A recent statistics exam yielded the following 25 scores. Construct a grouped frequency
distribution with the class limits shown below.
64 84 71 59 67
58 88 68 70 94
90 81 43 77 86
72 81 79 98 52
72 72 47 81 96
To construct a grouped frequency distribution, follow these steps:
Step 1: Find the minimum and maximum values in the dataset:
Minimum value: 43
Maximum value: 98
Step 2: Determine the range:
Range = Maximum value - Minimum value
Range = 98 - 43 = 55
Step 3: Decide on the number of intervals (classes):
Generally, it is recommended to have between 5 and 15 classes. Let's choose 7 classes for this example.
Step 4: Calculate the class width:
Class width = Range / Number of classes
Class width = 55 / 7 ≈ 7.86 (round it up to 8 for easier calculations)
Step 5: Determine the class limits:
Start with the minimum value and add the class width successively to define the upper limit of each class.
Class 1: 43 - 50
Class 2: 51 - 58
Class 3: 59 - 66
Class 4: 67 - 74
Class 5: 75 - 82
Class 6: 83 - 90
Class 7: 91 - 98
Step 6: Count the number of scores falling into each class:
Count how many scores fall into each class and record them in a frequency table.
Class 1 (43 - 50): 2 scores
Class 2 (51 - 58): 2 scores
Class 3 (59 - 66): 4 scores
Class 4 (67 - 74): 6 scores
Class 5 (75 - 82): 7 scores
Class 6 (83 - 90): 4 scores
Class 7 (91 - 98): 0 scores
Here's the grouped frequency distribution table:
+---------------+-------+
| Class Limits | Count |
+---------------+-------+
| 43 - 50 | 2 |
| 51 - 58 | 2 |
| 59 - 66 | 4 |
| 67 - 74 | 6 |
| 75 - 82 | 7 |
| 83 - 90 | 4 |
| 91 - 98 | 0 |
+---------------+-------+
Each row represents a class. The "Class Limits" column shows the range of values included in each class, and the "Count" column shows the number of scores that fall within each class.