The data listed below are the areas of U.S. state capitals (except Juneau, Alaska) as obtained from Wikipedia on 9/3/22. Enter the data in your calculator and generate one-variable statistics, then use the calculator output to answer the questions that follow.

Areas: 6.7, 7.7, 8.1, 10.2, 13.0, 14.0, 14.7, 16.7, 17.3, 18.5, 21.1, 21.4, 22.4, 26.9, 27.3, 31.6, 35.0, 37.3, 45.7, 52.8, 54.0, 55.4, 56.0, 60.1, 63.8, 64.3, 68.4, 68.7, 74.6, 75.8, 76.8, 89.6, 95.7, 97.9, 104.9, 109.1, 114.6, 116.2, 125.2, 133.5, 143.4, 153.3, 159.8, 210.3, 305.1, 361.5, 517.6, 525.9, 620.3

Round your numerical answers to the nearest first decimal place and enter the numbers only; do not enter units or symbols. If you do any calculations, please use numbers that are rounded to the nearest first decimal place in your calculations.

(a) What is the mean state area?

(b) What is the median state area?

(c) What is the five-number summary of the state areas? Enter your answers in the correct left-to-right order.

Let's go through the steps to understand how to find the solutions for the given data of areas of U.S. state capitals:

### (a) Mean State Area

To find the mean, you add up all the values and divide by the total number of values.

1. Add all areas: Sum up all the given areas.
2. Count the number of areas: There are 49 areas provided.
3. Calculate the mean: Divide the total sum by 49.

The mean state area is approximately 105.1.

### (b) Median State Area

To find the median, which is the middle value when the numbers are arranged in order:

1. Order the areas: List all areas from smallest to largest.
2. Find the middle value:
- Since there are 49 areas (an odd number), the median is the 25th value in this ordered list.

The median state area is 63.8.

### (c) Five-Number Summary

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

1. Minimum: The smallest area in the list is 6.7.
2. First Quartile (Q1): This is the value below which 25% of the data fall. It is about 22.4.
3. Median: As calculated before, the median is 63.8.
4. Third Quartile (Q3): This point marks where 75% of the data fall below it. It is about 114.6.
5. Maximum: The largest area in the list is 620.3.

The five-number summary is: (6.7, 22.4, 63.8, 114.6, 620.3).

These steps help understand how the statistical measures were determined.