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<p>Estimating the sample mean and standard deviation from summary statistics such as the median, range and quartiles is an important problem in medical research. The established methods relying on normality assumptions and linear approximation yields the inaccurate results for the skewed distributions. The authors propose a supervised learning framework using a hierarchical neural network trained on a diverse synthetic data. This data-driven approach is theoretically well-founded and substantially outperforms the existing methods, particularly in non-normal scenarios. To facilitate broad adoption, the authors provide a user-friendly online calculator and a Python package, both of which ensure data privacy by performing all computations locally on the user’s machine.</p>

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Neural Network-Based Estimation of Sample Mean and Standard Deviation from Some Quartiles

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Qinyuan Zhang,
  • Qizhai Li

摘要

Estimating the sample mean and standard deviation from summary statistics such as the median, range and quartiles is an important problem in medical research. The established methods relying on normality assumptions and linear approximation yields the inaccurate results for the skewed distributions. The authors propose a supervised learning framework using a hierarchical neural network trained on a diverse synthetic data. This data-driven approach is theoretically well-founded and substantially outperforms the existing methods, particularly in non-normal scenarios. To facilitate broad adoption, the authors provide a user-friendly online calculator and a Python package, both of which ensure data privacy by performing all computations locally on the user’s machine.