Suppose the expected number of blowouts for 15 trucks is $\mu=4$, the variance is $\sigma^2=3$, and the standard deviation $\sigma \approx 1.72$.
What does the variance with respect to this problem mean? I understand what the words mean. For instance, the variance and standard deviation measures the spread of the data's distribution across the mean where the former is measured in units squared and the latter is just units. But I am having trouble describing the above data.
I would really appreciate any legitimate insight.
Remember that the goal of variance/standard deviation is to quantify how much the data differs from the mean, on average.
In this case, we have that for a sample of 15 trucks, we expect on average to have 4 blowouts. But since we have a variance that is significantly greater than zero, we would not be surprised for some sample of 15 trucks to have somewhere close to 4 blowouts, such as 3 or 5, or sometimes more/less. The deviation of the number of blowouts from the mean are expected to be greater the larger the variance is.