To construct the grouped frequency distribution table (GFDT) for the given data set, we will follow these steps:

Steps:

1. Find the Range of the Data:

   • Identify the minimum and maximum values.
   • Compute the range = $\text{Max} - \text{Min}$.

2. Determine the Class Width:

   • Divide the range by the desired number of classes (10 in this case).
   • Round up the result to a "nice" number (convenient multiple).

3. Create Class Intervals:

   • Start from the minimum value or a lower convenient value.
   • Create 10 intervals, each with the calculated class width.

4. Count the Frequency for Each Class:

   • Count how many data points fall within each class interval.

Let me extract the data and calculate the GFDT for you. numpy as np

Given dataset

data = [ 559, 624, 526, 507, 592, 508, 831, 654, 559, 682, 519, 634, 541, 560, 389, 570, 418, 507, 389, 487, 540, 679, 619, 507, 485, 389, 681, 629 ]

Step 1: Find the range of the data

min_value = min(data) max_value = max(data) data_range = max_value - min_value

Step 2: Determine class width

num_classes = 10 class_width = np.ceil(data_range / num_classes)

Step 3: Create class intervals

lower_limit = np.floor(min_value) upper_limit = lower_limit + class_width * num_classes

class_intervals = [(lower_limit + i * class_width, lower_limit + (i + 1) * class_width - 1) for i in range(num_classes)]

Step 4: Count frequencies for each class

frequencies = [sum(lower <= x <= upper for x in data) for lower, upper in class_intervals]

class_intervals, frequenciesHere is the grouped frequency distribution table (GFDT) based on the given data:

Explanation:

1. Class Intervals:

   • The range of each interval was determined using a class width of $\lceil (831 - 389) / 10 \rceil = 45$.
   • Each interval is created as [lower limit, upper limit], ensuring all values are included without overlap.

2. Frequencies:

   • For each interval, the frequency was counted based on the number of data points falling within the range.

Would you like further clarification or a graph of this distribution?

Here are 5 related questions:

1. How can the GFDT be used to create a histogram?
2. What happens if we increase or decrease the number of classes?
3. How does the choice of class width affect the frequency distribution?
4. Can this data distribution be analyzed for skewness or symmetry?
5. What are the benefits of using grouped data versus raw data?

Tip: When constructing a GFDT, always ensure the intervals do not overlap and cover the entire data range.