Answer to Question #139838 in Statistics and Probability for Climar

Question

The weights of 10 boxes of a certain brand of cereal have a mean content of 278 grams with a standard deviation of 9.64 grams. If these boxes were purchased at 10 different stores and the average price per box is $1.29 with a standard deviation of $0.09, can you conclude that the weights are relatively more homogeneous than the prices?

Answer 1

$\bar{x}_w=278, s_w=9.64$

$\bar{x}_p=1.29, s_p=0.09$

For answering this question we use coefficient of variation:

$CV=\frac{s}{\bar{x}}\cdot100$

$CV_w=\frac{9.64}{278}\cdot100=3.48$

$CV_p=\frac{0.09}{1.29}\cdot100=6.98$

Comparing these two coefficients of variation we can conclude that :

$CV_w<CV_p\implies$ the weights are more homogeneous than the prices.