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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]
### 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]
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