Question

A sample of lake water was analyzed to determine the amount of metals found in the lake. The standard deviation of the sampling method was found to be ±6.0%±6.0% . The standard deviation of the analytical method used to determine the amount of metals in the sample was determined to be ±2.4%±2.4% . What is the overall standard deviation?

Answer 1

Answer:

The overall standard deviation, s = 6.46 %

Given:

Sampling variance, $s_{b} = \pm 6.0% = 0.06$

Analytical variance, $s_{a} = \pm 2.4% = 0.024$

Solution:

Variance additive is given by:

$s^{2} = s_{a}^{2} + s_{b}^{2}$                        (1)

where

s = overall variance

Also, we know that:

Standard Deviation, $\sigma = \sqrt{variance}$

Therefore the standard deviation of the sampling, analytical and overall sampling is given by taking the square root of eqn (1) on both the sides:

$s = \sqrt{s_{a}^{2} + s_{b}^{2}}$

$s = \sqrt{0.024^{2} + 0.06^{2}} = 0.0646$

s = 6.46 %