https://file.aiquickdraw.com/mathbot/file/17281061541021twq89iq.jpg

Let's analyze the data set and solve the problem step-by-step.

### Data Set:
The data set is as follows:

\[
\begin{matrix}
575 & 519 & 510 & 430 \\
464 & 510 & 521 & 446 \\
486 & 517 & 488 & 543 \\
470 & 542 & 540 & 488 \\
546 & 527 & 618 & 534 \\
491 & 514 & 551 & 578 \\
547 & 526 & 575 & 464 \\
\end{matrix}
\]

### Steps to Answer Each Part:
(a) **Maximum value** of the data set:
- The maximum value is the largest number present in the entire data set.

(b) **Minimum value** of the data set:
- The minimum value is the smallest number present in the entire data set.

(c) **Range** of the data set:
- The range is calculated by subtracting the minimum value from the maximum value:
  
  \[
  \text{Range} = \text{Max} - \text{Min}
  \]

(d) **Class width**:
- The formula for class width is:

  \[
  \text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}
  \]

For 6 classes, we plug in the values obtained above.

### Calculations:
1. **Maximum Value**:
- The highest value in the data set is \(618\).

2. **Minimum Value**:
- The lowest value in the data set is \(430\).

3. **Range**:
- \[
\text{Range} = 618 - 430 = 188
\]

4. **Class Width** (for 6 classes):
- \[
\text{Class Width} = \frac{188}{6} \approx 31.33
\]
Rounding up, the class width will be \(32\).

### Final Answers:
- **Maximum**: 618
- **Minimum**: 430
- **Range**: 188
- **Class Width**: 32

Would you like more details on any of the calculations? 

Here are 5 related questions to deepen your understanding:
1. How would the class width change if the number of classes were 8 instead of 6?
2. What is the mean (average) value of the given data set?
3. How can you determine the mode of this data set?
4. How would you construct a frequency distribution table with the given class width?
5. What is the standard deviation of this data set?

**Tip:** When calculating class width, always round up to ensure all data points are covered within the defined classes.

Given a data set, determine the maximum, minimum, range, and class width for 6 classes.

Learn how to calculate the maximum, minimum, range, and class width from a given data set. This step-by-step guide covers the core concepts of data analysis and frequency tables, using formulas such as Range = Max - Min and Class Width = Range / Number of Classes. Suitable for students in Grades 9-11.

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