3. the number of calories in each sandwich listed on the menu at a fast food restaurant: {320, 420, 580…

Explanation:

Step1: Sort the data

Sort the set ${320, 420, 580, 270, 320, 380, 360, 270, 320, 310, 440, 470}$ in ascending - order: ${270, 270, 310, 320, 320, 320, 360, 380, 420, 440, 470, 580}$.

Step2: Find the minimum

The minimum value is the first number in the sorted list. So, the minimum is $270$.

Step3: Find the lower quartile

There are $n = 12$ data - points. The position of the lower quartile ($Q_1$) is $\frac{n + 1}{4}=\frac{12+1}{4}=3.25$. The lower quartile is $310+(320 - 310)\times0.25=312.5$.

Step4: Find the median

The position of the median for $n = 12$ (an even number of data - points) is $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The median is $\frac{320 + 360}{2}=340$.

Step5: Find the upper quartile

The position of the upper quartile ($Q_3$) is $\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75$. The upper quartile is $420+(440 - 420)\times0.75=435$.

Step6: Find the maximum

The maximum value is the last number in the sorted list. So, the maximum is $580$.

Answer:

Minimum: $270$ Lower Quartile: $312.5$ Median: $340$ Upper Quartile: $435$ Maximum: $580$