Variance mainly exists in scientific experiments and engineering, such as the deviation of sample mice and steel samples from expected values under different experimental conditions. In the process of steelmaking, we know from experience that the temperature range corresponding to steels with different characteristic hardness and elasticity may be almost a little or a very small range. Our production expectation is to determine this interval or point as soon as possible to reduce the number of experiments or speed up the progress of experiments. Without the guidance of mathematics, we might have to do it many times, many times.

If we can accurately or roughly estimate the experimental data at a certain stage, then the mathematical calculation itself, variance and expectation come from real life, with a certain apriori. Variance can well reflect the characteristics or trends of production experiments such as steelmaking, because the experiment has a process, so we look forward to completing the experiment as soon as possible or within a certain period of time. At this time, the calculation of mathematical expectations is of great use:

After all, this expectation or prediction comes from samples and experimental data with similar or completely different experiences, so it is biased in practical guidance. However, with these calculations, we can make plans and arrange production better, provide basic data for decision-making and avoid blindness. It can effectively shorten the cycle and be more purposeful. The mathematical expectation here is to predict the number of experiments. At the same time, we can calculate the temperature rise of 0. 1℃ or 1℃ or 10℃ in the temperature range. Without mathematical calculation, our experiment is entirely a chance, but with calculation, the theoretical mathematical expectation sample is not applicable if it is completely nonlinear and has great differences, so as to better design the experimental methods and steps. ...

The example of students' height may not have practical significance, but it can be said in theory, such as the variance of the same group of samples. If the variance is small, it means that the population is stable in development and balanced in nutrition, otherwise ...; What's the difference between groups? Variance is still meaningful here, and the mathematical expectation is: individual balance or difference, the longer, the higher. If the sample here is replaced by a pig, it will have practical significance:

Variance guides people to eat in a balanced way, while mathematical expectation predicts in advance when it is most suitable for slaughter.