Question

The marks obtained by nine students in Physics and Mathematics are given below:

Physics	$48$	$60$	$72$	$62$	$56$	$40$	$39$	$52$	$30$
Mathematics	$62$	$78$	$65$	$70$	$38$	$54$	$60$	$32$	$31$

Interpret the result.

• A. This indicates a moderate positive relationship between marks in Physics and Mathematics.
• B. This indicates a high positive relationship between marks in Physics and Mathematics.
• C. This indicates a negative relationship between marks in Physics and Mathematics.
• D. None of the above

Answer 1

The correct option is A This indicates a moderate positive relationship between marks in Physics and Mathematics.

Descending order arranged data will be as follows:

Physics: $72,62,60,56,52,40,39,30$

Mathematics: $78,70,65,62,60,54,38,32,31$

Thus data will be

Physics$\left(P\right)$	Mathematics $\left(M\right)$	Rank $\left(P\right)$	Rank $\left(P\right)$	$|d|$	$d^2$
98 60 72 62 56 40 39 52 30	62 78 65 70 38 54 60 32 31	6 3 1 2 4 7 8 5 9	4 1 3 2 7 6 5 8 9	2 2 2 0 3 1 3 3 0	4 4 4 0 9 1 9 9 0

$n=9,\sum d^2=40$

$r=1-\frac{6\sum d^2}{n(n^2-1)}=1-\frac{40\times 6}{9(9^2-1)}=1-\frac{240}{720}=0.66$

Since $r>0$ we can say that this indicate a moderate positive relationship between marks of physics and mathematics.