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Collecting your own data

Statistics and data · level 3, lesson 1 of 6

A question to start

Maya wants to know: "Do children in my school sleep enough?" She asks the five friends sitting at her lunch table how long they slept last night. Four of them say "about 7 hours". Maya writes in her report: "Most children in our school sleep about 7 hours."

Is she right? Maybe. But think about it for a moment. Five children is not a school. Her friends are all the same age. "About 7 hours" is a guess, not a measurement. And "last night" was a Saturday night, when people often stay up late.

Maya did not do anything silly. She just did not plan. In this lesson you will learn to plan before you collect, so that your data can really answer your question.

The idea

What data are

Data are facts we collect so that we can answer a question. They can be numbers (heights, hours of sleep, the temperature) or words (favourite fruit, the colour of a car). One piece of data, such as "Ali slept 9 hours", is called a value or an observation.

Data come in two main kinds:

  • Category data are answers that sort things into groups: favourite sport, eye colour, "yes" or "no". You count how many fall in each group.
  • Number data are answers that are numbers you can put in order: how many pets you have (you count them), how tall you are (you measure it). You can find averages of number data, which is what the rest of this level is about.

A good test: does it make sense to ask "what is the average?" The average height of a class makes sense. The average favourite colour does not.

Primary data and secondary data

There are two ways to get data.

Primary data are data you collect yourself, for your own question. You ask the questions, you hold the measuring tape, you count the cars. "Primary" means "first": you are the first person to have these data.

Secondary data are data someone else collected, often for a different reason, that you then use. Tables in books, weather records on a website, the sports results in a newspaper and the numbers from a census are all secondary data. "Secondary" means "second-hand".

Primary data you collect it yourself Secondary data someone else collected it

Each kind has good and bad points.

Primary data Secondary data
Good It answers exactly your question. You know how it was collected. It is quick. It can be huge (millions of people, a hundred years of weather).
Not so good It takes time. You can usually only collect a little. It was collected for someone else's question. You may not know how carefully.

Scientists use both. The rover Curiosity has a small weather station on Mars that measures the air temperature and the air pressure many times every day. For the engineers who built that station, those measurements are primary data. For a student who downloads the numbers later to draw a graph of a Martian day, they are secondary data. The same numbers can be primary for one person and secondary for another: it depends on who collected them.

A data plan

Before you collect anything, write a short data plan. It answers five questions.

  1. What is my question? Make it clear enough that data can answer it. "Do children like sport?" is vague. "How many minutes of sport do children in grade 4 play on a school day?" is clear.
  2. What exactly will I record? Minutes? Hours? A choice from a list? Decide the unit (minutes, centimetres) and, for choices, write the list of choices.
  3. Who or what will I collect from, and how many? The whole class? Every second car that passes? The more you collect, the more you can trust the answer, but it takes longer.
  4. How will I collect it? Ask a question, measure, count, watch, or look it up (secondary data). Write down where secondary data came from.
  5. How will I record and show it? A tally chart, a table, a graph. Decide this before you start, so you have the right sheet ready.

Why plan? Fairness

The most important reason to plan is to make the data fair: it should represent the people or things your question is about, and it should be measured the same way every time.

Look at Maya again.

  • Her question was about the school, but she asked only her table. Her friends are not a fair picture of the whole school: they might all be in the same grade, or all like staying up late. A group like this, chosen because it is handy, often gives a lopsided answer.
  • "About 7 hours" is a guess. Asking "What time did you fall asleep, and what time did you wake up?" gives better data, because people can work out the hours.
  • She asked about Saturday night. To answer "do children sleep enough on school nights?", she should ask about a school night.

A plan catches these problems before you waste a day collecting the wrong thing.

Recording sheets

A recording sheet is the paper (or screen) where you write data as you collect it. A good one has a title, the date, the question as you will ask it, and a column for each thing you record. For number data, write the actual numbers, not tally marks: later you will want to find the mean and median, and for that you need every value.

Child Grade Fell asleep Woke up Hours of sleep
1 4 8:30 pm 7:00 am 10.5
2 4 9:15 pm 7:15 am 10
3 5 10:00 pm 6:45 am 8.75

Writing the child's number, not their name, keeps the answers private. People answer more honestly when they know their name will not be shown.

Worked examples

1. Primary or secondary? Sort these.

  • (a) You time how long each friend can stand on one foot. Primary: you collected it.
  • (b) You copy the heights of the ten tallest buildings in Canada from an encyclopedia. Secondary: someone else measured them.
  • (c) Your teacher gives you last year's class marks to study. Secondary for you: your teacher (or last year's class) collected them.
  • (d) You count the birds at a feeder every morning for two weeks. Primary.

2. Category or number? For each, say what kind of data it gives.

  • (a) "What is your favourite season?" Category: four groups, nothing to average.
  • (b) "How many books did you read this month?" Number, counted.
  • (c) "How far can you throw a ball?" Number, measured (in metres).
  • (d) "What month is your birthday?" Category, even though months have an order. You would count how many people have each month; "the average birthday month" is not a useful idea.

3. Writing a data plan. Leo wants to know whether the school bus is often late.

  1. Question: How many minutes late is the morning bus on school days in March?
  2. Record: minutes late (0 if on time or early), and the date.
  3. Who/how many: the morning bus, every school day in March (about 20 days).
  4. How: he writes the time the bus arrives and compares it with the timetable.
  5. Record and show: a table with the date and minutes late; later a line plot or a graph over time.

Notice how the plan turned "often late" into something that can be measured: minutes, on given days.

4. Fixing a plan. Priya's plan: "Question: What is the most popular fruit? Ask 3 people. Write what they say." Three problems: (a) "most popular" with whom? Say "in my class". (b) Three people is too few; ask the whole class. (c) "Write what they say" will give "apple", "red apples", "apples I guess": give a list of choices (apple, banana, orange, grapes, other) so the answers can be counted.

Try it

  1. Primary or secondary? (a) You measure the length of your classmates' hands. (b) You look up the populations of Canadian provinces online. (c) You record the temperature on your balcony at 8 am each day.
  2. Category or number? (a) Shoe size. (b) Type of pet. (c) Minutes spent reading yesterday. (d) Favourite planet.
  3. Give one good point and one weak point of using secondary data about rainfall from a weather website.
  4. Make this question clear enough to collect data: "Is our playground busy?"
  5. Sam asks the children in the chess club, "Do you like chess?" and reports that "every child in the school loves chess". What went wrong?
  6. Write a five-part data plan for the question "How long does it take children in my class to walk to school?"
  7. A sheet records hours of sleep as tally marks in groups: "less than 8", "8 to 10", "more than 10". Why might this be a problem later, when you want the mean?
Answers
  1. (a) Primary. (b) Secondary. (c) Primary.
  2. (a) Number (you can order and average shoe sizes, though in level 4 you will see the mode is often more useful for shoes). (b) Category. (c) Number. (d) Category.
  3. Good: it is quick, and it may cover many years, far more than you could collect. Weak: you do not know exactly where or how it was measured, and it was collected for someone else's purpose.
  4. One answer: "How many children are on the playground at the start of lunch, on each school day for two weeks?" It says what to count, when and for how long.
  5. He asked only chess club members, who are very likely to like chess. They are not a fair picture of the whole school. He also turned "the children I asked" into "every child in the school".
  6. One plan: (1) How many minutes does it take children in my class to walk to school? (2) Minutes, a whole number, only for children who walk. (3) Every child in my class who walks. (4) Ask each child to time their walk one morning with a watch, rather than guess. (5) A table of minutes, then a stem-and-leaf plot (lesson 5).
  7. With only groups, you no longer know the actual numbers, so you cannot add them up to find the mean. Record the real hours; you can always group them later, but you cannot un-group.

Common mistake

Collecting from whoever is handy and then talking about everyone. Your friends, your club or your family are easy to ask, but they are usually more like you than the whole group is. If you ask only some people, say clearly who they were ("the 5 children at my table"), and do not claim more than your data show.

Starting without deciding what to record. If half the class gives hours and half gives minutes, or some give names of fruit and others give colours, the data cannot be counted or compared. Decide the unit and the choices first.

Where it leads