he cities with the highest life expectancy are​ Nowhereville: 78.4 ​years; Somewhereopolis: 78.4 ​years; Kinch​ City: 90.8 ​years; Tortuga: 82.6 ​years; Euler​ Town: 85.6 ​years; Godelville: 82.6 ​years; Sirap: 78.4 years. Find the​ mean, the​ median, and the mode.

Question

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Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Answer 1

To find the mean life expectancy, we need to sum all the life expectancies of the cities and divide by the number of cities:

1. Add the life expectancies:
\[ 78.4 + 78.4 + 90.8 + 82.6 + 85.6 + 82.6 + 78.4 \]

2. Calculate the sum:
\[ 78.4 + 78.4 + 90.8 + 82.6 + 85.6 + 82.6 + 78.4 = 577.2 \]

3. Divide the sum by the number of cities (7):
\[ \frac{577.2}{7} = 82.4571 \]

So, the mean life expectancy is approximately \( 82.457 \) years.

Now, let's find the median.

1. Arrange the life expectancies in ascending order:
\[ 78.4, 78.4, 78.4, 82.6, 82.6, 85.6, 90.8 \]

2. The median is the middle value. Since there are 7 (an odd number) of data points, the median is the 4th value in the ordered list:
\[ 82.6 \]

So, the median life expectancy is \( 82.6 \) years.

Finally, let's find the mode.

1. The mode is the value that appears most frequently. From the list:
\[ 78.4, 78.4, 78.4, 82.6, 82.6, 85.6, 90.8 \]

2. The value \( 78.4 \) appears 3 times, more often than any other value.

So, the mode is \( 78.4 \) years.

Summarized:
- Mean: \( 82.457 \) years
- Median: \( 82.6 \) years
- Mode: \( 78.4 \) years