 30 with frequency density 1.5. What is the total frequency?

  1. 50 Correct answer.
  2. 45
  3. 35
  4. 60

Explanation

Frequency equals density multiplied by class width. The first class gives 2 times 10 = 20, and the second gives 1.5 times 20 = 30. Adding these gives a total frequency of 50, which equals the total area of the two bars.

Question 50Data Presentation and Display

A student records the colours of 30 cars passing a school. Which display is most suitable for showing how many cars of each colour were seen?

  1. A cumulative frequency curve
  2. A scatter graph
  3. A bar chart Correct answer.
  4. A histogram

Explanation

Colour is categorical data, so each colour is a separate category and the counts are compared with bars of equal width. A bar chart is the standard display for comparing frequencies of named categories.