Given this set of data: 49, 34, 12, 10, 53, 20, 65, 34, 90, 100, 33. (a) Determine the range.  (b) What is the median?

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.

Given this set of 49, 34, 12, 10, 53, 20, 65, 34, 90, 100, 33. (a) Determine the range. (b) What is the median?

Learn how to determine the range and median of the data set 49, 34, 12, 10, 53, 20, 65, 34, 90, 100, 33. This problem covers key statistical concepts such as the range and median, suitable for students in Grades 6-8.

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