Thống kê Mô tả - Độ đo Phân tán

1import numpy as np
2
3data = [10, 30, 50, 70, 90]
4range_value = np.max(data) - np.min(data)
5print(f"Range: {range_value}")  # 80
6
7# Hoặc dùng np.ptp (peak to peak)
8print(f"Range (ptp): {np.ptp(data)}")  # 80

1import numpy as np
2
3data = [2, 4, 4, 4, 5, 5, 7, 9]
4
5# Population Variance (ddof=0)
6pop_var = np.var(data, ddof=0)
7print(f"Population Variance: {pop_var}")  # 4.0
8
9# Sample Variance (ddof=1) - mặc định trong pandas
10sample_var = np.var(data, ddof=1)
11print(f"Sample Variance: {sample_var:.2f}")  # 4.57

1import numpy as np
2
3data = [2, 4, 4, 4, 5, 5, 7, 9]
4
5# Population Std
6pop_std = np.std(data, ddof=0)
7print(f"Population Std: {pop_std}")  # 2.0
8
9# Sample Std
10sample_std = np.std(data, ddof=1)
11print(f"Sample Std: {sample_std:.2f}")  # 2.14

1import numpy as np
2
3# Height
4height_mean, height_std = 170, 10
5cv_height = (height_std / height_mean) * 100
6
7# Weight
8weight_mean, weight_std = 65, 8
9cv_weight = (weight_std / weight_mean) * 100
10
11print(f"CV Height: {cv_height:.2f}%")  # 5.88%
12print(f"CV Weight: {cv_weight:.2f}%")  # 12.31%
13
14# Sử dụng scipy
15from scipy.stats import variation
16data = [2, 4, 4, 4, 5, 5, 7, 9]
17print(f"CV: {variation(data) * 100:.2f}%")

1import numpy as np
2import matplotlib.pyplot as plt
3from scipy import stats
4
5# Generate normal distribution
6mu, sigma = 100, 15
7x = np.linspace(mu - 4*sigma, mu + 4*sigma, 1000)
8y = stats.norm.pdf(x, mu, sigma)
9
10plt.figure(figsize=(12, 6))
11plt.plot(x, y, 'b-', linewidth=2)
12
13# Fill regions
14plt.fill_between(x, y, where=(x >= mu-sigma) & (x <= mu+sigma), 
15                 alpha=0.3, color='green', label='68% (μ±1σ)')
16plt.fill_between(x, y, where=(x >= mu-2*sigma) & (x <= mu+2*sigma), 
17                 alpha=0.2, color='yellow', label='95% (μ±2σ)')
18plt.fill_between(x, y, where=(x >= mu-3*sigma) & (x <= mu+3*sigma), 
19                 alpha=0.1, color='red', label='99.7% (μ±3σ)')
20
21# Add vertical lines
22for i, color in zip([1, 2, 3], ['green', 'orange', 'red']):
23    plt.axvline(mu - i*sigma, color=color, linestyle='--', alpha=0.5)
24    plt.axvline(mu + i*sigma, color=color, linestyle='--', alpha=0.5)
25
26plt.xlabel('IQ Score')
27plt.ylabel('Probability Density')
28plt.title('Empirical Rule (68-95-99.7 Rule)')
29plt.legend()
30plt.grid(True, alpha=0.3)
31plt.show()
32
33# Verify with actual calculations
34print("=== Empirical Rule Verification ===")
35data = np.random.normal(mu, sigma, 100000)
36print(f"% within 1σ: {np.mean((data >= mu-sigma) & (data <= mu+sigma))*100:.1f}%")
37print(f"% within 2σ: {np.mean((data >= mu-2*sigma) & (data <= mu+2*sigma))*100:.1f}%")
38print(f"% within 3σ: {np.mean((data >= mu-3*sigma) & (data <= mu+3*sigma))*100:.1f}%")

1import numpy as np
2from scipy import stats
3
4# Data
5mu, sigma = 100, 15
6iq_score = 130
7
8# Z-score
9z = (iq_score - mu) / sigma
10print(f"Z-score: {z:.2f}")  # 2.0
11
12# Standardize entire array
13data = [85, 100, 115, 130, 145]
14z_scores = stats.zscore(data)
15print(f"Z-scores: {z_scores}")
16
17# Percentile từ Z-score
18percentile = stats.norm.cdf(z) * 100
19print(f"Percentile: {percentile:.1f}%")  # 97.7%

1import numpy as np
2import pandas as pd
3from scipy import stats
4
5def descriptive_stats(data, name="Data"):
6    """Tính tất cả các độ đo thống kê mô tả"""
7    
8    result = {
9        'Count': len(data),
10        'Mean': np.mean(data),
11        'Median': np.median(data),
12        'Mode': stats.mode(data, keepdims=True).mode[0],
13        'Min': np.min(data),
14        'Max': np.max(data),
15        'Range': np.ptp(data),
16        'Variance (pop)': np.var(data, ddof=0),
17        'Variance (sample)': np.var(data, ddof=1),
18        'Std (pop)': np.std(data, ddof=0),
19        'Std (sample)': np.std(data, ddof=1),
20        'CV (%)': (np.std(data) / np.mean(data)) * 100
21    }
22    
23    print(f"\n=== {name} ===")
24    for key, value in result.items():
25        print(f"{key}: {value:.4f}" if isinstance(value, float) else f"{key}: {value}")
26    
27    return result
28
29# Ví dụ sử dụng
30data = [2, 4, 4, 4, 5, 5, 7, 9]
31descriptive_stats(data, "Example Data")
32
33# Hoặc dùng pandas
34df = pd.DataFrame({'values': data})
35print("\n=== Pandas describe() ===")
36print(df.describe())