Construct a grouped frequency distribution for the following 28 scores using a class width of 4:

64 63 58 46 52 62 47 49 56 47 43 41 45 51
60 62 51 61 50 55 56 53 54 58 48 48 58 46

46-49 = ?

50-53 = ?
53-56 = ?
57-60 = ?
61-64 = ?

I get -3 for all of those??

To construct a grouped frequency distribution with a class width of 4, follow these steps:

1. Determine the range of the data: Find the difference between the highest and lowest values in the given scores.
Range = Highest Score - Lowest Score

In this case, the highest score is 64 and the lowest score is 41.
Range = 64 - 41 = 23

2. Decide on the number of classes. One common way is to use the "square root rule" by taking the square root of the total number of scores.
Number of Classes = √(Total Number of Scores)

In this case, there are 28 scores.
Number of Classes = √28 = 5.29 (Round it up to a whole number)
Number of Classes = 6

3. Calculate the class width by dividing the range by the number of classes (rounded up).
Class Width = Range / Number of Classes

In this case, the range is 23 and there are 6 classes.
Class Width = 23 / 6 ≈ 3.83 (Round it up to a whole number)
Class Width = 4

4. Determine the lower limits for each class. Start with the lowest score and add the class width to get the new lower limit.
Lower Limit = Lowest Score

In this case, the lowest score is 41.
Lower Limit = 41

5. Construct the grouped frequency distribution table:

- Create columns for "Class Interval," "Lower Limit," "Upper Limit," and "Frequency."
- Fill in the first row with the lower limit and upper limit of the first class interval: [41 - 44].
- Calculate and fill in the lower limits and upper limits for the remaining class intervals by adding the class width to the previous upper limit.
- Count the number of scores that fall into each class interval and record the frequencies accordingly.

Here is the completed grouped frequency distribution table:

Class Interval | Lower Limit | Upper Limit | Frequency
-----------------------------------------------------
41 - 44 | 41 | 44 | 2
45 - 48 | 45 | 48 | 5
49 - 52 | 49 | 52 | 5
53 - 56 | 53 | 56 | 7
57 - 60 | 57 | 60 | 4
61 - 64 | 61 | 64 | 5

Note: The upper limits are calculated by adding the class width to the lower limits, and the frequency is the count of scores falling in each class interval.