Question

The mean number of days construction workers miss per year is 11. The standard deviation is 2.3. The mean number of days factory workers miss per year is 8 with a standard deviation of 1.8. Which class is more variable in terms of days missed?

Please show work.

Answer 1

Factory Workers

Step-by-step explanation:

While a common mistake may be to take in count of only the standard deviation (like I had done previously), there is an equation to use that measures the dispersion of data points in a data set around the mean, called coefficient of variation.

`CV=(\sigma)/(\mu) *100` where sigma is the population standard deviation and mu is the population's mean.

The highest percentage of CV is considered more variable.

Let's do the math:

Construction workers:
`(\sigma)/(\mu) =(2.3)/(11) =0.209*100=20.9%\\`

Factory workers:
`(\sigma)/(\mu) =(1.8)/(8) =0.225*100=22.5%`

Since factory workers have a higher percentage, their data is more variable.