Question 1171253: Construct a grouped frequency distribution table below of the scores of 40 students on their Prelim Exam.
45 49 50 53 26 23 30 30 45 46
48 55 38 57 23 35 45 48 50 24
48 56 39 42 41 29 59 21 54 53
48 49 48 41 43 37 36 43 46 49
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! <\ctrl75>Okay, let's construct a grouped frequency distribution table for the given scores. Here's a step-by-step approach:
**1. Find the Range**
* Identify the highest score: 59
* Identify the lowest score: 21
* Calculate the range: Highest score - Lowest score = 59 - 21 = 38
**2. Determine the Number of Classes**
* There's no hard-and-fast rule, but a common guideline is to use between 5 and 15 classes. Let's aim for around 6 classes in this case.
**3. Calculate the Class Width**
* Class Width = Range / Number of Classes
* Class Width = 38 / 6 = 6.33
* Since we need whole numbers for scores, we'll round the class width up to 7.
**4. Determine the Class Limits**
* Start with the lowest score (21) as the lower limit of the first class.
* Add the class width (7) to find the lower limit of the next class, and so on.
* The upper limit of each class is one less than the lower limit of the next class.
Here's how we'll set up the classes:
* **Class 1:** 21 - 27
* **Class 2:** 28 - 34
* **Class 3:** 35 - 41
* **Class 4:** 42 - 48
* **Class 5:** 49 - 55
* **Class 6:** 56 - 62
**5. Tally the Frequencies**
* Go through the list of scores and tally how many fall into each class.
Here's how the tallying would work:
* **Class 1 (21-27):** 26, 23, 23, 24, 21, 29 = 6
* **Class 2 (28-34):** 30, 30, 35 = 3
* **Class 3 (35-41):** 38, 39, 42, 41, 41, 37, 36 = 7
* **Class 4 (42-48):** 45, 46, 48, 45, 48, 48, 48, 43, 43, 46 = 10
* **Class 5 (49-55):** 49, 50, 53, 55, 50, 54, 53, 49, 49 = 9
* **Class 6 (56-62):** 57, 59, 56 = 3
**6. Create the Grouped Frequency Distribution Table**
Here's the final grouped frequency distribution table:
| Class Interval | Frequency |
| :-------------: | :-------: |
| 21 - 27 | 6 |
| 28 - 34 | 3 |
| 35 - 41 | 7 |
| 42 - 48 | 10 |
| 49 - 55 | 9 |
| 56 - 62 | 5 |
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