Meaning of mathematical symbol $\pm$

Question

What is the meaning of the $\pm$ symbol in relation to this expression?

For example, the perceived area of a circle probably grows somewhat more slowly than actual (physical, measured) area: $$ \text{the reported perceived area} = (\text{actual area})^x, \text{where }x= \color{red}{\underline{\color{black}{.8 \pm .3}}}, $$ a discouraging result. Different people see the same areas somewhat…

and how does it apply to the whole formula?

Thank you

Answer 1

It means that $x$ varies between $0.8-0.3 \,\, \text{and} \,\, 0.8+0.3$ giving '$\text{area}$' is between $$ \text{area}_{-}=\left(\text{actual area} \right)^{0.8-0.3}=\left(\text{actual area} \right)^{0.5} $$ and $$ \text{area}^+=\left(\text{actual area} \right)^{0.8+0.3}=\left(\text{actual area} \right)^{1.1}. $$

Answer 2

$z=y\pm x$ is read as "$z=y$ Plus-Minus $x$" and means that $z$ can be both $y+x$ and $y-x$ which depends on certain conditions.

Answer 3

It meanw $x = .8 \text{ give or take } .3$ meaning $.5 \le x \le 1.1$

In terms of the whole formula $(actual area)^{.5} ... perceived area ... (actual area)^{1.1}$ which means $\sqrt{actual area} ... perceived area ... (actual area)*\sqrt[10]{actual area}$ which is damned near useless result. (Hence the word "discouraging").

This is a margin of error of $37.5\%$ which is terrible and when applied to the formula is literally exponentially worse.