How to estimate the population with samples? (mean, variance, standard deviation)

How to estimate the population with samples ？

Note source ：Population and Estimated Parameters, Clearly Explained!!!

Draw the above results into a histogram

The normal distribution corresponding to the histogram is as follows ：

We cannot measure all liver cells based on X Of mRNA, We need samples to estimate the population , Here we use 240 billion Medium 5 Cells as samples , Each green dot in the figure represents a cell , Its value represents the gene in this cell X It contains mRNA The number of

Let's take a look when the sample data has 2 Time , What is the difference between the calculated sample mean and the overall mean , What is the difference between the sample standard deviation and the overall standard deviation

We found that the more sample data , The closer our sample mean is to the overall mean , The closer the sample standard deviation is to the overall standard deviation

One of the main goals of statistics is to quantify our confidence in estimating the population

Statisticians often calculate p Values and confidence intervals , To quantify the estimated parameters （ That is, the average value calculated by the sample 、 Standard deviation and so on ） Credibility of

Personal understanding ： because The overall Too much , Sometimes it is impossible to measure , Or it will cost a lot of manpower and material resources , Now let's use some sample To estimate this unpredictable or unpredictable population , And it is estimated that there are always good and bad , Later people used confidence interval To judge whether this estimate is good or bad, or how reliable