Question #061d2

1 Answer
Mar 8, 2016

The difference in the averages depends on the range between the gas prices and how often they appear in the given set of data.


Recall that an average is a number that represents the central value in a given set of data.

Reason 1
In your case, the averages could have been different because the average price of gasoline in the report covered a larger area, compared to the small area surrounding Nancy's home. For example, the report could have used gas prices from all over the United States. In contrast, the average price of #$3.03# only represented the gas prices within the vicinity of Nancy's home. The fact that gas prices were taken from all over the country reveals that the average may be different compared to Nancy's area since gas prices are different throughout the country.

For example, given the following gas prices, the average would be:

#stackrel(color(brown)("large range and number of terms"))overbrace($2.46,$2.62,$2.84,$3.05,$3.13)stackrel(color(red)(" average "" "))(rArr)$2.82#

Alternatively, the calculation of the average near Nancy's home would contain less gas prices, since there are less gas stations, as well as the gas prices having approximately the same value.

For example, given the following gas prices, the average would be:

#stackrel(color(brown)("small range and number of terms"))overbrace($2.99,$3.02,$3.08)stackrel(color(red)(" average "" "))(rArr)$3.03#

Reason 2
The average gas price in the report could also be lower than the average gas price near Nancy's home if there are many values close to #$2.82# being used. Similarly, the same would apply for #$3.03#.

For example, in the report, you could have:

#$2.65, $2.80,color(blue)($2.82),color(blue)($2.82),color(blue)($2.82),color(blue)($2.82),color(blue)($2.82),$3.01stackrel(color(red)(" average "" "))(rArr)$2.82#

Whereas near Nancy's home, you could have:

#$2.98,color(blue)($3.03),color(blue)($3.03),color(blue)($3.03),$3.08stackrel(color(red)(" average "" "))(rArr)$3.03#

Thus, the more a value appears in the set of data, the more close the average will be to that value. The value that appears most in a set of data is also known as the mode.