When performing lead testing, how should the weighted mean be calculated?

The weighted mean is a valuable statistical tool used in lead testing when the samples vary significantly in importance or frequency. To accurately calculate the weighted mean, one needs to take into account both the weight of each sample and the value of each subsample.

By multiplying each sample's weight by its corresponding subsample, you ensure that more significant samples have a proportional influence on the final mean. This method accounts for the varying relevance or size of samples, delivering a more accurate representation of the overall lead levels.

Dividing the total of these weighted values by the total number of subsamples ensures that the final average reflects the contribution of each sample, appropriately adjusted for its weight. This approach is crucial in lead testing, as it helps to provide a precise assessment of lead exposure, which can be critical in environments where lead exposure risks vary across different areas or materials.

The other methods do not consider the varying importance of each sample, potentially leading to skewed results that do not accurately reflect the true lead levels in the tested materials. Thus, using the weighted approach provides necessary clarity and reliability in lead testing results.