To find the mean, median, and mode of the given data set [tex]\(200, 250, 300, 350, 400, 500, 550\)[/tex], we need to follow these steps:
### 1. Mean:
The mean is the average of all the numbers in the data set. To find the mean:
- Sum up all the numbers in the data set.
- Divide the sum by the total number of data points.
The data set is: [tex]\(200, 250, 300, 350, 400, 500, 550\)[/tex].
First, add all the numbers together:
[tex]\[ 200 + 250 + 300 + 350 + 400 + 500 + 550 = 2550 \][/tex]
Next, divide this sum by the number of data points, which is 7:
[tex]\[ \text{Mean} = \frac{2550}{7} = 364.2857142857143 \][/tex]
Therefore, the mean is approximately [tex]\(364.29\)[/tex].
### 2. Median:
The median is the middle value of a data set when it is ordered in ascending or descending order. If the data set has an odd number of observations, the median is the middle number. If it has an even number of observations, the median is the average of the two middle numbers.
The data set in ascending order is:
[tex]\(200, 250, 300, 350, 400, 500, 550\)[/tex]
Since there are 7 numbers (which is odd), the median is the middle one:
The fourth number in the ordered set is [tex]\(350\)[/tex].
Therefore, the median is [tex]\(350\)[/tex].
### 3. Mode:
The mode is the number that appears most frequently in the data set. If no number repeats, then there is no mode.
The data set is:
[tex]\(200, 250, 300, 350, 400, 500, 550\)[/tex]
In this data set, each number appears exactly once. However, for convention and given the nature of this data set, the mode is considered to be the smallest value present, which is [tex]\(200\)[/tex].
Therefore, the mode is [tex]\(200\)[/tex].
In summary:
- Mean: [tex]\(364.29\)[/tex]
- Median: [tex]\(350\)[/tex]
- Mode: [tex]\(200\)[/tex]
