Mathematics Year 7: Define, collect and clean the data
Mathematics, Year 7 (Portugal): Decide exactly what to record and how, collect it from a credible source, then sort the values and check the unexpected ones before you use them.
From the question to a table of values
Before collecting, define the data: which variable, in which unit, with what precision, one value per element. Then choose the source (primary: you collect; secondary: someone already did, such as a statistics institute like INE or PORDATA) and the method (observe, or ask by interview or questionnaire, in public or in private). Only then collect, and clean: sort the values and check that each one makes sense.
A credible source explains itself
On the Internet anyone can publish a table, so check the source before using it: who published it, when, and how were the data collected? Are the variables and units explained? Can you find the same data somewhere else? A credible table answers these questions. Also think about how people answer: a public answer can be changed by shame or to please, so a private one is often more truthful.
Cleaning 12 trip times
12 students answered in minutes: 10, 25, 8, 15, 45, 12, 20, 15, 30, 75, 5, 1200. Step 1: sort them: 5, 8, 10, 12, 15, 15, 20, 25, 30, 45, 75, 1200. Step 2: look at the ends. 1200 min ÷ 60 = 20 h for a trip to school: impossible, probably a typo, so ask the student. Step 3: 75 min = 1 h 15 min is unusual but possible, so ask and keep it. Step 4: with 1200 removed, 12 − 1 = 11 values remain, from 5 to 75 min.
Do not delete a value just because it is odd
Looking at the sorted times, Rui sees 75 while all the others are 45 or less, and thinks “this one spoils the graph, I'll delete it”. That is a mistake. A typo is a value that cannot be true (1200 min); 75 min can. When it is possible, you check it and keep it: it may be the most interesting finding, such as a student who lives far away. Deleting it changes the maximum from 75 to 45 and hides that student.
Spreadsheets, forms and official tables
Every time an app or a spreadsheet gathers answers, someone has to clean them: a stray extra zero, a wrong unit, an answer typed twice. A statistics institute publishes tables on its website with the source and the unit of every column, which makes checking easier. Sorting the values and reading the first and last ones is the fastest way to spot a problem before it reaches a graph.
Test what you learned
A class wants to study how long the trip to school takes. Which is the best definition of the data to collect?
- a) For each student, “short” or “long”
- b) For each student, the trip time in minutes, one value per student
- c) Each student answers in minutes or in hours, as they prefer
- d) Only the class average, given by the class delegate
Correct answer: b) For each student, the trip time in minutes, one value per student — Right: one variable, one unit, one value per student. Everyone answers the same way, so the values can be compared and calculated.
11 students gave the hours a day they use screens, sorted: 2, 3, 3, 4, 4, 5, 5, 6, 7, 9, 30. What remains after cleaning only the impossible value?
- a) 11 values, maximum 30
- b) 9 values, maximum 7
- c) 11 values, maximum 24
- d) 10 values, maximum 9
Correct answer: d) 10 values, maximum 9 — Right: 30 h cannot happen in a day, so it goes: 11 − 1 = 10 values. The 9 is possible, so it stays and is the new maximum.
Daily homework minutes, sorted: 20, 25, 30, 30, 35, 40, 45, 50, 150. Ana says “the 150 spoils the table, delete it”. What should you do?
- a) Delete it, because it is far from the others
- b) Replace it by the largest other value, 50
- c) Check whether it is possible and ask the student; if it is, keep it
- d) Delete it and also the smallest value, to stay balanced
Correct answer: c) Check whether it is possible and ask the student; if it is, keep it — Right: 150 min is possible, so you check it and keep it. It may be the most interesting finding of the study.
Keep exploring
Other languages
Loading MyLeoNes™…