In a certain local market, the average price of the Panther conertible is $45,000, with a standard deviation?
of $4000. The average price of a mid-sized station wagon is $22,500 with a standard deviation of $2000. Which price is more variable? Explain.
- tomsing98Lv 69 years agoFavorite Answer
Let's make the comparison more extreme. A Ferrari costs $100,000 on average, with a standard deviation of $1. A toy car costs $2 on average with a standard deviation of $1. Which price is more variable?
You get the sense that it should be the toy car, right? How can you formalize that? What if we divide the standard deviation by the mean value? Intuitively, that makes sense. $1 is a huge fraction of $2, but a tiny fraction of $100,000. Since we're talking about fractions of the average price, mathematically, we're talking about $1 / $2, and $1 / $100,000.
So, standard deviation divided by the mean value. We need a name for the result. How about the "coefficient of variation", or CV for short? Sounds good to me. Now, let's write an equation that defines it.
CV = σ / µ
where σ is the standard deviation, and µ is the mean value. Note that both σ and µ have the same units, so the CV is unitless.
So, use that definition to calculate the variation for the convertible and the station wagon. I hope that helps!