Fitting a Normal Distribution to a Histogram: Theft Losses Example

① This example demonstrates how to fit a normal distribution curve to a histogram of theft loss data, visually showing the match between a theoretical model and empirical observations. ② Core mathematical concepts include the normal distribution, expected value, histograms, probability density functions, and integration (to compute areas under the curve), along with random variables and quadratic equations (from the exponential term in the normal formula). ③ Construction highlights: The GeoGebra Histogram command is used to plot the data, while the Integral command computes areas between the normal curve and histogram bins; numerous objects (A2 to A41) store data points, bin boundaries, and fitting parameters, allowing dynamic adjustment of distribution parameters to optimize the fit. ④ This is suitable for high school or university statistics courses when teaching data distribution fitting, the central limit theorem, or applications of probability density functions, and also for introductory mathematical modeling or data analysis, helping students understand how theoretical models describe real-world data.