The applied knowledge of statistics

　Let's start!

Qualitative variable

　Qualitative variable is the data that we can't calculate the average on the statistics.
Example
Do you know bigdata?
「Yes」・・・8
「No」・・250

Quantitative variables

　Quantitative variable is the data that we can calculate the average on the statistics.
Example
How tall are you?
168cm 190cm 193cm 174cm 178cm

Covariance

　Covariance is the product of the deviation of the two data.
Examples
The relationship between the thickness of tree and the height of tree.
Tree１Tree２Tree３Tree４Tree５AverageVarianceStandard deviation
Thickness22272919332624.8√24.8
Height1315181420166.8√6.8

The covariance of the data is
{(22-26)(13-16)+(27-26)(15-16)+(29-26)(18-16)+(19-26)(14-16)+(33-26)(20-16)}÷5=59÷5=11.8

Correlation coefficient

　Correlation coefficient is the correlation of the two data and the covariance divided by the two standard deviations.
Correlation coefficient(=r) is certainly -1≦r≦1. It has three features.
　(1)If r is near 1, it is called strong positive correlation.
　The biggger one data become, the bigger another data become.
　(2)If r is near 0, it has no relationship between of two data.
　(3)If r is near -1, it is called strong negative correlation.
　The smaller one data become, the smaller another data become.
Example
　We use the example of covariance.
r=11.8÷(√24.8√6.8)≒0.91
So, the thickness of tree and the height of tree has strong positive correlation