Given the data set: $49, 34, 12, 10, 53, 20, 65, 34, 90, 100, 33$

(a) Range

The range of a data set is the difference between the maximum and minimum values.

• Maximum value = $100$
• Minimum value = $10$

Range = Maximum - Minimum
Range = $100 - 10 = 90$

(b) Median

To find the median, first, we need to arrange the data in ascending order: $10, 12, 20, 33, 34, 34, 49, 53, 65, 90, 100$

The median is the middle value of an ordered data set. Since this data set has $11$ numbers (an odd number of values), the median is the $6$th value: $10, 12, 20, 33, 34, \textbf{34}, 49, 53, 65, 90, 100$

So, the median is $34$.

Summary

• Range: $90$
• Median: $34$

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What is the mean of this data set?
2. How would the median change if another number is added to the data set?
3. What is the mode of this data set?
4. How is the range affected by outliers in a data set?
5. What is the interquartile range (IQR) for this data set?

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