Let's solve the problem by following the steps you provided. I'll extract the data from the image and then construct the frequency distribution, calculate the mean, median, and mode.

Step 1: Extract the Data

The weekly duty hours of the nursing students as provided in the image are:

Data: 28, 32, 35, 30, 38, 40, 30, 38, 40, 32
48, 39, 33, 37, 38, 36, 40, 36, 32, 40
44, 37, 35, 38, 33, 39, 41, 35, 39, 35
41, 37, 36, 34, 35, 37, 34, 33, 32, 34
32, 34, 31, 33, 31, 35, 41, 34, 40

Step 2: Estimate Number of Classes (k)

The formula for estimating the number of classes $k$ is:

$k = 1 + 3.322 \log n$

Where $n$ is the number of observations.

Let's calculate this.

Step 3: Determine the Range (r)

The range $r$ is calculated as:

$r = \text{Highest Value} - \text{Lowest Value}$

Step 4: Obtain the Class Size (c)

The class size $c$ can be calculated as:

$c = \frac{r}{k}$

Step 5: Set the Lower and Upper Limits for the Classes

Using the class size, set the lowest value as the first lower limit, and calculate the upper limit by adding the class size. Repeat the process until all data points are covered.

Now, I'll perform these calculations for you.### Results:

1. Estimated Number of Classes (k): 6.61 (rounded to 7 classes)
2. Range (r): 20 (highest value 48 - lowest value 28)
3. Class Size (c): 4

Frequency Distribution:

Next, we can calculate the mean, median, and mode if needed. Let me know if you'd like to proceed with that.

Relative Questions:

1. How do you interpret the class intervals in this distribution?
2. What are the implications of having most data in one or two classes?
3. Why is class size important in frequency distribution?
4. How could we use this data to create a histogram?
5. How do outliers affect the frequency distribution?

Tip:

When constructing frequency distributions, always ensure your class intervals are mutually exclusive to avoid double-counting any data point.