← ACARA Digital Technologies Years 7–8

Choosing who to survey: sample and sample size

The group of people you actually ask in a survey. A bigger, fairer sample gives more trustworthy data than asking only a few friends.

Part of: ACARA Digital Technologies Years 7–8 — Acquiring and Storing Data — Module 10

Understanding Choosing who to survey: sample and sample size in ACARA Digital Technologies Years 7–8

What it does: Mixing different year levels gives a fairer sample that matches the whole school, so the data is more trustworthy. Asking everyone in a small group is possible, but for a big group a sample saves time. The sample should still be fair and big enough. With more responses, one odd answer matters less, so the results are more reliable. Asking only friends is a biased sample. Friends often share the same opinions, so other views are missed. Size helps, but fairness matters too. A sample needs to include different kinds of people.

Common mistakes: The percentage of the group you asked is the sample size divided by the whole group, times 100. It should be size / total * 100. Asking only your mates gives a biased sample. The sample should be picked fairly at random: random(whole, 10).

Class: _____________________  ·  Name: _____________________  ·  Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

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This module's key terms are also in a printable crossword (Modules 204–236) and word search (Modules 189–236).

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Learning
Duo
You want to know what the whole school thinks about the canteen menu. Which sample is better?
Ask 40 students picked from every year levelAsk only your 4 best friends
Matches
sample = my 3 best friends
↓
Asking only a few friends gives a biased sample. Friends often think alike, so the results won't match the whole group.
Applying
Meanings
Term
sample
Meaning
The group of people you actually ask in a survey. A bigger, fairer sample gives more trustworthy data than asking only a few friends.
Practice
=ROUND(COUNTA(A2:A9)/30*100,0)
Testing
Gaps
=(B2:B31)
Check Answer
Spots
3pick ← random(total, size)
4pct ← total / size * 100

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Quick Questions

1. You want to know what the whole school thinks about the canteen menu. Which sample is better?
A. Ask 40 students picked from every year level ✓
B. Ask only your 4 best friends
Friends often think like you do. A sample from every year level is fairer and gives more trustworthy data.
2. What is a sample?
A. The group of people you actually ask in a survey ✓
B. Every single person in the whole school
A sample is only the group you actually ask. Everyone in the group you want to know about is called the whole population.
3. Which statement about sample size is true?
A. A bigger sample usually gives more trustworthy data ✓
B. A sample of 3 people is just as trustworthy as 60
With more responses, one odd answer matters less, so the results are more reliable.
4. Mia surveys only the students sitting at her lunch table. What is the problem?
A. Her sample is too fair, because she knows everyone
B. Her sample is not fair, because it only includes friends ✓
Asking only friends is a biased sample. Friends often share the same opinions, so other views are missed.
5. Your class has 28 students and you want to know their favourite sport. Which is a whole-class survey?
A. Ask 10 students chosen at random
B. Ask all 28 students in the class ✓
Asking everyone in the group is a whole-class survey. Asking only some of them is a sample.

Match the Pairs

sample → The group of people you actually ask in a survey, rather than everyone in the whole group.
sample size → How many people are in your sample. A bigger sample usually gives more trustworthy data.
A fair sample asks students from every year level, not only your own friends → sample = students from Year 7, 8, 9 and 10
Asking the whole class gets everyone's answer, but a sample of 20 out of 200 students is quicker → whole class = 30 of 30, sample = 20 of 200
sample = my 3 best friends → Asking only a few friends gives a biased sample. Friends often think alike, so the results won't match the whole group.
sample size = 2, so the results are reliable → Two responses is too small to be trustworthy. One unusual answer changes the results a lot.

Key Term

sample
The group of people you actually ask in a survey. A bigger, fairer sample gives more trustworthy data than asking only a few friends.

Fill in the Blanks

1. =COUNTA(B2:B31)
Hint: Type the function that counts how many cells are filled in, so you know your sample size.
2. =COUNTA(B2:B31)/COUNTA(A2:A101)
Hint: Type the operator that divides the sample size by the whole group size.
3. =COUNTA(A2:A101)-COUNTA(B2:B31)
Hint: Type the operator that subtracts the sample size from the whole group size to find who was not asked.
4. =IF(COUNTA(B2:B31)>=30,"Enough","Need more")
Hint: Type the function that chooses between two results depending on a test.
5. =COUNTIF(C2:C31,"Friend")
Hint: Type the function that counts only the cells matching a condition, to see how many answers came from friends.

Spot the Error

Question 1
A total ← 200
B size ← 40
C pick ← random(total, size)
D pct ← total / size * 100
Line D — The percentage of the group you asked is the sample size divided by the whole group, times 100. It should be size / total * 100.
Question 2
A whole ← 30
B sample ← my_mates(whole, 10)
C ask(sample)
Line B — Asking only your mates gives a biased sample. The sample should be picked fairly at random: random(whole, 10).
Question 3
A class ← 28
B sample ← 38
C IF sample < class THEN
D say("This is a sample")
E ENDIF
Line B — A sample is only part of the whole class, so it cannot be bigger than the class of 28. It should be a smaller number such as 8.
Question 4
A responses ← 0
B FOR each student in sample
C responses ← responses - 1
D OUTPUT responses
Line C — Each answer collected should add 1 to the count, not subtract. It should be responses ← responses + 1.
Question 5
A enough ← 30
B IF responses <= enough THEN
C say("Big enough sample")
D ELSE
E say("Ask more people")
Line B — The sample is big enough when responses reach or pass the target. The check should use >=, not <=.

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