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  1. Prepare
  2. Tutorials
  3. 10 Days of Statistics
  4. Day 7: Pearson Correlation Coefficient I

Day 7: Pearson Correlation Coefficient I

Objective
In this challenge, we practice calculating the Pearson correlation coefficient. Check out the Tutorial tab for learning materials!

Task
Given two -element data sets, and , calculate the value of the Pearson correlation coefficient.

Input Format

The first line contains an integer, , denoting the size of data sets and .
The second line contains space-separated real numbers (scaled to at most one decimal place), defining data set .
The third line contains space-separated real numbers (scaled to at most one decimal place), defining data set .

Constraints

  • , where is the value of data set .
  • , where is the value of data set .
  • Data set contains unique values.
  • Data set contains unique values.

Output Format

Print the value of the Pearson correlation coefficient, rounded to a scale of decimal places.

Sample Input

10
10 9.8 8 7.8 7.7 7 6 5 4 2 
200 44 32 24 22 17 15 12 8 4

Sample Output

0.612

Explanation

The mean and standard deviation of data set are:

The mean and standard deviation of data set are:

We use the following formula to calculate the Pearson correlation coefficient: