Collecting Data and Designing Surveys

Four ways of collecting data and how to choose one, how to write clear, fair survey questions with answer options that work, and how to plan a data collection.

Before you start

From the previous lesson, Types of Data: raw data are data as first collected; organised data have been sorted or counted and set out in a table.
Categorical data are names or labels (a CCA, a bus service number); numerical data are counted or measured amounts.
Numerical data are discrete if they take only certain separate values: counts (a count is always a whole number, such as the number of siblings) and amounts of money (which go up in steps of 1 cent). They are continuous if measured (height, time).

Four Ways of Collecting Data

How we collect data depends on the question we want to answer. There are four main ways.

Way of collecting	What we do	Example	Best for
Survey (with a questionnaire)	Ask people questions, face to face or with a questionnaire (a printed or online list of questions)	Asking Secondary 1 students which new CCA they would like the school to start	What people think, prefer, plan or do
Observation	Watch what happens and count or note it down, without asking anyone, changing anything or measuring anything	Counting the vehicles that pass the school gate between 7 a.m. and 8 a.m.	Things that happen by themselves and can be seen and counted
Experiment (measurement)	Measure with an instrument such as a stopwatch, a ruler or a scale, often the results of something we set up	Timing how long an ice cube takes to melt in the sun and in the shade	Measurements such as times, lengths and masses, and testing whether one thing affects another
Published records	Look up data that others have already collected, in books, reports or websites	Looking up the number of visitors to Singapore in each year, in a published report	Data too large, too far back in time or too hard to collect ourselves

Choosing a way of collecting data

A survey asks people. An observation watches and counts. An experiment measures, with an instrument such as a stopwatch, a ruler or a scale. Published records are data already collected by others, which we look up.

Choose the way that gives the data you need most accurately and most easily, and give a reason for your choice.

A survey gives what people say

Asking students how long they take to walk to school gives what they remember, which may be a guess. If the real time is needed, time them with a stopwatch: that is a measurement (an experiment). A survey is the right way to find out what people think, prefer or plan to do, which only they can tell us.

Example 1: Choosing a way of collecting data

Choose the best way of collecting the data for each of these, and give a reason.

(a) Whether Secondary 1 students prefer lessons online or in the classroom.

(b) The rainfall in Singapore in each month of last year.

(d) How many students arrive at school after 7.30 a.m. on each day of a week.

Solution

(a) A preference is something only the students themselves can tell us, so we ask them: a survey.

(b) Last year's rain cannot be measured now; it was measured at the time and the figures have been published: published records.

(d) We stand at the school gate at 7.30 a.m. each day and count the students who arrive after that time, without asking anyone anything: an observation.

(a) A survey. (b) Published records. (c) An experiment. (d) An observation.

Writing Good Survey Questions

A survey is only as good as its questions. A poor question gives answers that cannot be counted or compared, or answers that are not what people really think. Most survey questions give a list of answer options to tick, so that the answers are easy to count.

A good survey question

It is clear and exact: it asks about one thing only, says what time it is about ("last week", "on a school day"), and every person who reads it understands it in the same way.

It is not leading: it does not push people towards one answer.

Its answer options do not overlap: each possible answer fits exactly one option.

Its answer options cover every case: every possible answer fits some option (add "Other (please state)", "None of these" or "… or more" where needed).

It is polite and does not ask for private information that is not needed.

Example 2: Spotting poor survey questions

Say what is wrong with each survey question, and rewrite it.

(a) How much time do you spend reading? □ A little □ Some □ A lot

(b) How many books did you borrow from the school library last month? □ 0–2 □ 2–4 □ 4–6

(d) Do you like the food and the prices at the canteen? □ Yes □ No

Solution

(a) It is not exact. It does not say what time it is about (a day? a week?) or what reading counts, and "a little" and "a lot" mean different amounts to different people. Better: "Last week, how many hours did you spend reading for pleasure (not for homework)? □ Less than 2 hours □ 2 hours to less than 4 hours □ 4 hours to less than 6 hours □ 6 hours or more".

(b) The options overlap: a student who borrowed 2 books, or 4, fits two options. They also leave cases out: a student who borrowed 7 books has no option. Books are counted, so whole numbers can be used: "□ 0 □ 1–2 □ 3–4 □ 5 or more". Now every whole number fits exactly one option.

(c) It is leading: "Don't you agree" pushes people towards "yes". Better: "Should the canteen sell more healthy food? □ Yes □ No □ No opinion".

(d) It asks two things at once: a student who likes the food but not the prices cannot answer it. Ask two questions: "Do you like the food at the canteen? □ Yes □ No" and "Do you think the prices at the canteen are fair? □ Yes □ No".

(a) Not exact: rewritten with a time and options in hours. (b) Overlapping options with a case left out: □ 0 □ 1–2 □ 3–4 □ 5 or more. (c) Leading: asked plainly with Yes, No and No opinion. (d) Two questions in one: asked as two questions.

Example 3: Answer options that cover every case

Ali wants to find out how the 40 students of his class travel to school. Write a survey question for him, with answer options.

Solution

The question must say which journey is meant: the usual journey on a school day.

List the usual ways: walking, public bus, school bus, MRT, car, bicycle. A school bus is listed apart from a public bus, so that a student on a school bus knows which box to tick.

A student may travel some other way, so add "Other (please state)". Now every case is covered.

Some students use more than one way, such as a bus and then the MRT. If they could tick two boxes, some students would be counted twice, so the question tells them to tick one: the way used for the longest part of the journey. Now the options do not overlap.

On a usual school day, how do you travel to school? If you use more than one way, tick only the one you use for the longest part of the journey. □ Walk □ Public bus □ School bus □ MRT □ Car □ Bicycle □ Other (please state): ________

Planning a Data Collection

Before collecting any data, make a plan. A good plan answers these questions in order.

Planning a data collection

1. What question do I want to answer?

2. What data do I need, and what type are they (categorical, discrete or continuous)?

3. Which way of collecting suits these data best, and why?

4. Whom, or what, will I collect the data from? The data should come from all parts of the group the question is about (for example, from every class), not only from friends or from one class.

5. How will I record the data? Write the survey questions, or draw up a table for recording observations or measurements.

6. How will I organise and represent the data once they are collected?

Example 4: Planning a survey

The school is thinking of starting a robotics club for Secondary 1 students, meeting once a week after school. Hui Min is asked to find out whether enough students are interested and which day suits them best. Plan the data collection.

Solution

The question: Will enough Secondary 1 students join, and on which day should the club meet?

The method: a survey, because interest in a club and the days students are free are things only the students can tell us.

Whom to ask: students from every Secondary 1 class, not only Hui Min's own class or her friends, so that the answers stand for the whole of Secondary 1.

The questions, each with options that cover every case:

Q1. Would you join a robotics club that meets once a week after school? □ Yes □ No □ Not sure (categorical data)

Q2. On which days could you attend? Tick all that apply. □ Monday □ Tuesday □ Wednesday □ Thursday □ Friday □ None of these (categorical data)

Q3. How many CCA sessions do you already attend each week? □ 0 □ 1 □ 2 □ 3 or more (discrete numerical data; it shows how busy the students already are)

In Q2 a student may tick more than one day, because we want the number of students free on each day, not one answer for each student. So the day counts may add up to more than the number of students asked. In Q1 and Q3 each student ticks exactly one box, and those options do not overlap.

Organising: count the answers to each question in a table, and draw a bar graph of the number of students free on each day.

Why it matters: the data show whether enough students are interested before the school buys equipment and finds a teacher, and which day suits the most students.

A survey of students from every Secondary 1 class, with the three questions above; the answers are counted in tables to decide whether to start the club and on which day it should meet.

Common Mistakes

Using a survey for something that should be measured or watched: people's guesses are not measurements.
Collecting data only from friends: the data then describe the friends, not the whole group.
Answer options that overlap (0–2, 2–4) or leave cases out (no option for 7 or more).
Whole-number options such as 6–7 and 8–9 for something measured: a time of $7\frac{1}{2}$ hours fits neither. Run each option up to the start of the next one.
Asking a leading question ("Don't you agree …?"), or two questions in one.
Asking for private information, such as weight or family income, that the survey does not need.
Letting students tick more than one box and then expecting the counts to add up to the number of students asked.

Practice

Try each question before you open its solution. The questions get harder as you go.

Practice 1: Choosing a way of collecting data

Choose the best way of collecting the data for each of these, and give a reason.

(a) Whether a ball bounces higher on a wooden floor or on grass.

(b) Which new stall Secondary 1 students would like in the school canteen.

(d) Singapore's population in each year since 2000.

ShowHide solution

(a) Drop the same ball from the same height onto each surface several times and measure how high it bounces: an experiment.

(b) Which stall the students would like is something only they can tell us: a survey.

(d) The population of a whole country over many years is far too large to count ourselves; it has been counted and published: published records.

(a) An experiment. (b) A survey. (c) An observation. (d) Published records.

Practice 2: The wrong way of collecting

Each student below has chosen a poor way of collecting data. Say why it is poor and name a better way.

(a) To find how many cars pass the school gate between 7 a.m. and 8 a.m., Ali asks his classmates how many cars they saw there that morning.

(b) To find which new stall students would like in the canteen, Siti watches which of the present stalls has the longest queue.

(c) To find the rainfall in Singapore last year, Ravi puts a cup outside his window for one week and measures the water in it.

ShowHide solution

(a) Classmates did not count the cars, so their answers are guesses, and they were not all at the gate for the whole hour. Better: an observation: stand at the gate from 7 a.m. to 8 a.m. and count the cars.

(b) Watching the present stalls cannot show what students would like that is not there yet. Better: a survey asking students which new stall they would like.

(a) An observation at the gate. (b) A survey of the students. (c) Published records.

Practice 3: Options for a count

Write answer options for the survey question "How many glasses of water did you drink yesterday?" that do not overlap and cover every case. Check them with 0, 5, 6 and 12 glasses.

ShowHide solution

Glasses are counted, so the answers are whole numbers 0, 1, 2, …, and options in whole numbers leave no gaps.

Start at 0 and end with "… or more" so that every number is covered: □ 0–2 □ 3–5 □ 6–8 □ 9 or more.

Check: 0 fits only "0–2"; 5 only "3–5"; 6 only "6–8"; 12 only "9 or more".

□ 0–2 □ 3–5 □ 6–8 □ 9 or more (other groupings that start at 0, do not overlap and end with "… or more" are also right).

Practice 4: Options for a measurement

A survey question reads: "How many hours do you sleep on a school night? □ 4–6 □ 6–8 □ 8–10"

(a) Give two things wrong with the answer options.

(b) Rewrite the answer options.

ShowHide solution

(a) They overlap: a student who sleeps exactly 6 hours, or exactly 8 hours, fits two options. They leave cases out: a student who sleeps less than 4 hours, or more than 10 hours, has no option.

(b) Sleep is measured, so it can be any value, such as $7\frac{1}{2}$ hours. Whole-number options such as 6–7 and 8–9 would leave a gap for $7\frac{1}{2}$ hours, so each option is written to run up to the start of the next one:

□ Less than 6 hours □ 6 hours to less than 8 hours □ 8 hours to less than 10 hours □ 10 hours or more

Check: 3 hours fits only the first option, 6 hours only the second, 8 hours only the third and 11 hours only the fourth.

(a) The options overlap (6 and 8 hours each fit two of them) and leave cases out (less than 4 hours, more than 10 hours). (b) □ Less than 6 hours □ 6 hours to less than 8 hours □ 8 hours to less than 10 hours □ 10 hours or more

Practice 5: Leading questions and two questions in one

Say what is wrong with each survey question, and rewrite it.

(a) "Most students think recess is too short. Do you agree that recess should be longer?"

(b) "How often do you and your family eat at hawker centres and food courts?"

ShowHide solution

(a) It is leading: telling students what "most students think" and asking whether they "agree" pushes them towards "yes". Ask without taking a side, and give options for every view: "Do you think recess is: □ Too short □ About right □ Too long".

(b) It mixes two things (hawker centres and food courts) and two groups of people (you and your family), and "how often" has no time and no options, so the answers cannot be counted. Ask about one thing over a stated time, with options that do not overlap and cover every case: "In the last 7 days, how many times did you eat at a hawker centre? □ 0 □ 1–2 □ 3–4 □ 5 or more". Ask about food courts in a second question.

(a) Leading: "Do you think recess is: □ Too short □ About right □ Too long". (b) Two questions in one and not exact: "In the last 7 days, how many times did you eat at a hawker centre? □ 0 □ 1–2 □ 3–4 □ 5 or more", with a second question about food courts.

Practice 6: A question that asks too much

Mei Ling is surveying how much Secondary 1 students spend at the canteen. One of her questions is: "What is your weight, and how much money does your family earn each month?" Say what is wrong with it, and write a better question for her survey.

ShowHide solution

It asks two things in one question.

Both things are private, and neither is needed: the survey is about spending at the canteen, not about weight or family income. Many students would not answer, or would not answer truthfully.

Ask instead about what the survey needs. Money goes up in steps of 1 cent, so each option can end 1 cent before the next one starts: "On a usual school day, how much do you spend at the canteen? □ $0 to $1.99 □ $2.00 to $3.99 □ $4.00 or more".

It is two questions in one, and both ask for private information the survey does not need. Better: "On a usual school day, how much do you spend at the canteen? □ $0 to $1.99 □ $2.00 to $3.99 □ $4.00 or more".

Practice 7: A poor way of collecting data

Ravi wants to find out how long Secondary 1 students take to run 2.4 km. He asks the 8 Secondary 1 members of the school's athletics team, "How long do you take to run 2.4 km?", and writes down their answers.

(a) Give two reasons why his data may not show how long Secondary 1 students take.

(b) Suggest a better way of collecting the data.

ShowHide solution

(a) Whom he asked: members of an athletics team train to run and are likely to be faster than most students, so the data describe the team, not the whole of Secondary 1.

How he asked: a survey gives the times the runners remember or guess, which may not be their real times. To get the real times, he should measure them.

(b) Time students from every Secondary 1 class with a stopwatch when they run 2.4 km in a PE lesson (a measurement: an experiment), and record each time in a table.

(a) He asked only fast runners, and remembered times may not be real times. (b) Time students from every Secondary 1 class with a stopwatch and record the times in a table.

Practice 8: Bubble tea at Sports Day

The student council will sell bubble tea at Sports Day and can offer only four flavours. Siti wants to find out which flavours students like best.

(a) Which way of collecting data should she use? Why?

(b) Write a survey question for her, with answer options.

(d) Her friend tries a different question with 30 students: "Tick every flavour you like." The counts are brown sugar milk tea 18, classic milk tea 12, taro 9, mango green tea 11, passion fruit green tea 7 and other 3. Why do the counts add up to more than 30? Which four flavours do the most students like?

ShowHide solution

(a) A survey: which flavour a student likes is something only the student can tell us.

(b) Ask each student to choose one flavour, so that each student is counted once and the answers are easy to count. List the flavours the council could sell, and add options so that every case is covered: a flavour not on the list, and a student who does not drink bubble tea.

"Which ONE of these bubble tea flavours do you like best? □ Brown sugar milk tea □ Classic milk tea □ Taro □ Mango green tea □ Passion fruit green tea □ Other (please state): ________ □ I do not drink bubble tea"

The four listed flavours with the most votes are the ones to sell; the "Other" answers show whether a popular flavour has been missed.

(d) Each student could tick every flavour he or she likes, so a student who likes three flavours is counted three times. The counts add up to the number of ticks, $18 + 12 + 9 + 11 + 7 + 3 = 60$ , not to the number of students.

Each count is still the number of students who like that flavour, so the four flavours liked by the most students are brown sugar milk tea (18), classic milk tea (12), mango green tea (11) and taro (9).

(a) A survey. (b) The question above, with one choice, an "Other (please state)" option and an "I do not drink bubble tea" option. (c) Categorical data. (d) Students could tick more than one flavour, so many were counted more than once; the four flavours to sell are brown sugar milk tea, classic milk tea, mango green tea and taro.

Practice 9: Planning an observation

Mr Tan thinks that the queue at the school canteen's drinks stall is longest on Mondays. Plan how to collect data to check this. Say which way of collecting you would use, what you would record and when, and draw up a table for recording the data. What type of data will you collect?

ShowHide solution

The method: an observation. The length of a queue can be seen and counted; there is no need to ask anyone.

What and when: count the number of people in the queue at the same time each day, for example at 10.15 a.m., five minutes after recess begins, on every school day for two weeks. Counting at the same time each day makes the days fair to compare, and two weeks give two counts for each day of the week.

The recording table, with a box for each count:

Number of people in the drinks stall queue at 10.15 a.m.
	Monday	Tuesday	Wednesday	Thursday	Friday
Week 1
Week 2

The type of data: the number of people is counted, so the data are discrete numerical data.

Organising: compare the two Monday counts with the counts for the other days, in a table or a bar graph.

An observation: count the people in the queue at 10.15 a.m. on every school day for two weeks and record the counts in the table above. The data are discrete numerical.

Practice 10: Planning an experiment

Hui Min wants to find out whether a toy car rolls farther when it is let go from higher up a ramp. Plan the data collection: the way of collecting, what to keep the same, what to measure, a table for recording the results, and the type of data.

ShowHide solution

The method: an experiment: she sets up the ramp, lets the car go and measures the results.

Kept the same: the same car, the same ramp and the same floor, and the car is let go without a push. Then only the height changes, and any difference in distance comes from the height.

Changed: the height at which the car is let go, for example 10 cm, 20 cm and 30 cm above the floor.

Measured: the distance the car rolls from the bottom of the ramp, in centimetres. Each height is tried three times, because one roll may be unusual.

Distance rolled by the toy car (cm)
Height above the floor	Trial 1	Trial 2	Trial 3
10 cm
20 cm
30 cm

The type of data: distance is measured, so the data are continuous numerical data.

An experiment: the same car and ramp, let go from 10 cm, 20 cm and 30 cm above the floor, three trials each; the distance rolled is measured in centimetres and recorded in the table above. The data are continuous numerical.

Practice 11: Faults found in the results

Hui Min asked 40 students, "How much pocket money do you get on a school day?", with the options □ $0–$2 □ $2–$4 □ $4–$6. Each student ticked at most one box. Her results were:

Pocket money	$0–$2	$2–$4	$4–$6	Total
Number of students	9	17	11	37

(a) Her total is 37, not 40. Give a possible reason why 3 students ticked no box.

(b) Ali gets exactly $2 a day. Explain why he was not sure which box to tick.

(d) Rewrite the answer options.

ShowHide solution

(a) $40 - 37 = 3$ students ticked no box. Either of these reasons is right: the options stop at $6, so students who get more than $6 a day had no option; or students who get exactly $2 or exactly $4 fit two options and, not sure which to tick, ticked none.

(b) The options overlap: $2 fits both "$0–$2" and "$2–$4".

(c) A student who gets exactly $4 fits both "$2–$4" and "$4–$6". Some of the 17 students who ticked "$2–$4" may get exactly $4, which is not less than $4, and the table cannot tell her how many.

(d) Money goes up in steps of 1 cent, so each option can end 1 cent before the next one starts. The last option must cover every larger amount: □ $0 to $1.99 □ $2.00 to $3.99 □ $4.00 to $5.99 □ $6.00 or more.

(a) Students who get more than $6 had no box to tick (or students on exactly $2 or $4 could not decide between two boxes). (b) $2 fits two options. (c) Some of the 17 may get exactly $4, which is not less than $4. (d) □ $0 to $1.99 □ $2.00 to $3.99 □ $4.00 to $5.99 □ $6.00 or more

Key Points

A survey asks people; an observation watches; an experiment measures; published records are data already collected by others.
Choose the way that gives the data most accurately and most easily, and give a reason: a survey for opinions and choices, not for things that can be measured or watched.
Collect from all parts of the group the question is about (for example, from every class), not only from friends or one class.
A good survey question is clear and exact, asks one thing, is not leading, and does not ask for private information it does not need.
Answer options do not overlap and cover every case. A count is always a whole number, so use whole-number options (0, 1–2, 3–4, 5 or more); amounts of money go up in steps of 1 cent, so end each option 1 cent before the next starts ($0 to $1.99, $2.00 to $3.99, …); for measured data run each option up to the start of the next one; end with "… or more" or "Other".
Where people may tick more than one box, the counts may add up to more than the number of people asked.
Plan a data collection: the question, the data and their type, the way of collecting, whom to collect from, how to record, and how to organise.