Answer :
To find the mean, median, and mode for the given data set, we can follow these steps:
### Data set 1: {17, 11, 8, 15, 28, 20, 10, 16}
#### Mean:
1. Add all the numbers in the data set.
2. Divide the sum by the total number of values in the data set.
Let's calculate:
Sum = 17 + 11 + 8 + 15 + 28 + 20 + 10 + 16 = 125
Number of values (n) = 8
Mean = Sum / n = 125 / 8 = 15.625
So, the mean is 15.625.
#### Median:
1. Arrange the data in ascending order.
2. If there is an odd number of values, the median is the value in the middle. If there is an even number of values, the median is the average of the two middle numbers.
Let's arrange and calculate:
Arranged data set = {8, 10, 11, 15, 16, 17, 20, 28}
Since there are 8 numbers (even), we take the average of the 4th and 5th numbers in the arranged set:
(15 + 16) / 2 = 31 / 2 = 15.5
So, the median is 15.5.
#### Mode:
1. Identify the number that appears most frequently in the data set.
Let's identify:
In the data set {17, 11, 8, 15, 28, 20, 10, 16}, no number repeats, so there is no mode. It is a "no-mode" data set because each number appears only once.
### Summary:
- Mean of data set 1 = 15.625
- Median of data set 1 = 15.5
- Mode of data set 1 = No mode
Since the second data set has not been provided, we can only work with the first data set. If the second data set becomes available, we can apply the same steps as above to find the mean, median, and mode for that set.
### Data set 1: {17, 11, 8, 15, 28, 20, 10, 16}
#### Mean:
1. Add all the numbers in the data set.
2. Divide the sum by the total number of values in the data set.
Let's calculate:
Sum = 17 + 11 + 8 + 15 + 28 + 20 + 10 + 16 = 125
Number of values (n) = 8
Mean = Sum / n = 125 / 8 = 15.625
So, the mean is 15.625.
#### Median:
1. Arrange the data in ascending order.
2. If there is an odd number of values, the median is the value in the middle. If there is an even number of values, the median is the average of the two middle numbers.
Let's arrange and calculate:
Arranged data set = {8, 10, 11, 15, 16, 17, 20, 28}
Since there are 8 numbers (even), we take the average of the 4th and 5th numbers in the arranged set:
(15 + 16) / 2 = 31 / 2 = 15.5
So, the median is 15.5.
#### Mode:
1. Identify the number that appears most frequently in the data set.
Let's identify:
In the data set {17, 11, 8, 15, 28, 20, 10, 16}, no number repeats, so there is no mode. It is a "no-mode" data set because each number appears only once.
### Summary:
- Mean of data set 1 = 15.625
- Median of data set 1 = 15.5
- Mode of data set 1 = No mode
Since the second data set has not been provided, we can only work with the first data set. If the second data set becomes available, we can apply the same steps as above to find the mean, median, and mode for that set.
