Question:medium
What can be true regarding the coefficient of correlation between infant mortality rate (IMR) and economic status?
What can be true regarding the coefficient of correlation between infant mortality rate (IMR) and economic status?
Show Hint
IMR falls as economic status rises (negative r); real data rarely give a perfect plus or minus 1.
Updated On: Jul 8, 2026
- r = +1
- r = -1
- r = +0.22
- r = -0.8
Show Solution
The Correct Option is D
Solution and Explanation
Step 1: Recall the r scale.
$r$ runs from $-1$ to $+1$. The sign shows direction, the size shows strength, and only a truly exact linear relationship gives $r=\pm1$.
Step 2: Think about the biology first.
As a population's economic status improves, families get better food, cleaner water, and more access to doctors, so infant deaths go down. That is an inverse relationship, so $r$ should come out negative.
Step 3: Drop the perfect values.
Since many things besides income affect infant mortality, such as vaccination coverage or disease outbreaks, a perfect straight line fit with $r=+1$ or $r=-1$ is not realistic for this kind of health data.
Step 4: Drop the wrong sign option.
$r=+0.22$ has the wrong sign for this relationship and is also a weak value, so it does not fit the strong known link between poverty and child deaths.
Step 5: Settle on the fitting value.
$r=-0.8$ is negative and strong, matching a real, well documented inverse tie between economic status and infant mortality, without claiming an impossible perfect correlation.
\[ \boxed{r=-0.8} \]
$r$ runs from $-1$ to $+1$. The sign shows direction, the size shows strength, and only a truly exact linear relationship gives $r=\pm1$.
Step 2: Think about the biology first.
As a population's economic status improves, families get better food, cleaner water, and more access to doctors, so infant deaths go down. That is an inverse relationship, so $r$ should come out negative.
Step 3: Drop the perfect values.
Since many things besides income affect infant mortality, such as vaccination coverage or disease outbreaks, a perfect straight line fit with $r=+1$ or $r=-1$ is not realistic for this kind of health data.
Step 4: Drop the wrong sign option.
$r=+0.22$ has the wrong sign for this relationship and is also a weak value, so it does not fit the strong known link between poverty and child deaths.
Step 5: Settle on the fitting value.
$r=-0.8$ is negative and strong, matching a real, well documented inverse tie between economic status and infant mortality, without claiming an impossible perfect correlation.
\[ \boxed{r=-0.8} \]
Was this answer helpful?
0
