Population and sample

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. A school has 1,200 students. You survey 60 of them about canteen food. What is the 60 students?

A The sample

B The population

2. Which statement about sample size is better?

A A sample of 3 people is always enough for any population

B A larger sample usually represents the population more reliably

3. Which is a random sample of your year level?

A Asking the 50 friends sitting near you at lunch

B Drawing 50 student ID numbers at random from the full class list

4. Which is a convenience sample?

A Surveying only the students who are standing near the library

B Using a random number generator to pick students from the roll

5. You want to know how all students travel to school, but you survey only students at the bus stop. What is the problem?

A Sampling bias: bus users are over-represented

B No problem: any group of students will give the same answer

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1sample_size = 150		AThe sample is the same as the population, so this is a census, not a sample. A sample is only a part of the population, such as 100 students.
2sample = random.sample(population, 50)		BSets how many members of the population are included in the sample. A bigger sample usually represents the population better.
3A convenience sample only uses the people who are easiest to reach, so it may not represent the whole population.		Csample = random.sample(all_students, 40)
4A random sample gives every member of the population an equal chance of being picked.		DPicks 50 members of the population completely by chance, so each member has an equal chance of being chosen (a random sample).
5population = 1200 sample = 1200 # survey a sample of the whole school		EThe sample size is too small to represent a population of 1200, so the results could be unreliable. A larger sample is needed.
6sample = 5 # 5 students represent a school of 1200		Fsample = friends_in_my_class

Definitions

sample

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=___________(1,500)

=______(A2:A501)

SELECT * FROM students ORDER BY ______() LIMIT 5;

=COUNTA(D2:D31)_COUNTA(A2:A501)

=__(COUNTA(A2:A31)<30,"Too small","OK")

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A pop = list(range(1, 101))

B s = random.sample(pop, 150)

C print(len(s))

Question 2

A pop = all_students

B s = pop[:40]

C print(len(s))

Question 3

A population = 100

B sample = 120

C print(sample / population)

Question 4

A def pick(p, n):

B return random.sample(p, n)

C s = pick(50, students)

D print(len(s))

Question 5

A pop = load_students()

B n = 80

C s = random.sample(pop, n)

D print('Sample:', len(pop))

Answer Key

Population and sample

Section A: Quick Questions

A — The sample

B — A larger sample usually represents the population more reliably

B — Drawing 50 student ID numbers at random from the full class list

A — Surveying only the students who are standing near the library

A — Sampling bias: bus users are over-represented

Section B: Match the Pairs

sample_size = 150 → Sets how many members of the population are included in the sample. A bigger sample usually represents the population better.

sample = random.sample(population, 50) → Picks 50 members of the population completely by chance, so each member has an equal chance of being chosen (a random sample).

A convenience sample only uses the people who are easiest to reach, so it may not represent the whole population. → sample = friends_in_my_class

A random sample gives every member of the population an equal chance of being picked. → sample = random.sample(all_students, 40)

population = 1200 sample = 1200 # survey a sample of the whole school → The sample is the same as the population, so this is a census, not a sample. A sample is only a part of the population, such as 100 students.

sample = 5 # 5 students represent a school of 1200 → The sample size is too small to represent a population of 1200, so the results could be unreliable. A larger sample is needed.

Section C: Definitions

sample — The part of a population you collect data from. It must represent the whole population, so use a big enough size, choose randomly and avoid sampling bias.

Section D: Fill in the Blanks

=RANDBETWEEN(1,500)

=COUNTA(A2:A501)

SELECT * FROM students
ORDER BY RANDOM() LIMIT 5;

=COUNTA(D2:D31)/COUNTA(A2:A501)

=IF(COUNTA(A2:A31)<30,"Too small","OK")

Section E: Spot the Error

B — A sample is only part of a population. A sample of 150 cannot be taken from a population of 100. The sample size must be smaller than 100, for example 30.

B — pop[:40] takes the first 40 students, which is a convenience sample and not random. It should use random.sample(pop, 40) so every student has an equal chance of being chosen.

A — The population is the whole group, so it must be larger than the sample. A population of 100 is smaller than the sample of 120. It should be population = 1200.

C — The arguments are in the wrong order. pick() expects the population first and then the sample size, so the call should be pick(students, 50).

D — len(pop) gives the size of the whole population, not the sample. The sample size is len(s), so the line should be print('Sample size:', len(s)).