338

337

322

321

368

332

322

339

355

327

321

352

333

352

354

331

347

301

334

368

332

396

349

364

314

372

336

317


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 contains its lower class limit, and the lower class limits should all be multiples of the class width. In that the data appears to be discrete, use a closed-interval to label each class.



Data rangeFrequency

To construct a grouped frequency distribution table (GFDT) for this data set with 10 classes, we'll follow these steps:

### Step 1: Determine the Range of the Data Set
First, we calculate the range:

- **Minimum Value:** \( \min = 301 \)
- **Maximum Value:** \( \max = 396 \)

\[ \text{Range} = \max - \min = 396 - 301 = 95 \]

### Step 2: Choose a Suitable Class Width
To have approximately 10 classes, we divide the range by the desired number of classes:

\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{95}{10} = 9.5
\]

Since 9.5 is not a convenient class width, we'll round it up to the next "nice" number. The closest nice class width would be **10**.

### Step 3: Determine the Class Limits
Given a class width of 10, we start from the minimum value (or a convenient lower limit close to it that is a multiple of 10) and create intervals of width 10.

### Step 4: Create the Grouped Frequency Distribution Table
The classes will be:

- [300, 309]
- [310, 319]
- [320, 329]
- [330, 339]
- [340, 349]
- [350, 359]
- [360, 369]
- [370, 379]
- [380, 389]
- [390, 399]

Now, we count the frequency of data points falling into each class.

### Grouped Frequency Distribution Table

| Class Interval | Frequency |
|----------------|-----------|
| [300, 309]     | 1         |
| [310, 319]     | 3         |
| [320, 329]     | 6         |
| [330, 339]     | 8         |
| [340, 349]     | 4         |
| [350, 359]     | 5         |
| [360, 369]     | 3         |
| [370, 379]     | 2         |
| [380, 389]     | 0         |
| [390, 399]     | 1         |

### Summary
- **Class Width:** 10
- **Classes:** [300, 309], [310, 319], ..., [390, 399]
- **Frequencies:** As shown in the table above

Would you like any further details on this, or do you have any other questions?

Here are some questions related to this topic:

1. How can you create a histogram based on this frequency distribution?
2. How does the choice of class width affect the appearance of the GFDT?
3. What are some alternative methods for determining class width?
4. How do you handle outliers when constructing a GFDT?
5. Can you explain how cumulative frequency is calculated from the GFDT?

**Tip:** When constructing a GFDT, ensure that each data point falls into one and only one class interval, and that the intervals are mutually exclusive.

Learn how to construct a grouped frequency distribution table (GFDT) with 10 classes for a given dataset. This problem covers statistical concepts including determining class width, calculating frequencies, and organizing data into intervals. Suitable for high school students studying statistics.

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