A plumbing supplier’s mean monthly demand for vinyl washers is 24,212

with a standard deviation of 6,053. The mean monthly demand for steam boilers is 6.8 with
a standard deviation of 1.7. Compare the dispersion of these distributions. Which demand
pattern has more relative variation? Explain.

To compare the dispersion of the two distributions (vinyl washers and steam boilers), we can use a measure called the coefficient of variation (CV). The CV is a standardized measure of dispersion that allows us to compare the relative variation between two different datasets.

To calculate the CV, we divide the standard deviation by the mean and multiply by 100 to get it as a percentage. The formula is:

CV = (standard deviation / mean) * 100

Let's calculate the CV for both vinyl washers and steam boilers:

For vinyl washers:
CV_vinyl = (6,053 / 24,212) * 100 ≈ 25.01%

For steam boilers:
CV_steam = (1.7 / 6.8) * 100 ≈ 25%

Now, comparing the CVs, we see that the coefficient of variation for vinyl washers is approximately 25.01%, while for steam boilers, it is approximately 25%.

Since the CV for vinyl washers is slightly higher than for steam boilers, it means that vinyl washers have more relative variation or dispersion in demand compared to steam boilers.

In simpler terms, this means that the demand for vinyl washers tends to vary more relative to its mean demand compared to the demand for steam boilers.