Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Population Estimate, July 2016

\begin{tabular}{|l|l|l|l|}
\hline State & Population & State & Population \\
\hline Alaska & 741,894 & Missouri & [tex]$6,093,000$[/tex] \\
\hline Arizona & [tex]$6,931,071$[/tex] & Montana & [tex]$1,042,520$[/tex] \\
\hline California & [tex]$39,250,017$[/tex] & Nebraska & [tex]$1,907,116$[/tex] \\
\hline Colorado & [tex]$5,540,545$[/tex] & New Mexico & [tex]$2,081,015$[/tex] \\
\hline Connecticut & [tex]$3,576,452$[/tex] & North Dakota & 757,952 \\
\hline Florida & [tex]$20,612,439$[/tex] & Oklahoma & [tex]$3,923,561$[/tex] \\
\hline Illinois & [tex]$12,801,539$[/tex] & South Dakota & 865,454 \\
\hline Iowa & [tex]$3,134,693$[/tex] & Washington & [tex]$7,288,000$[/tex] \\
\hline Kansas & [tex]$2,907,289$[/tex] & West Virginia & [tex]$1,834,102$[/tex] \\
\hline Maryland & [tex]$6,016,447$[/tex] & Wyoming & 585,501 \\
\hline Source: U.S. Census & & \\
\hline
\end{tabular}

Using the data in the table, answer the following questions:
1. What is the sample mean? [tex]$\bar{x}=$[/tex] [tex]$\square$[/tex]
2. What is the median? [tex]$\square$[/tex] [tex]$x$[/tex]


Sagot :

To find the sample mean and median of the given population data, follow these steps:

### Step 1: List the Population Data
Here is the population data for the states:

- Alaska: 741,894
- Arizona: 6,931,071
- California: 39,250,017
- Colorado: 5,540,545
- Connecticut: 3,576,452
- Florida: 20,612,439
- Illinois: 12,801,539
- Iowa: 3,134,693
- Kansas: 2,907,289
- Maryland: 6,016,447
- Missouri: 6,093,000
- Montana: 1,042,520
- Nebraska: 1,907,116
- New Mexico: 2,081,015
- North Dakota: 757,952
- Oklahoma: 3,923,561
- South Dakota: 865,454
- Washington: 7,288,000
- West Virginia: 1,834,102
- Wyoming: 585,501

### Step 2: Calculate the Sample Mean
The sample mean is the sum of all population values divided by the number of values.

Given 20 state populations, the values are:

[tex]\[ \text{populations} = [741,894, 6,093,000, 6,931,071, 1,042,520, 39,250,017, 1,907,116, 5,540,545, 2,081,015, 3,576,452, 757,952, 20,612,439, 3,923,561, 12,801,539, 865,454, 3,134,693, 7,288,000, 2,907,289, 1,834,102, 6,016,447, 585,501] \][/tex]

The sample mean formula is:

[tex]\[ \bar{x} = \frac{\sum x_i}{n} \][/tex]

Plugging in the values:

[tex]\[ \bar{x} \approx 6,394,530.35 \][/tex]

### Step 3: Calculate the Median
The median is the middle value of a dataset when it is ordered from smallest to largest. If the number of observations (n) is even, the median is the average of the two middle numbers.

Ordered population data:

[tex]\[ [585501, 741894, 757952, 865454, 1042520, 1834102, 1907116, 2081015, 2907289, 3134693, 3576452, 3923561, 5540545, 6016447, 6093000, 6931071, 7288000, 12801539, 20612439, 39250017] \][/tex]

Number of data values (n) is 20, which is even. Thus, the median is the average of the 10th and 11th values:

[tex]\[ \text{Median} = \frac{3134693 + 3576452}{2} = 3355572.5 \][/tex]

### Answers:

1. Sample mean: [tex]\(\bar{x} = 6,394,530.35\)[/tex]
2. Median: [tex]\( 3,355,572.5 \)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.