Answer to Question #264521 in Statistics and Probability for Ronsoy

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

a). Standard Deviation:

Firstly needs to calculate mean of data for each city.

$\bar{X}=\frac{sum of prices in Davao }{6}$

$\bar{X_1}=\frac{(45.90+48.75+48.90+49.01+45.00+47.90)}{6}=47.58$

$\bar{X_2}=\frac{(46.20+47.95+48.95+45.52+46.83+47.98)}{6}=47.24$

Following table shows the calculation:

$\sigma=\sqrt{\frac{\Sigma (X-\bar{X})^{2}}{N}}$

Standard deviation of prices in Davao city:

$\sigma =\sqrt{\frac{14.74}{6}}=1.567$

Standard deviation of prices in Tagum city:

$\sigma =\sqrt{\frac{8.18}{6}}=1.168$

b).

Standard deviation measures the variability of data. The above calculation shows that standard deviation of prices in Davao city is greater than Tagum city. This means the price of unleaded gasoline at gas station has more variability in case of Davao city than Tagum.

Based on this, it can say that Tagum city has more consistently priced gasoline.