Decribtive Statistics

Descriptive statistics

Descriptive statistics is describing the main features of a collection of information. Some important descriptive statistics include range, mean, median, variance and standard deviation. Generally considered, measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance).Measures of distribution include kurtosis and skewness.

Use the following equation to calculate mean, variance and standard deviation

Range=max-min

x=xin

Var=(xi-x)2n-1

SD=(xi-x)2n-1

Or take advantage of excel, then get the result directly:

Max(X)= 46013.06

Min(X)= 507.46

Range=45505.6

Median=10368.6

x=14177.38

Var(X)= 128766896.6

SD(x)= 11347.55025

Make a conclusion by the result: With large value of variance and standard deviation , the volatility of the data is large. It also means the mean could not well represent the central tendency of the data.

Similarly, processing data series Y and get the result:

Max(Y)= 3803.47

Min(Y)= 25.28

Range=3778.19

Median=730.84

y=1054.887

Var(Y)= 912383.8684

SD(Y)= 955.1878707

Analyze according to the result: With large value of variance and standard deviation , the volatility of the data is large. It also means the mean could not well represent the central tendency of the data.

From the raw data, we may find out the reason why the value of variance is large is mainly because the existence of extreme. The extreme is the data from Tibet and its number is 25.8compared with the mean value is 1054.89