To find the mean and median of the given data set $48, 42, 30, 10, 5$:

1. Mean:

The mean is the average of the numbers in the data set.

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

Sum of the numbers:
$48 + 42 + 30 + 10 + 5 = 135$

Number of numbers:
$5$

So,
$\text{Mean} = \frac{135}{5} = 27$

2. Median:

The median is the middle value when the numbers are arranged in ascending order. First, arrange the numbers:

$5, 10, 30, 42, 48$

Since there are 5 numbers (an odd number of values), the median is the middle value, which is the 3rd value in the list.

So,
$\text{Median} = 30$

Final Answer:

• Mean = 27
• Median = 30

Would you like further details or have any questions?

Relative Questions:

1. What happens to the mean and median if we add another number to the data set?
2. How would the mean and median change if one of the numbers is doubled?
3. What is the difference between the mean and median in a data set with an even number of values?
4. How are the mean and median affected by outliers in the data set?
5. What is the relationship between mean and median in a symmetric data distribution?

Tip:

The mean is sensitive to extreme values (outliers), while the median is a better measure of central tendency when outliers are present.