Khan public class-Statistics study notes: (ii) General, sample, concentration trend, off-trend

iii. Statistics & concentration trends

Statistical statistics is the descriptive of data, not all data presented, according to statistics, can be inferential (inference), the judgment of the future.

Centralized trend central tendency, the middle value is average, usually refers to mean (arithmetic average), but also broadly includes median, and mode. The way of calculation is different, can not say which method is good, see the specific situation, which kind of more reactive. Generally use mean, but some cases, such as the average house price, if there is a very high deviation from the value, can be a wrong value, is to use median more in line with people's feelings.

Iv. General and sample

Total Ben Population, sample samples. The selected sample should be random.

The general mean, the population mean formula is as follows. n represents the number of total.

Sample mean, that is, the sample mean formula is as follows. Sometimes it is impossible to ask for an overall mean, such as the rise of a man in a country, it is difficult to measure at the same time, some people come to this world, some people leave, so use a sample way. n indicates the number of samples.

v. Trends in departures: total Variance, unbiased sample variance, standard deviation

Discrete: Dispersion, variance: variance, used to measure the off-trend of data.

For the total variance, the formula is:

Similarly, we can give the sample variance formula according to the picture scoop, but because the sample sample is difficult to evenly distribute 100%, the sample value is not necessarily consistent with the overall mean value, and the sample mean value is calculated from the sample, so the sample obtained by the similar formula is usually smaller than the total variance, so it is modified by using unbiased Sample variance, that is, unbiased sample variance, the formula is as follows:

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

Standard deviation (deviation), which is expressed in square notation, is different on the unit, and the standard deviation is the open root of the variance.

We make some interesting calculations on the formula of total variance

In the back of the two red boxes, more suitable for calculation, but now is a computer, it doesn't matter.

RELATED Links: My quartet Library