First, the definition of standard deviation
Standard deviation is a method to measure the deviation between each data point in a data set and the average of the data set. The greater the standard deviation, the greater the deviation between data points and the average value, and the greater the data volatility.
Second, the calculation steps of standard deviation
1. Calculate the average value: first calculate the average value of the data set, that is, the sum of all data points divided by the number of data points n. It is expressed by the following formula: mean (μ) = (x1+x2+...+xn)/n.
2. Calculate the difference between each data point and the average value: for each data point Xi, calculate the difference between it and the average value, that is, Xi-μ. Calculate the square of the difference and square each difference obtained in step 2. This is to eliminate the sign of the difference, so that the information about the distance from the average does not cancel each other out. The square difference can be expressed as (Xi-μ)? .
3. Calculate the mean square deviation: the average of the calculated mean square deviation, that is, the average mean square deviation. Expressed by the following formula: mean square error (variance, σ? )=[(X 1-μ)？ +(X2-μ)？ +……+(Xn-μ)？ ]/n. Finally calculate the standard deviation, which is the square root of variance. Expressed by the following formula: standard deviation (σ) = √ variance (σ? )。
Importance of data
1. Decision Support: Data provides past and present information to help organizations and individuals make more informed decisions. Data-based decision-making can reduce risks, improve efficiency and help achieve goals.
2. Discover trends and patterns: By analyzing data, we can discover trends, patterns and relationships. This helps to predict the future trend, so as to plan and prepare better.
3. Improve products and services: By collecting and analyzing customer data, enterprises can understand customer needs and improve products and services to meet customer expectations. This helps to improve customer satisfaction and market competitiveness.
4. Improve efficiency and productivity: Data can be used to optimize processes, resource allocation and production plans to improve efficiency and productivity. This is especially important for enterprises because it can reduce costs and improve profitability.