For the data set shown 5, 6, 6, 8, 9, 10 which measure is the greatest? O a. Median O b. Range O c. Mean O d. Mode

To determine which measure is the greatest, let's calculate the following measures:

1. **Median**: The median is the middle value when the data is arranged in order. The data set is already arranged:  
   \( 5, 6, 6, 8, 9, 10 \)  
   Since there are 6 numbers, the median is the average of the two middle values (6 and 8):  
   \[
   \text{Median} = \frac{6 + 8}{2} = 7
   \]

2. **Range**: The range is the difference between the highest and lowest values:  
   \[
   \text{Range} = 10 - 5 = 5
   \]

3. **Mean**: The mean is the average of the numbers:  
   \[
   \text{Mean} = \frac{5 + 6 + 6 + 8 + 9 + 10}{6} = \frac{44}{6} \approx 7.33
   \]

4. **Mode**: The mode is the most frequent value. In this case, the number 6 appears twice, so:  
   \[
   \text{Mode} = 6
   \]

### Comparison:
- Median = 7
- Range = 5
- Mean ≈ 7.33
- Mode = 6

Thus, the **mean** (option **c**) is the greatest.

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How is the mean different from the median in skewed distributions?
2. What happens to the range if the highest or lowest value changes?
3. Can a data set have more than one mode?
4. How do outliers affect the mean and median?
5. Why is the median often used in real-world data sets like income?

**Tip**: The mean is sensitive to extreme values (outliers), while the median gives a better central tendency for skewed data sets.

Learn how to calculate and compare the mean, median, range, and mode for the data set 5, 6, 6, 8, 9, 10. This detailed step-by-step guide is suitable for students in Grades 6-8 and covers important concepts in statistics and measures of central tendency.

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