Collecting and reading information

Every look into information starts with a question, and the data you collect must answer that question:

• “What is the favourite sport of the grade 7 pupils?” – each pupil’s answer: football, basketball, swimming …
• “How long does the way to school take the pupils?” – each pupil’s number of minutes.
• “Do the pupils sleep enough?” – how many hours each pupil slept, and also how many hours of sleep are recommended at this age.
• Data on how the pupils come – on foot, by bus – do not answer how much time the way takes.

A survey asks many people the same question and writes down the answers. A good survey question:

• is clear, and everyone understands it the same way: “How many books did you read last month?”, not “Do you read a lot?” – one person’s “a lot” is not another’s.
• does not steer towards an answer: “Isn’t the break too short?” pushes you to say “yes”. Better: “Is the break too long, about right or too short?”
• has answers you can count: a number, or a choice from a few options.

Usually you cannot ask everyone, so you ask only some of them. The part you ask is called a sample. The sample’s answers tell you about everyone – provided the sample is like everyone.

• You want to know the favourite sport of the pupils in the grade, and you ask only the basketball team: most of them will say basketball, but that is not the picture of the whole grade.
• A better sample: a few pupils from every class in the grade, boys and girls.

This chart appeared in a newspaper, under the headline “Ice cream B sells three times as much as ice cream A”:

• The numbers: 420 tubs of ice cream A a week, and 460 of B. The difference is only 40 tubs – less than a tenth of 420.
• B’s bar looks three times as tall because the axis starts at 400, not at 0: you see only the top end of each bar.
• With the axis starting at 0, the difference looks as it is:

An advert says: “80% of dentists recommend our toothpaste.”
Before believing a figure, ask what it leaves out:

• How many dentists were asked? If 5 were asked, 80% is only 4 dentists.
• Whom did they ask? Perhaps only dentists who work for the company that sells the toothpaste.
• What exactly did they ask? Perhaps the question was “Is this toothpaste good?”, and the dentists said “yes” about other toothpastes too.

For each question, write which data you must collect to answer it:

• How long a day do the pupils of the class play computer games?
• Which ice cream flavour is the class’s favourite?
• Do more pupils in class 7A have brothers or sisters than in class 7B?

For each survey question, write what is wrong with it, and write a better question:

• Do you eat a lot of sweets?
• Isn’t it true that the playground needs more equipment?
• What do you think of the school?

To find out how many hours a week the pupils of the grade read books, the pupils sitting in the library at break were asked.
What is the problem with this sample? Suggest a better sample.

The chart shows how many pupils took part in the robotics club last year and this year.

By how many pupils did the number taking part grow?

In the chart this year’s bar looks 2.5 times as tall as last year’s.
Did the number taking part grow 2.5 times? Explain.

A newspaper headline: “3 out of 4 teenagers prefer our social network!”
Write two questions you would ask before believing the headline.