误差及数据分析.pptVIP

Error and Data Handling 3 3. The rule of random error 3-1. Frequency distribution 3-2. Gaussian equation 3-3. Gaussian Curve 3-4. Standard normal distribution 3-4-2. Standard normal distribution A simple example 1 某试样中含Co的质量分数的标准值为1.75%，σ=0.10%，现对其钴的质量分数进行测定，求分析结果大于2.00%出现的概率。 A simple example 2 同上例，求分析结果在1.60%~1.80%范围内出现的概率 * —Random errors in analytical results follow a Normal Distribution/Gaussian Curve —Follow mathematical laws of probability Definition of terms 术语 The population and the sample 样本与总体 总体━━统计学中考虑对象的全体 (the theoretical infinite无穷大) POPULATION = total (infinite) number of observations 样本━━自总体随机抽出的一组测量值 SAMPLE = finite number of observations = total (infinite) number of observations 样本容量━━样本中所含测量值的数目 Statistical sample analytical sample Example 有一矿石样品，在相同条件下测定Ni的百分含量。共有90个测定值，这些测定值彼此独立，属随机变量。 In order to study the regularity of the distribution of measurement data, According to the following steps to prepare frequency distribution table in order to conduct investigations. 1. range R=1.74-1.49=0.25 2. Determine the group number group interval The number of group depending on sample size ， For example:1.48?1.51, 1.51?1.54 In order to avoid a group of data points in the two That is: 1.485?1.515, 1.515?1.545, 1.51 in one range Frequency(频数):落在每个组内测定值的数目。 Relative frequency(相对频数):频数与样本容量总数之比。 100% 90 ∑ 1.1% 1 1.725 ? 1.755 6.7% 6 1.695 ? 1.725 11.1% 10 1.665 ? 1.695 22.2% 20 1.635 ? 1.665 24.4% 22 1.605 ? 1.635 18.9% 17 1.575 ? 1.605 6.7% 6 1.545 ? 1.575 6.7% 6 1.515 ? 1.545 2.2% 2 1.485 ? 1.515 Relative Frequency Frequency Group Table. Frequency Tables In the range of values abscissa(横坐标)，draw the frequency histograms for the vertical axis(纵坐标). 测量数据有明显的集中趋势这种既分散又集中的特性，就是其 规律性。 Characteristic: 1 2 The Characteristics Normal Distribution Curve (1) General Characteristics Unimodality (单峰性) Boun