statistical-distribution-and-outlier-analysis

Imported from MichaelYang-lyx/AIDABench (skills/sn-da-excel-workflow/capability/excel-data-visualization/histogram-visualization/SKILL.md). Install upstream with npx skills add MichaelYang-lyx/AIDABench --skill histogram-visualization. Copyright stays with the author.

Step 1 加载数据并进行预处理，配置中文字体与环境参数

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
import re

# 设置中文字体，兼容不同环境
plt.rcParams['font.sans-serif'] = ['SimHei', 'WenQuanYi Zen Hei', 'DejaVu Sans']
plt.rcParams['axes.unicode_minus'] = False

# 加载数据并处理合并单元格
file_path = 'input_data.xlsx'
df = pd.read_excel(file_path)
df.ffill(inplace=True) # 处理可能的合并单元格空值

# 统一重命名列名以便于程序化处理
original_columns = df.columns.tolist()
df.columns = [f'col_{i+1}' for i in range(df.shape[1])]

print(f"数据形状: {df.shape}")
print(f"原始列映射: {dict(zip(df.columns, original_columns))}")

Step 2 生成多子图箱线图，直观展示各维度数据的分布特征与统计量

# 计算子图布局
num_cols = len(df.columns)
rows = (num_cols + 2) // 3
fig, axes = plt.subplots(rows, 3, figsize=(18, 5 * rows))
fig.suptitle('数据分布维度分析', fontsize=16, fontweight='bold')
axes_flat = axes.flatten()

for i, column in enumerate(df.columns):
    data_series = df[column].dropna()
    if pd.api.types.is_numeric_dtype(data_series):
        axes_flat[i].boxplot(data_series, patch_artist=True,
                            boxprops=dict(facecolor='lightblue', alpha=0.7),
                            medianprops=dict(color='red', linewidth=2))
        
        stats = data_series.describe()
        axes_flat[i].set_title(f'{column} (n={len(data_series)})', fontsize=12)
        axes_flat[i].text(0.05, 0.95, f'均值: {stats["mean"]:.2f}\n中位数: {stats["50%"]:.2f}',
                         transform=axes_flat[i].transAxes, verticalalignment='top',
                         bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
    axes_flat[i].grid(True, alpha=0.3)

plt.tight_layout(rect=[0, 0.03, 1, 0.95])
output_path = 'individual_boxplots.png'
plt.savefig(output_path, dpi=300, bbox_inches='tight')
plt.show()

Step 3 执行异常值检测算法，计算四分位距（IQR）并生成统计报告

analysis_results = []

for col in df.columns:
    data = df[col].dropna()
    if not pd.api.types.is_numeric_dtype(data):
        continue
        
    Q1 = data.quantile(0.25)
    Q3 = data.quantile(0.75)
    IQR = Q3 - Q1
    lower_bound = Q1 - 1.5 * IQR
    upper_bound = Q3 + 1.5 * IQR
    
    outliers = data[(data < lower_bound) | (data > upper_bound)]
    
    analysis_results.append({
        '维度': col,
        '样本量': len(data),
        '异常值数量': len(outliers),
        '偏度': round(data.skew(), 3),
        '峰度': round(data.kurtosis(), 3),
        '范围': f"{data.min():.2f} ~ {data.max():.2f}"
    })

report_df = pd.DataFrame(analysis_results)
print("=== 数据质量与分布报告 ===")
print(report_df.to_string(index=False))

Step 4 使用正则表达式从文本列中提取误差值（±模式）并进行量化分析

# 假设 target_col 包含类似 "10.5 ± 0.2" 的文本
target_col = df.columns[0] 
text_data = df[target_col].astype(str).str.cat(sep=' ')

# 正则表达式提取 ± 后面的数值
error_pattern = r'±(\d+\.?\d*)'
extracted_errors = [float(val) for val in re.findall(error_pattern, text_data)]

if extracted_errors:
    print(f"提取到误差样本量: {len(extracted_errors)}")
    print(f"误差均值: {np.mean(extracted_errors):.4f}")
else:
    print("未在指定列中检测到符合 ± 模式的误差数据")

Step 5 绘制误差分布直方图，并标注核心统计参考线

if extracted_errors:
    plt.figure(figsize=(10, 6))
    # 自动计算 bins 数量
    n, bins, patches = plt.hist(extracted_errors, bins='auto', color='skyblue', 
                                edgecolor='black', alpha=0.7)
    
    # 在柱体上方标注频次
    for i in range(len(n)):
        if n[i] > 0:
            plt.text(bins[i] + (bins[i+1]-bins[i])/2, n[i] + 0.1, 
                    str(int(n[i])), ha='center', va='bottom', fontweight='bold')

    # 添加均值参考线
    mean_val = np.mean(extracted_errors)
    plt.axvline(mean_val, color='red', linestyle='--', linewidth=2, 
                label=f'误差均值: {mean_val:.3f}')
    
    plt.title('误差项分布特征直方图', fontsize=14)
    plt.xlabel('误差量级', fontsize=12)
    plt.ylabel('出现频次', fontsize=12)
    plt.legend()
    plt.grid(axis='y', alpha=0.3)
    
    plt.tight_layout()
    plt.savefig('error_distribution_histogram.png', dpi=300)
    plt.show()

Step 6 导出分析摘要并生成下载链接

summary_file = 'analysis_summary.csv'
report_df.to_csv(summary_file, index=False, encoding='utf_8_sig')

from IPython.display import FileLink
print("分析完成，点击下方链接下载报告：")
display(FileLink(summary_file))
display(FileLink('individual_boxplots.png'))