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.