The cities with the highest life expectancy are​ Nowhereville: 76.7 ​years; Somewhereopolis: 76.7 ​years; Kinch​ City: 80.7 ​years; Tortuga: 90.2 ​years; Euler​ Town: 80.7 ​years; Godelville: 78.9 ​years; Sirap: 80.7 years. Find the​ mean, the​ median, and the mode.

Question

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Part 1
Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The mean life expectancy is
  
enter your response here years. ​(Round to the nearest tenth as​ needed.)
B.
The mean does not exist.
Part 2
Find the median. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The median life expectancy is
  
enter your response here years. ​(Round to the nearest tenth as​ needed.)
B.
The median does not exist.

Answer 1

To find the mean, median, and mode of the life expectancies of the cities listed, let's start with the mean.

### Part 1: Mean
The mean is the average of a set of numbers, calculated by summing all the values and dividing by the count of values.

Given life expectancies:
- Nowhereville: 76.7 years
- Somewhereopolis: 76.7 years
- Kinch City: 80.7 years
- Tortuga: 90.2 years
- Euler Town: 80.7 years
- Godelville: 78.9 years
- Sirap: 80.7 years

**Step 1:** Sum the life expectancies:
\[ 76.7 + 76.7 + 80.7 + 90.2 + 80.7 + 78.9 + 80.7 = 564.6 \]

**Step 2:** Count the number of cities:
\[ 7 \]

**Step 3:** Calculate the mean:
\[ \text{Mean} = \frac{564.6}{7} \approx 80.7 \text{ years} \]

So the mean life expectancy is:
\[ \boxed{80.7 \text{ years}} \]

### Part 2: Median
The median is the middle value in a list of numbers ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.

**Step 1:** Organize the life expectancies in ascending order:
\[ 76.7, 76.7, 78.9, 80.7, 80.7, 80.7, 90.2 \]

**Step 2:** Locate the middle value:
Since there are 7 values, the middle one is the 4th value in the ordered list.

So the median life expectancy is:
\[ \boxed{80.7 \text{ years}} \]

### Mode
The mode is the number that appears most frequently in a dataset.

In the list:
\[ 76.7, 76.7, 78.9, 80.7, 80.7, 80.7, 90.2 \]

The value 80.7 appears three times, more frequently than other values.

So the mode life expectancy is:
\[ \boxed{80.7 \text{ years}} \]

### Summary:
- **Mean:** 80.7 years
- **Median:** 80.7 years
- **Mode:** 80.7 years