Why is it that if you have two data points [tex]a \pm b[/tex] and [tex]c \pm d[/tex] whose uncertainties are symmetrically distributed, the sum of the points is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a+c \pm \sqrt{b^2+d^2}[/tex]

Can someone please help me with this derivation.

Also, another separate question, suppose I have many uncertain data points: [tex]x_1 \pm y_1[/tex], [tex]x_2 \pm y_2+...[/tex]. And I have a function that acts on all of them: [tex]f(x_1 \pm y_1, x_2 \pm y_2,...,x_n \pm y_n)[/tex]

Is the following reasoning valid:

Choose [tex]x_i \pm y_i[/tex] in order to maximize f.

(For instance, if I had f(\frac{1}{x \pm y}) you would choose [tex]x -y[/tex] to maximize f.)

Next, you choose [tex]x_i \pm y_i[/tex] in order to minimize f.

Once you have f_{max} and f_{min}, you find the average of the two, so you have:

f(x_1 \pm y_1, x_2 \pm y_2,..., x_n \pm y_n) = \frac{f_{max}+f_{min}}{2} \pm \frac{f_{max}-f_{min}}{2}

(SORRY FOR NO LATEX, THE LATEX CODE IS GIVING A COMPLETELY DIFFERENT EQUATION!)

Thanks!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Math with experimental uncertainties

**Physics Forums | Science Articles, Homework Help, Discussion**