To calculate the mean, median, mode, and range for the dataset you've provided (108, 101, 108, 9), let's first arrange the data in ascending order.
Step 1: Arrange the data
The data in ascending order is: 9, 101, 108, 108
Step 2: Calculate Mean
To find the mean, sum all the numbers and then divide by the total count.
\[ \text{Mean} = \frac{(9 + 101 + 108 + 108)}{4} = \frac{326}{4} = 81.5 \]
Step 3: Calculate Median
The median is the middle value of a dataset when it is ordered. Since there is an even number of values (4), the median will be the average of the two middle numbers.
The two middle values are 101 and 108.
\[ \text{Median} = \frac{(101 + 108)}{2} = \frac{209}{2} = 104.5 \]
Step 4: Calculate Mode
The mode is the value that appears most frequently. In this case, 108 appears twice while other values appear once.
\[ \text{Mode} = 108 \]
Step 5: Calculate Range
The range is the difference between the highest and lowest values.
\[ \text{Range} = 108 - 9 = 99 \]
Summary of Results:
- Mean: 81.5
- Median: 104.5
- Mode: 108
- Range: 99
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