0.1.1 - Order of Operations

When performing a series of mathematical operations, begin with those inside parentheses or brackets. Next, calculate any exponents or square roots. This is followed by multiplication and division, and finally, addition and subtraction.

Order of Operations

Example: Standard Error for Two Proportions Section

This is a formula that you will see in Lesson 9: \( \sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}\)

\(p\) is a proportion and \(n\) is a sample size. Let's look at an example of working through this formula with the following values:

\(p_1=0.60\)

\(p_2=0.35\)

\(n_1=40\)

\(n_2=80\)

 

We can begin by plugging these values into the formula:

\( \sqrt{\frac{0.60(1-0.60)}{40}+\frac{0.35(1-0.35)}{80}}\)

The first operations that we perform are the ones in the parentheses:

\( \sqrt{\frac{0.60(0.40)}{40}+\frac{0.35(0.65)}{80}}\)

Though not typically shown, the values under the square root symbol in the fractions are treated as if they are in parentheses:

\(\sqrt{\left ( \frac{0.60(0.40)}{40}\right )+ \left (  \frac{0.35(0.65)}{80}\right ) } \)

Working within each set of parentheses, are next step is to multiply in the numerators:

\(\sqrt{\left (  \frac{0.24}{40} \right ) + \left (   \frac{0.2275}{80}\right ) } \)

Then, the division (i.e., the fractions):

\( \sqrt{0.006+0.00284375}\)

The addition underneath the square root:

\( \sqrt{0.00884375}\)

And finally, we take the square root:

\(0.0940\) 

Example: Pooled Proportion Section