Aprende Implementing Sampling to Python | Probability & Statistics

Sampling is a core concept in statistics and data science, helping us analyze populations without observing every individual.
In this tutorial, you'll see how to implement four different sampling methods using Python: Simple Random Sampling, Stratified Sampling, Cluster Sampling, and Systematic Sampling.

Simple Random Sampling


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import random

N = 30   # population size
n = 5    # sample size

sample_srs = random.sample(range(1, N+1), n)
print(f"Simple Random Sample: {sample_srs}")

random.sample(range(1, N+1), n) randomly selects n unique values from the population;
Works without replacement (no repeats);
Every member of the population has an equal chance of being chosen.

Stratified Sampling


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N_males = 18
N_females = 12
N_total = N_males + N_females
n_total = 10

n_males = round((N_males / N_total) * n_total)
n_females = round((N_females / N_total) * n_total)

print(f"Stratified Sample Size -> Males: {n_males}, Females: {n_females}")

Population is divided into subgroups (strata);
Sample is drawn proportionally from each subgroup;
Ensures representation of key groups.

Cluster Sampling


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import random

clusters = 5
students_per_cluster = 25

selected_cluster = random.randint(1, clusters)
print(f"Selected cluster (classroom): {selected_cluster} containing {students_per_cluster} students")

Population divided into clusters (e.g., classrooms);
One or more clusters are selected randomly;
Everyone in chosen cluster(s) is surveyed;
Efficient when listing every individual is impractical.

Systematic Sampling


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import random

N = 1000
n = 100

k = N // n                # Sampling interval
start = random.randint(1, k)  # Random start

sample_systematic = list(range(start, N+1, k))
print(f"Sampling interval k = {k}")
print(f"Random start = {start}")
print(f"First 10 samples: {sample_systematic[:10]}")

Interval $k = \frac{N}{n}$ ;
Start point chosen randomly between 1 and $k$ ;
Select every $k$ -th element from ordered population.

Summary of Methods

Simple Random: equal chance for all, no repeats;
Stratified: ensures subgroup representation;
Cluster: randomly selects whole groups;
Systematic: selects at fixed intervals after random start.

1.

3. Which sampling method requires subgroup proportions? A) Cluster sampling B) Systematic sampling C) Stratified sampling ✅ D) Simple random sampling

5. If N = 1000 and n = 100, what is k? A) 5 B) 10 ✅ C) 100 D) 1

6.

8. What is a drawback of cluster sampling? A) Too random B) Time-consuming C) Lack of subgroup representation ✅ D) Expensive to implement

9. Which sampling method is best when you can't list the full population? A) Stratified sampling B) Systematic sampling C) Cluster sampling ✅ D) Simple random sampling

10. What is printed by sample_systematic[:10]? A) First 10 clusters B) Random numbers C) First 10 sample indices ✅ D) Entire population

11.

¿Todo estuvo claro?

¡Gracias por tus comentarios!

Sección 5. Capítulo 6

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Suggested prompts:

Can you explain the differences between these four sampling methods?

When should I use each sampling method in practice?

Can you provide more real-world examples for each sampling method?

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Simple Random Sampling


              1234567
            
import random

N = 30   # population size
n = 5    # sample size

sample_srs = random.sample(range(1, N+1), n)
print(f"Simple Random Sample: {sample_srs}")

random.sample(range(1, N+1), n) randomly selects n unique values from the population;
Works without replacement (no repeats);
Every member of the population has an equal chance of being chosen.

Stratified Sampling


              123456789
            
N_males = 18
N_females = 12
N_total = N_males + N_females
n_total = 10

n_males = round((N_males / N_total) * n_total)
n_females = round((N_females / N_total) * n_total)

print(f"Stratified Sample Size -> Males: {n_males}, Females: {n_females}")

Population is divided into subgroups (strata);
Sample is drawn proportionally from each subgroup;
Ensures representation of key groups.

Cluster Sampling


              1234567
            
import random

clusters = 5
students_per_cluster = 25

selected_cluster = random.randint(1, clusters)
print(f"Selected cluster (classroom): {selected_cluster} containing {students_per_cluster} students")

Population divided into clusters (e.g., classrooms);
One or more clusters are selected randomly;
Everyone in chosen cluster(s) is surveyed;
Efficient when listing every individual is impractical.

Systematic Sampling


              123456789101112
            
import random

N = 1000
n = 100

k = N // n                # Sampling interval
start = random.randint(1, k)  # Random start

sample_systematic = list(range(start, N+1, k))
print(f"Sampling interval k = {k}")
print(f"Random start = {start}")
print(f"First 10 samples: {sample_systematic[:10]}")

Interval $k = \frac{N}{n}$ ;
Start point chosen randomly between 1 and $k$ ;
Select every $k$ -th element from ordered population.

Summary of Methods

Simple Random: equal chance for all, no repeats;
Stratified: ensures subgroup representation;
Cluster: randomly selects whole groups;
Systematic: selects at fixed intervals after random start.

1.

3. Which sampling method requires subgroup proportions? A) Cluster sampling B) Systematic sampling C) Stratified sampling ✅ D) Simple random sampling

5. If N = 1000 and n = 100, what is k? A) 5 B) 10 ✅ C) 100 D) 1

6.

8. What is a drawback of cluster sampling? A) Too random B) Time-consuming C) Lack of subgroup representation ✅ D) Expensive to implement

9. Which sampling method is best when you can't list the full population? A) Stratified sampling B) Systematic sampling C) Cluster sampling ✅ D) Simple random sampling

10. What is printed by sample_systematic[:10]? A) First 10 clusters B) Random numbers C) First 10 sample indices ✅ D) Entire population

11.

¿Todo estuvo claro?

¡Gracias por tus comentarios!

Sección 5. Capítulo 6

Implementing Sampling to Python

Simple Random Sampling

Stratified Sampling

Cluster Sampling

Systematic Sampling

Summary of Methods

1.

6.

1. What function is used for simple random sampling without replacement?

2. In `random.sample(range(1, N+1), n)`, what does `range(1, N+1)` represent?

3. What does the variable `k` represent in systematic sampling?

4. Why is `random.randint(1, k)` used in systematic sampling?

5. In stratified sampling, what does `round((N_group / N_total) * n_total)` calculate?

6. What Python function selects one random cluster?

Awesome!

Implementing Sampling to Python

Simple Random Sampling

Stratified Sampling

Cluster Sampling

Systematic Sampling

Summary of Methods

1.

6.

1. What function is used for simple random sampling without replacement?

2. In `random.sample(range(1, N+1), n)`, what does `range(1, N+1)` represent?

3. What does the variable `k` represent in systematic sampling?

4. Why is `random.randint(1, k)` used in systematic sampling?

5. In stratified sampling, what does `round((N_group / N_total) * n_total)` calculate?

6. What Python function selects one random cluster?

Implementing Sampling to Python

Simple Random Sampling

Stratified Sampling

Cluster Sampling

Systematic Sampling

Summary of Methods

1.

6.

1. What function is used for simple random sampling without replacement?

2. In random.sample(range(1, N+1), n), what does range(1, N+1) represent?

3. What does the variable k represent in systematic sampling?

4. Why is random.randint(1, k) used in systematic sampling?

5. In stratified sampling, what does round((N_group / N_total) * n_total) calculate?

6. What Python function selects one random cluster?

Awesome!

Implementing Sampling to Python

Simple Random Sampling

Stratified Sampling

Cluster Sampling

Systematic Sampling

Summary of Methods

1.

6.

1. What function is used for simple random sampling without replacement?

2. In random.sample(range(1, N+1), n), what does range(1, N+1) represent?

3. What does the variable k represent in systematic sampling?

4. Why is random.randint(1, k) used in systematic sampling?

5. In stratified sampling, what does round((N_group / N_total) * n_total) calculate?

6. What Python function selects one random cluster?

2. In `random.sample(range(1, N+1), n)`, what does `range(1, N+1)` represent?

3. What does the variable `k` represent in systematic sampling?

4. Why is `random.randint(1, k)` used in systematic sampling?

5. In stratified sampling, what does `round((N_group / N_total) * n_total)` calculate?

2. In `random.sample(range(1, N+1), n)`, what does `range(1, N+1)` represent?

3. What does the variable `k` represent in systematic sampling?

4. Why is `random.randint(1, k)` used in systematic sampling?

5. In stratified sampling, what does `round((N_group / N_total) * n_total)` calculate?