Collecting and Organising Data

Trust starts with collection

Statistics questions often end with a conclusion, but the marks for judging that conclusion are earned much earlier. Every investigation follows the same cycle. First you SPECIFY the problem and plan: you turn a question into a HYPOTHESIS, a statement you can test with data, such as "pupils in Year 11 spend longer on homework than pupils in Year 9". Then you COLLECT data, PROCESS and REPRESENT it, and finally INTERPRET and DISCUSS the results. Discussing includes saying what the data cannot show, its limitations, and spotting any ANOMALY, a value that does not fit the pattern and may be a mistake. The idea this module keeps returning to is simple: a conclusion is only as trustworthy as the way its data was collected. A biased question, a lopsided sample or a sample that is too small spoils the answer before any calculation is done.

Data handling words

Seven terms for describing data and how it is gathered.

Run the canteen investigation

Ffion wants to know whether the school canteen should add a new vegetarian meal. Put her five steps in order.

• Write a statement she can test: at least half of pupils would choose the new meal once a week
• Decide who to ask and write fair questions for them
• Give out the questionnaire and gather the replies
• Tally the replies into a frequency table and draw a chart
• Decide whether the statement is supported and say what the data cannot show

Match each survey answer to its kind of data

Fair questions and biased ones

A questionnaire is only fair if every person can give their true answer and every answer has exactly one place to go.

Spot the two unfair library questions

A library is surveying its users. Tap the TWO questions that would give unfair or unreliable data.

• How many times did you visit the library last month? 0, 1 to 2, 3 to 5, 6 or more
• Do you agree that the new opening hours are much better?
• Which do you borrow most: fiction, non-fiction, magazines, or none of these?
• How old are you? Under 12, 12 to 14, 14 to 16, over 16
• On your last visit, how long did you stay? Under half an hour, half an hour up to an hour, more than an hour
• Would you visit on a Sunday if the library opened then? Yes, no, not sure

What is wrong with the pocket money boxes

A survey asks: How much pocket money do you get each week? The boxes are 0 to 5 pounds, 5 to 10 pounds and 10 to 15 pounds. What is the problem?

• Someone with exactly 5 or 10 pounds fits two boxes, and anyone with more than 15 pounds has none
• The question leads people towards a particular amount
• The boxes should all be different widths
• Nothing is wrong, because three boxes can hold any amount

Choosing who to ask

Asking a whole population is often impossible, so most investigations use a sample, and the sample must represent the population fairly. In a RANDOM sample every member has the same chance of being picked, for example by drawing numbers. In a SYSTEMATIC sample the members are listed, a random starting point is chosen, and then members are picked at regular gaps through the list; this is fair as long as the order of the list has no pattern that repeats at the same gap. In a STRATIFIED sample the population is split into groups, such as year groups, and each group gets a share of the sample in proportion to its size, so no group is left out or overloaded. Size matters too: a larger sample usually gives more reliable results, because one unusual reply has less effect, but a large sample collected from the wrong people is still biased.

Pick a sample from the members list

A club has 400 members listed in alphabetical order and wants a sample of 40. Choose the option in each gap.

Sharing a sample out fairly

A running club has 200 members: 120 adults and 80 juniors. The coach wants a stratified sample of 30 to ask about new training times. Adults are 120 out of 200 members, which is three fifths of the club, so they get three fifths of the sample: three fifths of 30 is 18. Juniors are 80 out of 200, two fifths of the club, so they get two fifths of 30, which is 12. A quick check: 18 and 12 make 30, the size of the whole sample. Within each group, the actual people are then chosen at random. If the coach had simply asked the first 30 runners to arrive at training, the sample might have been almost all adults, and the juniors would have had almost no say.

How many Year 7 pupils in the sample

A school has 750 pupils, and 150 of them are in Year 7. A stratified sample of 50 pupils is chosen by year group. How many Year 7 pupils should be in the sample?

Choose classes for the seedling heights

A pupil measures the heights of 30 seedlings in centimetres. No seedling is taller than 15 cm. Select EVERY set of classes that puts each possible height in exactly one class.

• More than 0 up to 5, more than 5 up to 10, more than 10 up to 20
• More than 0 up to 4, more than 4 up to 8, more than 8 up to 12, more than 12 up to 16
• 0 to 5, 5 to 10, 10 to 15
• 1 to 5, 6 to 10, 11 to 15
• More than 0 up to 5, more than 5 up to 10

Complete the sleep study

Cai wants to find out whether pupils in Year 11 sleep less than pupils in Year 7. He writes a _____ he can test: on a school night, Year 11 pupils sleep for fewer hours than Year 7 pupils. Asking all 1200 pupils in the school, the _____, would take too long, so he asks 80 of them, picked at random. One reply says 30 hours a night, which is impossible, so he treats it as an _____ and checks it instead of including it. In his write-up he names one _____: the hours are what pupils remember, not what was measured.

Plan the Saturday session survey

A youth club with 300 members, 180 seniors and 120 juniors, wants to know whether to open on Saturdays. Make each decision.

• Which statement should the club test?
• Seniors and juniors may answer differently. Which sample of 50 should the club use?
• Of the 50 asked, 28 say they would come at least twice a month. What should the club conclude?

Judge the leisure centre survey

A leisure centre asked 15 people in its gym on a Monday morning: Our new prices are great value, do you agree? Twelve said yes, so the centre announced that the town supports its new prices. Explain why this conclusion is not reliable, and how the survey should be done instead.

• The wording of the question
• Who was asked, and who was left out
• The size of the sample
• A better question and a better way to choose people