Summary of "in-depth statistics"

Graphical

Pie chart: Divides the data into distinct groups that are effective when compared to the base scale, but not when the proportions are close.

Bar chart: Accurate display of the frequency, the length of the value, when the type of data used; When the name is longer, you can use a horizontal bar chart, or multiple conditions, you can use a segmented bar or a stacked bar chart.

Histogram: The area is the frequency, there is no interval between rectangles, when the numerical data is used.

Line chart: Show trend, add multiple contrast groups easy, only for numeric data, compared to bar chart, not so accurate and intuitive. Average

Data skew: Outliers are on the right, called right skew, tails on the right.

Mean: When there is an outlier, the typical value is not in the data-set area. The right-biased average is higher, at the right-hand side of the median. The mean value is more stable for sampled data.

Median: The above problem occurs when the number is even. symmetric data, with equal median and mean values. The probability density function equals 0.5 when the corresponding x is the median number.

Number of people: in public when a lot of failure. The highest point of the probability density function corresponds to the majority of the X.

Variance, standard deviation, standard score (compare two datasets when mean and variance are different)

Remove outliers: four interval probability distribution geometric distribution: The probability of how many trials will be required to succeed at one time. Two distributions: The probability of the number of successes in N-times trials. Poisson distribution: The probability of the number of occurrences of a given interval. Poisson distribution is approximately two conditions of distribution: N is very large >5,p very small <0.1,λ=np (when n is very large, the two-item distribution is difficult to calculate, so it needs to be approximated). These are the probability distributions of discrete data. The
is distributing approximately two conditions: np>5,npq>5, which requires continuous correction, that is, taking x<n-0.5 instead of two x<n. Conditions for the distribution of approximate Poisson distributions: λ>15. Sampling Statistics calculates variance with the exception of n is the sample variance of the estimated sample data, except that n-1 estimates the population variance with sample data. Because the overall variance is larger than the sample variance. Sampling distribution of proportions: the probability of the occurrence of a particular sample's proportions is calculated by the distribution. Sampling distribution of mean: the probability of calculating the mean of the sample. The small sample estimates the total variance with t distribution, and the large sample is distributed positively. hypothesis Testing The original hypothesis, the alternative hypothesis (assuming that the original hypothesis is incorrect). The X 2 distribution is used to verify the difference between the observed frequency and the desired frequency (1 verifies the degree to which the given data matches the specified distribution and the independence of the 22 variables).