Answer to Question #264879 in Statistics and Probability for Hai

Question

Melvin surveyed the price of unleaded gasoline at gas stations in Davao City and Tagum City. The raw data, in pesos per liter, are given below.

a. Find the standard deviation of prices in each city.

b. Which city has more consistently priced gasoline? Why?

Davao City 45.90 48.75 48.90 49.01 45.00 47.90

Tagum City 46.20 47.95 48.95 45.52 46.83 47.98

Answer 1

Solution:

(a): For Davao City:

n=6

$\bar X=\dfrac{\Sigma x_i}n=\dfrac{45.90+ 48.75 +48.90+ 49.01+ 45.00+ 47.90}6=47.577$

$\Sigma x_i^2=45.90^2+ 48.75^2+ 48.90^2+ 49.01^2+ 45.00^2+ 47.90^2=13595.973$

Then, $s=\sqrt{\dfrac{\Sigma x_i^2}n-(\bar X)^2}=\sqrt{\dfrac{13595.973}6-47.577^2}=1.557$

For Tagum city:

n=6

$\bar X=\dfrac{\Sigma x_i}n=\dfrac{46.20+ 47.95+ 48.95 +45.52+ 46.83+ 47.98}6=47.238$

$\Sigma x_i^2=46.20^2+ 47.95^2+ 48.95^2+ 45.52^2+ 46.83^2+ 47.98^2=13396.945$

Then, $s=\sqrt{\dfrac{\Sigma x_i^2}n-(\bar X)^2}=\sqrt{\dfrac{13396.945}6-47.238^2}=1.181$

(b):

For Davao city:

$CV=\dfrac{s}{\bar X}\times 100\%=\dfrac{1.557}{47.577}\times 100\%=3.27\%$

For Tagum city:

$CV=\dfrac{s}{\bar X}\times 100\%=\dfrac{1.181}{47.238}\times 100\%=2.50\%$

Since, coefficient of variation is less for Tagum city, we can say that Tagum city has more consistently priced gasoline.