A study of gasoline prices in 1990 found the average price i

A study of gasoline prices in 1990 found the average price in dollars at 9 gas stations to be:

1.27, 1.25, 1.20, 1.30, 1.27, 1.24, 1.35, 1.29, 1.26

It can be shown that the mean is nearly $1.27 and the standard deviation is nearly $.04. What percentage of the data lies within one standard deviation of the mean?

Solution

1.27, 1.25, 1.20, 1.30, 1.27, 1.24, 1.35, 1.29, 1.26

Mean = $1.27 ; Standard deviation = $0.4

So prices with (1.27-0.4 , 1.27+0.4) i.e. ($1.23 , $1.31) = 1.27, 1.25, 1.20, 1.30, 1.27, 1.24, 1.29, 1.26

Thus 8 out of 9 prices are within one standard deviation of the mean i.e 88.9%