To calculate the mean, median, mode, and range for the data set you've provided, we first need to organize the numbers. The provided data appears to be a sequence of numbers:
6, 5, 8, 10, 4, 6, 3
Step 1: Organize the Numbers
Let's list the numbers in ascending order: 3, 4, 5, 6, 6, 8, 10
Step 2: Calculate the Mean
The mean is calculated by adding all the numbers together and dividing by the total number of values.
\[ \text{Mean} = \frac{3 + 4 + 5 + 6 + 6 + 8 + 10}{7} = \frac{42}{7} = 6 \]
Step 3: Calculate the Median
The median is the middle number in a sorted list. Since there are 7 numbers (an odd count), the median will be the 4th number in the ordered list.
Ordered List: 3, 4, 5, 6, 6, 8, 10
\[ \text{Median} = 6 \]
Step 4: Calculate the Mode
The mode is the number that appears most frequently. In this list:
- 3 appears 1 time
- 4 appears 1 time
- 5 appears 1 time
- 6 appears 2 times
- 8 appears 1 time
- 10 appears 1 time
The mode is 6, as it appears the most frequently.
\[ \text{Mode} = 6 \]
Step 5: Calculate the Range
The range is the difference between the highest and lowest values in the data set.
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 10 - 3 = 7 \]
Summary:
- Mean: 6
- Median: 6
- Mode: 6
- Range: 7
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