> ## Documentation Index
> Fetch the complete documentation index at: https://ai.tharung.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Statistics Code

## Imports

```python theme={null}
import numpy as np
import pandas as pd
from scipy import stats
```

***

# 1. Population vs Sample

```python theme={null}
import numpy as np

population = np.arange(1, 101)

sample = np.random.choice(population, size=10, replace=False)

print("Population Size:", len(population))
print("Sample:", sample)
```

***

# 2. Types of Data

```python theme={null}
age = 22              # Integer

height = 175.8        # Float

gender = "Male"       # String

is_student = True     # Boolean

print(age, height, gender, is_student)
```

***

# 3. Levels of Measurement

```python theme={null}
nominal = ["Red", "Blue", "Green"]

ordinal = ["Low", "Medium", "High"]

interval = [-5, 10, 20]

ratio = [5, 10, 20]

print(nominal)
```

***

# 4. Descriptive Statistics

```python theme={null}
import pandas as pd

df = pd.DataFrame({
    "Marks": [70, 80, 90, 85, 95]
})

print(df.describe())
```

***

# 5. Mean

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.mean(marks))
```

***

# 6. Median

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.median(marks))
```

***

# 7. Mode

```python theme={null}
from scipy import stats

marks = [70, 80, 80, 90, 95]

print(stats.mode(marks))
```

***

# 8. Range

```python theme={null}
marks = [70, 80, 90, 85, 95]

print(max(marks) - min(marks))
```

***

# 9. Variance

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.var(marks))
```

***

# 10. Standard Deviation

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.std(marks))
```

***

# 11. Percentiles

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.percentile(marks, 90))
```

***

# 12. Quartiles

```python theme={null}
import numpy as np

marks = [70, 80, 90, 85, 95]

print(np.percentile(marks, [25, 50, 75]))
```

***

# 13. Interquartile Range (IQR)

```python theme={null}
from scipy.stats import iqr

marks = [70, 80, 90, 85, 95]

print(iqr(marks))
```

***

# 14. Outlier Detection

```python theme={null}
import numpy as np

data = np.array([10, 12, 14, 16, 100])

Q1 = np.percentile(data, 25)
Q3 = np.percentile(data, 75)

IQR = Q3 - Q1

lower = Q1 - 1.5 * IQR
upper = Q3 + 1.5 * IQR

print(data[(data < lower) | (data > upper)])
```

***

# 15. Skewness

```python theme={null}
from scipy.stats import skew

data = [10, 12, 14, 16, 100]

print(skew(data))
```

***

# 16. Kurtosis

```python theme={null}
from scipy.stats import kurtosis

data = [10, 12, 14, 16, 100]

print(kurtosis(data))
```

***

# 17. Covariance

```python theme={null}
import numpy as np

x = [1, 2, 3, 4]

y = [2, 4, 6, 8]

print(np.cov(x, y))
```

***

# 18. Correlation

```python theme={null}
import numpy as np

x = [1, 2, 3, 4]

y = [2, 4, 6, 8]

print(np.corrcoef(x, y))
```

***

# 19. Random Sampling

```python theme={null}
import pandas as pd

df = pd.DataFrame({
    "Marks": [60, 70, 80, 90, 95]
})

print(df.sample(2))
```

***

# 20. Sampling Distribution

```python theme={null}
import numpy as np

sample = np.random.choice([10,20,30,40,50], size=3)

print(sample.mean())
```

***

# 21. Central Limit Theorem

```python theme={null}
import numpy as np

population = np.random.normal(50, 10, 1000)

sample = np.random.choice(population, 30)

print(sample.mean())
```

***

# 22. Confidence Interval

```python theme={null}
from scipy import stats
import numpy as np

data = [10,20,30,40,50]

ci = stats.t.interval(
    confidence=0.95,
    df=len(data)-1,
    loc=np.mean(data),
    scale=stats.sem(data)
)

print(ci)
```

***

# 23. Statistical Inference

```python theme={null}
import numpy as np

sample = [10,20,30,40]

population_mean = np.mean(sample)

print(population_mean)
```

***

# 24. Hypothesis Testing

```python theme={null}
from scipy import stats

data = [20,22,19,24,21]

result = stats.ttest_1samp(data, popmean=20)

print(result)
```

***

# 25. P-value

```python theme={null}
from scipy import stats

data = [20,22,19,24,21]

t, p = stats.ttest_1samp(data, 20)

print(p)
```

***

# 26. Type I & Type II Error

```python theme={null}
alpha = 0.05

p_value = 0.03

if p_value < alpha:
    print("Reject H0")
else:
    print("Fail to Reject H0")
```

***

# 27. Z-Test

```python theme={null}
from statsmodels.stats.weightstats import ztest

data = [10,20,30,40,50]

print(ztest(data, value=30))
```

***

# 28. T-Test

```python theme={null}
from scipy import stats

group1 = [10,20,30]

group2 = [15,25,35]

print(stats.ttest_ind(group1, group2))
```

***

# 29. Chi-Square Test

```python theme={null}
from scipy.stats import chi2_contingency

table = [
    [10,20],
    [20,30]
]

print(chi2_contingency(table))
```

***

# 30. ANOVA

```python theme={null}
from scipy.stats import f_oneway

group1 = [10,20,30]

group2 = [15,25,35]

group3 = [18,28,38]

print(f_oneway(group1, group2, group3))
```

***

# 31. Feature Scaling

```python theme={null}
import pandas as pd

X = pd.DataFrame({
    "Age":[20,25,30],
    "Salary":[30000,50000,80000]
})

print(X)
```

***

# 32. Standardization

```python theme={null}
from sklearn.preprocessing import StandardScaler

X = [[20],[25],[30]]

scaler = StandardScaler()

print(scaler.fit_transform(X))
```

***

# 33. Normalization

```python theme={null}
from sklearn.preprocessing import MinMaxScaler

X = [[20],[25],[30]]

scaler = MinMaxScaler()

print(scaler.fit_transform(X))
```

***

# 34. Z-Score

```python theme={null}
from scipy.stats import zscore

marks = [70,80,90,85,95]

print(zscore(marks))
```

***

# 35. Missing Data

```python theme={null}
import pandas as pd

df = pd.DataFrame({
    "Marks":[80,None,90]
})

print(df.fillna(df.mean()))
```

***

# Useful Libraries

```python theme={null}
import numpy as np
import pandas as pd
from scipy import stats
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import MinMaxScaler
```

***