Question

What can be true regarding the coefficient of correlation between infant mortality rate (IMR) and economic status?

• A. r = +1
• B. r = -1
• C. r = +0.22
• D. r = -0.8

Hint:

IMR falls as economic status rises (negative r); real data rarely give a perfect plus or minus 1.

Answer 1

The Correct Option is D

Step 1: Recall what the correlation coefficient r tells us.
The correlation coefficient r ranges from \(-1\) to \(+1\). A positive r means the two variables rise and fall together, a negative r means one rises as the other falls, and the size of r (ignoring the sign) tells us how tight that relationship is. A value of exactly \(+1\) or \(-1\) means a perfect, exact straight line relationship.

Step 2: Decide the expected direction for IMR versus economic status.
Infant mortality rate (IMR), the number of infant deaths per \(1000\) live births, tends to fall as economic status rises, because better economic status usually brings better nutrition, sanitation, and access to health care. So biologically, we expect a negative correlation between IMR and economic status.

Step 3: Rule out a perfect correlation.
Real biological and social data almost never show a perfect straight line relationship, because many other factors (education, health infrastructure, disease burden, and so on) also affect IMR. So
\[ r = +1 \quad \text{and} \quad r = -1 \] are both unrealistic here.

Step 4: Rule out the positive, weak value.
A value like \(r = +0.22\) is both the wrong sign (IMR should fall, not rise, as economic status improves) and too weak to reflect the strong, well documented link between poverty and infant mortality.

Step 5: Confirm the remaining option.
A value of \(r = -0.8\) is negative, matching the expected inverse relationship, and it is strong without being a suspicious, unrealistic perfect \(-1\). This fits a real world epidemiological correlation.

Final Answer:
\[ \boxed{r = -0.8} \]