Question

What mass of sample in Figure 28-3 is expected to give a sampling standard deviation of \( \pm 6\% \)?

Short answer

The mass of the sample which produces the relative standard deviation of \(1\% \)

Step-by-step solution

Definition of Standard deviation.

• The standard deviation is a measure of how far something deviates from the mean (for example, spread, dispersion, or spread). A "typical" variation from the mean is represented by the standard deviation.
• Because it returns to the data set's original units of measurement, it's a common measure of variability.
• The standard deviation, defined as the square root of the variance, is a statistic that represents the dispersion of a dataset relative to its mean.

Determine the Sampling Standard deviation.

In this task we will calculate the mass of sample in Figure \(28 - 3\) expected to give a sampling standard deviation of\( \pm 6\% \).

Here we will use the equation \(28 - 5\) for relative variance\(\left( {{R^2}} \right)\) :

\(\begin{array}{l}{R^2} = {\left( {\frac{{{\delta _n}}}{n}} \right)^2}\\ = \frac{{pq}}{n}n\\{R^2} = pq\end{array}\)

Where, \(p\) and \(q\) are the fraction of particles present

Next we will rearrange the equation \(28 - 5\)to the following and calculate the mass of sample:

\(\begin{array}{l}m{R^2} = {K_a}\\m = \frac{{{K_a}}}{{{R^2}}}\\m = \frac{{36\;{\rm{g}}}}{{{6^2}}}\\m = 1\;{\rm{g}}\end{array}\)

Where, \(R\) is the relative standard deviation and \({K_a}\) is the sampling constant

Therefore, the mass of the sample which produces the relative standard deviation of \(1\% \)