Learn Implementing Sampling to Python | Probability & Statistics

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.

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Section 5. Chapter 6

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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


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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


              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.

Everything was clear?

Thanks for your feedback!

Section 5. Chapter 6