During the 2011–12 winter seasons, a homeowner received four deliveries of heating oil, as shown in the following table.

 Gallons Purchased          Price per Gallon ($)

           209…………………...................  2.60

           182…………………...................  2.40

           157…………………...................  2.78

           149…………………...................  2.74

The homeowner claimed that the mean price he paid for oil during the season was (2.60 + 2.40 + 2.78 + 2.74)/4 = $2.63 per gallon. Do you agree with this claim? If not, explain why this method of calculating the mean is not appropriate in this case and find the correct value of the mean price.