Construct a frequency distribution with five classes for the following data:
82, 76, 88, 77, 90, 71, 66, 120, 111, 108, 93, 116, 74.
There are 13 data points, so how do I divide them into five classes of equal size?
Range is 66-120 = 54
To cover that range, 54/5 = almost 11.
To divide the data into five classes of equal size, you need to first determine the range of the data. The range is the difference between the largest and the smallest values in the dataset.
Let's sort the data in ascending order:
66, 71, 74, 76, 77, 82, 88, 90, 93, 108, 111, 116, 120.
The range of this dataset is 120 - 66 = 54.
To determine the class width, divide the range by the number of desired classes. In this case, you want five classes, so divide 54 by 5: 54 / 5 = 10.8 (rounded to 11 for simplicity).
Now that you have the class width, you can create the classes:
Class 1: (66 - 76)
Class 2: (77 - 87)
Class 3: (88 - 98)
Class 4: (99 - 109)
Class 5: (110 - 120)
Finally, you can count how many data points fall into each class:
Class 1: 1 (66)
Class 2: 3 (71, 74, 76)
Class 3: 3 (77, 82, 88)
Class 4: 4 (90, 93, 108, 111)
Class 5: 2 (116, 120)
This gives you the frequency distribution with five classes for the given data.