Respuesta :
Answer:
Step-by-step explanation:
To create a set of data with the given properties, we can start by setting the median, mean, mode, and range to the desired values and then adjust the remaining values to meet these criteria.
Given:
- Median = 6
- Mean = 9
- Mode = 4
- Range = 16
Let's construct the dataset:
1. Set the median:
We'll have three values less than 6 and three values greater than 6 to keep the median at 6.
2. Set the mode:
The mode is 4, so at least one value in the dataset must be 4.
3. Set the mean:
To find the sum of all values, we can multiply the mean by the number of values (6): \( 9 \times 6 = 54 \).
4. Set the range:
The range is 16, so the difference between the maximum and minimum values should be 16.
Now, let's construct the dataset:
Let's have the first three values as 4 (to satisfy the mode and keep the mean closer to the mode) and the last three values as 12 (to satisfy the median and increase the mean).
\[ \{ 4, 4, 4, 12, 12, 12 \} \]
Now, let's check if this dataset satisfies all the given criteria:
- Median: The median is the middle value when the data is ordered. In this case, the median is 6, which is satisfied because it's the middle value of the dataset.
- Mean: The mean is calculated by summing all values and dividing by the number of values. \( (4 + 4 + 4 + 12 + 12 + 12) / 6 = 9 \), which satisfies the mean of 9.
- Mode: The mode is the value that appears most frequently. In this case, the mode is 4, which is satisfied because it's the most frequent value in the dataset.
- Range: The range is the difference between the maximum and minimum values. In this case, the range is \( 12 - 4 = 8 \), which doesn't satisfy the given range of 16.
So, this dataset doesn't fully satisfy the given criteria. We need to adjust it to meet the desired range of 16.
Let's increase the last three values to 16:
\[ \{ 4, 4, 4, 16, 16, 16 \} \]
Now, let's check if this dataset satisfies all the given criteria:
- Median: 6 (satisfied)
- Mean: 9 (satisfied)
- Mode: 4 (satisfied)
- Range: \( 16 - 4 = 12 \) (not satisfied)
The range is not yet satisfied. We need to adjust the dataset further.
Let's decrease the first three values to 0:
\[ \{ 0, 0, 0, 16, 16, 16 \} \]
Now, let's check if this dataset satisfies all the given criteria:
- Median: 6 (satisfied)
- Mean: 9 (satisfied)
- Mode: 4 (satisfied)
- Range: \( 16 - 0 = 16 \) (satisfied)
Now, all the given criteria are satisfied. So, the dataset is:
\[ \{ 0, 0, 0, 16, 16, 16 \} \]
