Calculate the coefficient of correlation

The data below gives the marks obtained by 10 pupils taking Maths and Physics tests

 

Pupil	A	B	C	D	E	F	G	H	I	J
Maths Marks  (out of 30)    x	20	23	8	29	14	11	11	20	14	14
Physics Marks  (out of 30)   y	30	35	21	33	33	26	22	31	33	36

 

Calculate the coefficient of correlation.

Solution:

 

Pupil	Maths Marks  (out of 30)    X	Physics Marks  (out of 30)   Y	XY	`X^2`	`Y^2`
A	20	30	600	400	900
B	23	35	805	529	1225
C	8	21	168	64	441
D	29	33	899	841	1089
E	14	33	462	196	1089
F	11	26	286	121	676
G	11	22	242	121	484
H	20	31	620	400	961
I	14	33	462	196	1089
J	14	36	504	196	1296
∑	146	300	5048	3064	9250

 

Here n = 10

`r = \frac{n \times (\sum (XY ) - (\sum X \times \sum Y))}{\sqrt {(n \times \sum X^2 - \sum ( X )^2) \times (n \times \sum Y^2 - \sum ( Y )^2)}}`

`r = \frac{10 \times (5048 - (146 \times 300))}{\sqrt {(10 \times 3064 - \sum (146)^2) \times (10 \times 9250 - \sum ( 300)^2 ) }}`

`r = \frac{10 \times (5048 - 43800)}{\sqrt {(30640 - 21316) \times (92500 - 90000)}}`

`r = \frac{10 \times  - 38752}{\sqrt {9324 \times 2500}}`

 `r = \frac{ - 387520}{\sqrt {23310000}}`

 `r = \frac{- 387520}{4828.0431}`

`r =  - 80.2644`