Here is a data set: Construct a grouped frequency distribution table (GFDT) for this data set. You want 10 classes with a “nice” class width. Your classes should be labeled using interval notation. Each class contains its lower class limit, and the lower class limits should all be multiples of the class width. In that the data appears to be discrete, use a closed-interval to label each class.
The Correct Answer and Explanation is :
I will first process the dataset from the provided link, construct a grouped frequency distribution table (GFDT) with 10 classes, and then generate an image representation of the table. Let me begin.
Constructing a Grouped Frequency Distribution Table (GFDT) involves organizing raw data into specified intervals, making it easier to analyze and interpret. Here’s how to create a GFDT with 10 classes, each having a suitable class width, and labeled using interval notation:
1. Determine the Range of the Data:
- Identify the Minimum and Maximum Values: Subtract the smallest data point from the largest to find the range.
2. Calculate the Class Width:
- Class Width Formula: Divide the range by the desired number of classes (in this case, 10) and round up to a convenient number to ensure all data points are included.
3. Establish Class Intervals:
- Starting Point: Begin with the smallest data point or a convenient value below it.
- Construct Intervals: Add the class width to the starting point to create subsequent intervals, ensuring each class is mutually exclusive and exhaustive.
4. Tally the Frequencies:
- Count Data Points: For each class interval, count the number of data points that fall within the range.
5. Compile the GFDT:
- Table Structure: Create a table with columns for Class Interval, Tally, and Frequency.
- Interval Notation: Use closed intervals [a, b] to denote that both endpoints are included in each class.
Example:
Assuming a dataset with a minimum value of 4 and a maximum value of 97:
- Range: 97 – 4 = 93
- Class Width: 93 ÷ 10 ≈ 9.3, rounded up to 10 for simplicity.
- Class Intervals:
- [0, 9]
- [10, 19]
- [20, 29]
- [30, 39]
- [40, 49]
- [50, 59]
- [60, 69]
- [70, 79]
- [80, 89]
- [90, 99]
- Frequency Distribution:
| Class Interval | Tally | Frequency |
|---|---|---|
| [0, 9] | ||
| [10, 19] | ||
| [20, 29] | ||
| [30, 39] | ||
| [40, 49] | ||
| [50, 59] | ||
| [60, 69] | ||
| [70, 79] | ||
| [80, 89] | ||
| [90, 99] |
Explanation:
- Class Width Selection: Choosing a class width of 10 simplifies the intervals and ensures they are easy to interpret.
- Interval Notation: Using closed intervals [a, b] indicates that both endpoints are included, which is appropriate for discrete data.
- Tally Marks: These provide a quick visual representation of the frequency of data points within each interval.
- Frequency Count: This column quantifies the number of data points in each class, facilitating further statistical analysis.
By organizing data into a GFDT, patterns and trends become more apparent, aiding in data interpretation and decision-making.
For a visual demonstration of constructing a grouped frequency table, you may find this video helpful: