a) Find the mean and median of the following gasoline prices per gallon in California:
regular: 
$
3.78
$3.78​, mid-grade: 
$
3.87
$3.87​, premium: 
$
3.96
$3.96​, diesel: 
$
4.28
$4.28​. Round to the nearest cent.
$
$
Mean
Preview

$
$
Median
Preview

b) Find the mean and median of the following gasoline prices per gallon in Missouri:
regular: 
$
3.09
$3.09​, mid-grade: 
$
3.19
$3.19​, premium: 
$
3.29
$3.29​, diesel: 
$
3.64
$3.64​. Round to the nearest cent.
$
$
Mean
Preview
$
$
Median
Preview

c) How would one calculate the "average amount" of money a Californian paid for gasoline for an entire month?

Most expensive fillup 
−
 Least expensive fillup
Number of fillups
Number of fillups
Most expensive fillup − Least expensive fillup
​
 

Number of fillups
Sum of $ spent for each fill up
Sum of $ spent for each fill up
Number of fillups
​
 

Sort from highest to lowest then find the middle value

Sum of $ spent for each fill up
Number of fillups
Number of fillups
Sum of $ spent for each fill up
​
 

Find the most common value
Find the most common value

### Part (a): Mean and Median of Gasoline Prices in California

Given prices:
- Regular: $3.78
- Mid-grade: $3.87
- Premium: $3.96
- Diesel: $4.28

#### Mean Calculation
To find the mean, add all the prices together and divide by the number of prices.

\[
\text{Mean} = \frac{3.78 + 3.87 + 3.96 + 4.28}{4} = \frac{15.89}{4} = 3.9725
\]

Rounded to the nearest cent:

\[
\text{Mean} = \$3.97
\]

#### Median Calculation
To find the median, arrange the prices in order and find the middle value. Since there are 4 prices, the median will be the average of the 2 middle values.

Ordered prices: $3.78, $3.87, $3.96, $4.28

\[
\text{Median} = \frac{3.87 + 3.96}{2} = \frac{7.83}{2} = 3.915
\]

Rounded to the nearest cent:

\[
\text{Median} = \$3.92
\]

### Part (b): Mean and Median of Gasoline Prices in Missouri

Given prices:
- Regular: $3.09
- Mid-grade: $3.19
- Premium: $3.29
- Diesel: $3.64

#### Mean Calculation
\[
\text{Mean} = \frac{3.09 + 3.19 + 3.29 + 3.64}{4} = \frac{13.21}{4} = 3.3025
\]

Rounded to the nearest cent:

\[
\text{Mean} = \$3.30
\]

#### Median Calculation
Ordered prices: $3.09, $3.19, $3.29, $3.64

\[
\text{Median} = \frac{3.19 + 3.29}{2} = \frac{6.48}{2} = 3.24
\]

Rounded to the nearest cent:

\[
\text{Median} = \$3.24
\]

### Part (c): Calculating the "Average Amount" of Money a Californian Paid for Gasoline for a Month

The best way to calculate the "average amount" of money a Californian paid for gasoline over an entire month would be:

\[
\text{Average amount per fill-up} = \frac{\text{Sum of dollars spent for each fill-up}}{\text{Number of fill-ups}}
\]

This method gives you the average cost of each fill-up over the month.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How does the median change if diesel prices increase by 10% in California?
2. If the price of regular gasoline in Missouri decreases by $0.10, how does that affect the mean?
3. What would the mean gasoline price be in California if all prices increase by 5%?
4. How would the average change if the number of fill-ups varied each month?
5. How can outlier gasoline prices (very high or low) affect the mean and median?

**Tip:** The median is a more robust measure than the mean when dealing with outliers or skewed distributions.

Calculate the mean and median gasoline prices per gallon in California and Missouri. Understand how to find the average amount a Californian paid for gasoline in a month based on fill-up costs. Detailed step-by-step solutions and rounded results provided.

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