830, 835, 890, 810, 835, 836, 869, 845, 898, 890,820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.
Draw a frequency distribution table for the given data.

To create a frequency distribution table, we first need to organize the data into classes (intervals) and then count the frequency of values falling into each class. Here’s how to do it:

### Step 1: Find the Range
The range is the difference between the maximum and minimum values in the data set.

- **Maximum value:** 898
- **Minimum value:** 804

**Range:** \( 898 - 804 = 94 \)

### Step 2: Determine the Number of Classes
The number of classes can be determined by using Sturges' formula:

\[
k = 1 + 3.322 \log n
\]

where \( n \) is the number of data points.

Here, \( n = 30 \).

\[
k = 1 + 3.322 \log 30 \approx 6
\]

So, let's use 6 classes.

### Step 3: Determine the Class Width
The class width \( w \) is calculated by dividing the range by the number of classes:

\[
w = \frac{\text{Range}}{\text{Number of Classes}} = \frac{94}{6} \approx 15.67 \approx 16
\]

### Step 4: Create the Class Intervals
We start with the minimum value and create class intervals with the class width.

1. \( 804 - 819 \)
2. \( 820 - 835 \)
3. \( 836 - 851 \)
4. \( 852 - 867 \)
5. \( 868 - 883 \)
6. \( 884 - 899 \)

### Step 5: Tally the Frequencies
Now we tally the frequency of data points in each class interval.

| Class Interval | Frequency |
|----------------|-----------|
| 804 - 819      | 6         |
| 820 - 835      | 9         |
| 836 - 851      | 7         |
| 852 - 867      | 3         |
| 868 - 883      | 3         |
| 884 - 899      | 2         |

This is your frequency distribution table.

### Do you want more details or have any questions?
#### Related Questions:
1. How do we calculate the mean from the frequency distribution table?
2. How does changing the number of classes affect the frequency distribution?
3. What is a histogram, and how can it be used to visualize this data?
4. How would the frequency distribution table look if we used 7 classes instead of 6?
5. Can we use different class intervals, and how does it affect the results?

**Tip:** When choosing the number of classes in a frequency distribution, it’s often helpful to experiment with different intervals to see which gives the most meaningful insights.

Learn how to create a frequency distribution table from a dataset with detailed steps and examples. This problem involves using Sturges' formula to determine the number of classes and organizing data into intervals. Suitable for advanced high school students studying statistics.

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