Of course! Let's go through the calculations step-by-step with the given data set: 3, 5, 7, 5, 11, 5, 1, and 12.
Step 1: Determine the Range
The range is the difference between the maximum and minimum values in the data set.
- The maximum value in the data set is 12.
- The minimum value in the data set is 1.
Thus, the range is calculated as:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 12 - 1 = 11 \][/tex]
Step 2: Determine the Median
The median is the middle value of a data set when it is ordered from least to greatest. If the number of data points is odd, the median is the middle number. If even, the median is the average of the two central numbers.
First, let's sort the data set in ascending order:
[tex]\[ 1, 3, 5, 5, 5, 7, 11, 12 \][/tex]
Since there are 8 numbers (an even count), the median will be the average of the 4th and 5th numbers in this ordered list.
- The 4th number is 5.
- The 5th number is 5.
Thus, the median is:
[tex]\[ \text{Median} = \frac{5 + 5}{2} = \frac{10}{2} = 5.0 \][/tex]
Step 3: Calculate the Difference between the Range and the Median
Now, we subtract the median from the range.
[tex]\[ \text{Difference} = \text{Range} - \text{Median} = 11 - 5.0 = 6.0 \][/tex]
So, the range is 11, the median is 5.0, and the difference between the range and the median is 6.0.
