- Practice
- Artificial Intelligence
- Statistics and Machine Learning
- Day 5: Computing the Correlation

# Day 5: Computing the Correlation

# Day 5: Computing the Correlation

You are given the scores of **N** students in three different subjects - **Mathematics**,**Physics** and **Chemistry**; all of which have been graded on a scale of 0 to 100. Your task is to compute the Pearson product-moment correlation coefficient between the scores of different pairs of subjects (Mathematics and Physics, Physics and Chemistry, Mathematics and Chemistry) based on this data.
*This data is based on the records of the CBSE K-12 Examination - a national school leaving examination in India, for the year 2013.*

**Pearson product-moment correlation coefficient**

This is a measure of linear correlation described well on this Wikipedia page. The formula, in brief, is given by:

where **x** and **y** denote the two vectors between which the correlation is to be measured.

**Input Format**

The first row contains an integer **N**.

This is followed by **N** rows containing three tab-space (*'\t'*) separated integers, **M P C** corresponding to a candidate's scores in Mathematics, Physics and Chemistry respectively.

Each row corresponds to the scores attained by a unique candidate in these three subjects.

**Input Constraints**

1 <= N <= 5 x 10^{5}

0 <= **M, P, C** <= 100

**Output Format**

The output should contain three lines, with correlation coefficients computed

and rounded off **correct to exactly 2 decimal places**.

The first line should contain the correlation coefficient between Mathematics and Physics scores.

The second line should contain the correlation coefficient between Physics and Chemistry scores.

The third line should contain the correlation coefficient between Chemistry and Mathematics scores.

So, your output should look like this (these values are only for explanatory purposes):

```
0.12
0.13
0.95
```

**Test Cases**

There is one sample test case with scores obtained in Mathematics, Physics and Chemistry by 20 students.
The hidden test case contains the scores obtained by all the candidates who appeared for the examination and took all three tests (Mathematics, Physics and Chemistry).

** Think:*** How can you efficiently compute the correlation coefficients within the given time constraints, while handling the scores of nearly 400k students?*

**Sample Input**

```
20
73 72 76
48 67 76
95 92 95
95 95 96
33 59 79
47 58 74
98 95 97
91 94 97
95 84 90
93 83 90
70 70 78
85 79 91
33 67 76
47 73 90
95 87 95
84 86 95
43 63 75
95 92 100
54 80 87
72 76 90
```

**Sample Output**

```
0.89
0.92
0.81
```

There is **no special library support** available for this challenge.