Here is a data set:
406	286	522	622
435	584	267	351
491	554	327	544
483	490	390	409
543	495	486	436
729	400	426	267
330	568	468	358


Construct a grouped frequency distribution table (GFDT) for this data set. You want 10 classes with a "nice" class width. Your classes should be labeled using interval notation. Each class should contain its lower class limit and each sequential lower class limit should increase by increments of the class width. In that the data appears to be discrete, use a closed-interval to label each class.

To construct a grouped frequency distribution table (GFDT) for this data set, we need to follow these steps:

### Steps:
1. **Determine the range** of the dataTo construct a grouped frequency distribution table (GFDT) for this data set, we need to follow these steps:

### Steps:
1. **Determine the range** of the 
   - The smallest value in the data set: 267
   - The largest value in the data set: 729
   - Range = Largest value - Smallest value = \( 729 - 267 = 462 \)

2. **Select the number of classes**: Given that we want 10 classes.

3. **Determine the class width**: We can calculate the class width using the formula:

   \[
   \text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{462}{10} = 46.2
   \]

   To make the class width a "nice" number, we round up to the nearest whole number, which is 47.

4. **Determine class limits**: Start from the smallest value (267) and add the class width (47) to create each subsequent class. Since the data is discrete, we will use closed intervals.

5. **Tally the frequencies**: Count how many data points fall within each class.

### Grouped Frequency Distribution Table (GFDT):

| Class Interval   | Frequency |
|------------------|-----------|
| \([267, 313]\)   | 4         |
| \([314, 360]\)   | 3         |
| \([361, 407]\)   | 5         |
| \([408, 454]\)   | 7         |
| \([455, 501]\)   | 6         |
| \([502, 548]\)   | 4         |
| \([549, 595]\)   | 2         |
| \([596, 642]\)   | 1         |
| \([643, 689]\)   | 0         |
| \([690, 736]\)   | 1         |

### Explanation:
- **Class width**: We used 47 to ensure that the intervals are wide enough to cover the entire range of the data set.
- **Closed intervals**: Since the data is discrete, each class is written as a closed interval \([a, b]\), meaning that both the lower and upper class limits are included in the interval.
- **Frequencies**: The frequency column represents how many data points fall within each class.

Let me know if you'd like further details on any of the steps!

### Follow-up Questions:
1. How do you determine the midpoint of each class for a more detailed frequency analysis?
2. How can we represent this data using a histogram?
3. What other class widths could we choose for different grouped distributions?
4. What is the cumulative frequency for each class?
5. How would the distribution change if we grouped into 5 classes instead of 10?

### Tip: 
To ensure intervals are meaningful, always round the class width up to avoid missing any data values.

Construct a grouped frequency distribution table (GFDT) for the following data set: 406, 286, 522, 622, 435, 584, 267, 351, 491, 554, 327, 544, 483, 490, 390, 409, 543, 495, 486, 436, 729, 400, 426, 267, 330, 568, 468, 358. Use 10 classes with a 'nice' class width. Label the classes with interval notation, including both the lower and upper class limits in closed intervals.

Learn how to create a grouped frequency distribution table (GFDT) with 10 classes for the data set: 406, 286, 522, 622, 435, 584, 267, and more. This solution involves determining the range, calculating a 'nice' class width, and organizing data into closed-interval classes. Suitable for students in Grades 9-12, with a focus on statistics and data analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation