Let's find the mean and median of the given data set:

Given Data Set:

$35, 6, 21, 42, 8, 47$

---

1. Mean:

The mean is the average of the numbers. To calculate it, follow these steps:

$\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Number of values}}$

• Sum of the numbers: $35 + 6 + 21 + 42 + 8 + 47 = 159$

• Number of values: 6

So, $\text{Mean} = \frac{159}{6} \approx 26.5$

---

2. Median:

The median is the middle value when the numbers are arranged in order. For an even number of values, the median is the average of the two middle numbers.

• Arrange the numbers in ascending order: $6, 8, 21, 35, 42, 47$

• Since there are 6 values (even number), the median is the average of the 3rd and 4th numbers: $\text{Median} = \frac{21 + 35}{2} = \frac{56}{2} = 28$

---

Final Results:

• Mean: 26.5
• Median: 28

Would you like any additional details or have any further questions?

Here are some related questions:

1. What happens to the mean and median if a new number is added to the dataset?
2. How do the mean and median differ for a larger dataset?
3. Can you think of a scenario where the median is more useful than the mean?
4. What is the mode, and how would it apply to this dataset?
5. How would an outlier affect the mean and median?

Tip: The median is less affected by outliers than the mean, making it a better measure of central tendency in skewed distributions.