Find the range or range (R)

Determine the number of group segments and group distance (i)

List the segments from smallest to largest

Count the observation units included in each group segment

Organized into frequency distribution table

Reveal data distribution type: symmetric distribution, skewed distribution

Reveal data distribution characteristics: concentration distribution and degree of variation

Extraordinarily large or extremely small suspicious values ​​are found

Contributes to further calculation of indicators and statistical analysis

Lognormal distribution (G, log standard deviation)

Concentrated position—the middle of the range of observations

Degree of variation - the degree of variation or dispersion relative to a centralized location

Symbol (x̄, μ)

Statistical significance (characteristic): reflects the average level of a group of homogeneous observations in the data

Application: Describe the concentrated position (average level) of normal distribution and approximately normal distribution data

Symbol: G

Statistical significance (characteristic): reflects the average level

application

Symbol: M

Calculation: direct method and frequency method

Statistical significance: reflects the average level of a group of observations in rank

Features: (Normal distribution: mean=M) (Lognormal distribution: M=G) (Positive skewed distribution: M>mean) (Negative skewed distribution: M<mean)

Application: Theoretically used for the centralized location of any distributed data, not affected by extreme values, and robust. Skewed distribution, uncertain values ​​in data, extreme values ​​in small samples, and unclear data distribution

Symbol: R

Calculation: R=maximum value-minimum value

Statistical significance: reflects the fluctuation range of a set of observed values. The greater the range, the greater the degree of data variation.

Application: Not used alone

Symbol: Q/IQR

Calculation: Q=P75-P25

Statistical significance: The range of the middle half of the data is more stable and robust than the range. The larger the Q, the greater the degree of data variation.

application

Symbol: σ/S

calculate:

Statistical significance: The larger the variance, the more dispersed the individual values, and the greater the degree of variation. The smaller the standard deviation, the more concentrated the individual data, the smaller the degree of data variation, and the better representative the mean of the concentrated location, and vice versa.

Application: Normally distributed or approximately normally distributed data

The mean and standard deviation are used together to describe the concentration position and degree of variation of normally distributed data, expressed as x̄±S

Symbol: CV

Calculation: CV=(S/x̄)*100%

Statistical significance The larger the coefficient of variation, the greater the degree of variation.

Application: Compare