Khan Open Course-Statistical Study Notes: (2) Total book, sample, concentrated trend, off-center Trend

Iii. Statistics & concentrated trends

Statistics is the descriptive of the data, rather than presenting all the data. Based on statistics, inferential (inference) can be performed to determine the future.

Centralized trend central tendency. The median value is average, which usually refers to mean (arithmetic mean), but also broadly includes median, and mode. The calculation method is different. You cannot say which method is better, depending on the specific situation, and which one is more responsive. Mean is usually used, but in some cases, for example, the average price of the house, if there is a high deviation value, it can be a wrong value, it is more suitable for people to feel with median.

Iv. Sum and sample

Total population, sample. The selected samples should be random.

The total mean value, that is, the formula for population mean is as follows. N indicates the total quantity.

The sample mean formula is as follows. Sometimes it is impossible to calculate the overall mean. For example, it is difficult to measure the rise of men in a country within the same period of time. Some people come to this world, and some people leave, so they adopt the sample method. N indicates the number of samples.

5. off-center trend: total current variance, unbiased sample variance, and standard deviation

Discrete: dispersion, variance: variance, used to measure the deviation trend of data.

For the total variance, the formula is:

Similarly, we can give the formula of sample variance Based on the image watermark. However, since it is difficult for the sample to be evenly distributed 100% times, the sample mean value is different from the overall mean value, and the sample mean value is calculated by the sample, therefore, the sample obtained based on a similar formula is usually smaller than the total variance. Therefore, the unbiased sample variance is used for correction, that is, the unbiased sample variance. The formula is as follows:

Note that n-1 is not divided by the total number of samples, but may be based on experience values.

Standard deviation (standard deviation) is represented by square above. The unit is different, and the standard deviation is the root of the variance.

We make some interesting operations on the formula of the total variance.

In the next two red boxes, it is more suitable for computing, but it doesn't matter if it is a computer.

Link: My Library