To create a frequency distribution and fill in the columns based on the data provided, we need to follow these steps:

Step 1: Organize the Data

First, let's sort the data in ascending order:

{6, 12, 16, 17, 19, 22, 24, 26, 27, 29, 31, 33, 39, 40, 49, 50}

Step 2: Define the Classes

To create a frequency distribution, we need to define class intervals (or bins). Since the data spans from 6 to 50, let's consider the following intervals:

• Class Interval 1: 6 - 13
• Class Interval 2: 14 - 21
• Class Interval 3: 22 - 29
• Class Interval 4: 30 - 37
• Class Interval 5: 38 - 45
• Class Interval 6: 46 - 53

Step 3: Count the Frequency in Each Class Interval

Now, let's count the frequency of data points in each interval:

1. 6 - 13: 6, 12 → 2 data points
2. 14 - 21: 17, 19 → 2 data points
3. 22 - 29: 22, 24, 26, 27, 29 → 5 data points
4. 30 - 37: 31, 33 → 2 data points
5. 38 - 45: 39, 40 → 2 data points
6. 46 - 53: 49, 50 → 2 data points

Step 4: Fill in the Table with Shading Indication

Given the frequencies, we can now shade (x) or leave unshaded (0) the columns based on the frequency for each interval.

• Class Interval 1: 6 - 13 → Frequency = 2 → (xx000)
• Class Interval 2: 14 - 21 → Frequency = 2 → (xx000)
• Class Interval 3: 22 - 29 → Frequency = 5 → (xxxxx)
• Class Interval 4: 30 - 37 → Frequency = 2 → (xx000)
• Class Interval 5: 38 - 45 → Frequency = 2 → (xx000)
• Class Interval 6: 46 - 53 → Frequency = 2 → (xx000)

Shading Representation (x = Shaded, 0 = Unshaded)

Here's how the shading (x) or unshading (0) would look:

6 - 13  → xx000
14 - 21 → xx000
22 - 29 → xxxxx
30 - 37 → xx000
38 - 45 → xx000
46 - 53 → xx000

Would you like to dive into the details of frequency distributions, or do you have any specific questions?

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Relative Questions:

1. How do you determine the number of class intervals to use in a frequency distribution?
2. What are the advantages of using a frequency distribution to analyze data?
3. How can you create a histogram based on this frequency distribution?
4. What is the significance of the shape of the frequency distribution?
5. How does the choice of class intervals affect the interpretation of the data?

Tip: When creating class intervals, ensure that they are mutually exclusive and collectively exhaustive, meaning every data point should fall into exactly one interval without overlap.