Question 647628: Here is another I just can't figure out!
Construct a grouped frequency distribution for the following 28 scores using a class width of 4:
37 55 40 52 45 37 57 42 57 54 34 34 38 50 46 57 34 56 34 54 50 48 39 53 52 47 35 56.
Thanks in advance!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First sort the data from least to greatest
Original Data:
37,55,40,52,45,37,57,42,57,54,34,34,38,50,46,57,34,56,34,54,50,48,39,53,52,47,35,56
Sorted Data
34,34,34,34,35,37,37,38,39,40,42,45,46,47,48,50,50,52,52,53,54,54,55,56,56,57,57,57
Notice how the smallest number is 34. The first class will start with the smallest number (34) and it will be 4 units wide. So the first class will end with 34+4-1 = 37.
Note: There are 4 numbers from 34 to 37 and they are: 34, 35, 36, 37. This is why we don't end up on 38 (we would have gone too high)
This means that the first class will span from 34 (left boundary) to 37 (right boundary)
The second class will start with 37+1 = 38. It will not start with 37 because 37 is in the first class. So the second class will end with 38+4-1 = 41
The second class will span from 38 (left boundary) to 41 (right boundary)
Repeat this to generate the rest of the classes until you reach or pass 57, which is the max value.
You'll get the following classes
34-37
38-41
42-45
46-49
50-53
54-57
Notice how each particular class has exactly 4 whole numbers in it (eg: 42-45 has the numbers 42, 43, 44, 45 in it).
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Now you go through each number in the sorted data set and you assign it to the proper class. For instance, the first number 34 (in the sorted data set) belongs in the first class. This is because the first class of numbers ranges from 34 to 37 (inclusive)
Once you have found all of the numbers that belong in the first class, you count them up. The following numbers belong in the first class: 34,34,34,34,35,37,37
There are 7 of these numbers. So the frequency count for the first class is 7.
Repeat this to find the frequency count for the other classes.
So this boils down to assigning the numbers to the right groups, then counting the frequencies. Doing this will give us the table
| Interval |
Data |
Frequency |
| 34-37 |
34,34,34,34,35,37,37 |
7 |
| 38-41 |
38,39,40 |
3 |
| 42-45 |
42,45 |
2 |
| 46-49 |
46,47,48 |
3 |
| 50-53 |
50,50,52,52,53 |
5 |
| 54-57 |
54,54,55,56,56,57,57,57 |
8 |
Now erase the middle column since we really only care about the classes and the frequencies
This will give you the given grouped frequency table below. Which is the final answer.
| Class |
Frequency |
| 34-37 |
7 |
| 38-41 |
3 |
| 42-45 |
2 |
| 46-49 |
3 |
| 50-53 |
5 |
| 54-57 |
8 |
Note: if you need a visual aid and you need a graph, then here's the histogram of the grouped frequency distribution
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