Basic concepts

Here we need to know a few concepts ！

mean value （ Average ）： The average of a set of data , For example, my favorite average score in my student days ;

variance ： The degree to which a set of data deviates from the average ;

Standard deviation （ Standard error ）： Variance open root sign , Reflect the dispersion of data ;

confidence interval ： Statistical data error range , So there is an upper and lower value , For example, it is written on agricultural products 5kg±5%.

Confidence level ： Credible probability , For example, the confidence level is 95%, Such as 100 Data , Yes 95 Data is on the above confidence interval .

Calculate the confidence interval

① Calculating mean ;

② Find standard error ;

③ Look up the table z value , The following table ：

④ Calculate the confidence interval ：

a = Sample mean - |z| * Standard deviation

b = Sample mean +|z| * Standard deviation

Python example

The following code ：

import numpy as np
from scipy import stats
valueList = [95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 200]
if __name__ == '__main__':
averageValue = np.mean(valueList)
print(" The sample mean is ：", averageValue)
standardError = stats.sem(valueList)
print(" The sample standard error is ：", standardError)
a = averageValue - 1.96 * standardError
b = averageValue + 1.96 * standardError
print(" Interval estimate ：[", a, "," ,b, "]")
pass

The running screenshot is as follows ：

  Available information ：

① The average value of the sample is 108.33;

② The dispersion degree of the sample is 8.38;

③ The confidence level here is 95%, Corresponding |z| The value is 1.96;

④ Yes 95% Probability , The overall sample will fall to 91.90~124.76 In this range .