Use 6-point bins (94 to 99, to 88 to 93, etc.) to make a frequency table for the set of exam scores shown below. Include columns for relative frequency and cumulative frequency. 76 90 78 91 96 80 70 73 65 90 82 94 71 84 78 76 83 66 91 66
First, let's organize the data in ascending order:
65 66 66 70 71 73 76 76 78 78 80 82 83 84 90 90 91 91 94 96
Now, let's create the frequency table with the bins, frequency, relative frequency, and cumulative frequency.
Bins | Frequency | Relative Frequency | Cumulative Frequency
---------------------------------------------------------------
60-65 | 1 | 1/20 | 1
66-71 | 4 | 4/20 | 5
72-77 | 4 | 4/20 | 9
78-83 | 5 | 5/20 | 14
84-89 | 1 | 1/20 | 15
90-95 | 5 | 5/20 | 20
96-101 | 1 | 1/20 | 21 (extra bin just for the max value)
Note: Relative Frequency is calculated by dividing the frequency of each bin by the total number of data points (20 in this case).
To create a frequency table using 6-point bins for the given set of exam scores, follow these steps:
Step 1: Sort the scores in ascending order:
65, 66, 66, 70, 71, 73, 76, 76, 78, 78, 80, 82, 83, 84, 90, 90, 91, 91, 94, 96
Step 2: Determine the number of scores in each bin:
94 to 99: 96
88 to 93: 90, 90, 91, 91, 94
82 to 87: 84
76 to 81: 76, 76, 78, 78, 80, 82, 83
70 to 75: 70, 71, 73, 84
64 to 69: 65, 66, 66
Step 3: Create the frequency table:
Bins Frequency Relative Frequency Cumulative Frequency
94-99 1 0.05 1
88-93 4 0.20 5
82-87 1 0.05 6
76-81 7 0.35 13
70-75 4 0.20 17
64-69 3 0.15 20
Note: The "Frequency" column represents the count of scores falling into each bin, while the "Relative Frequency" column represents the percentage of scores compared to the total number of scores. The "Cumulative Frequency" column shows the running total of frequencies.
That's it! You've created a frequency table using 6-point bins for the given set of exam scores.
To create a frequency table with 6-point bins for the given set of exam scores, follow these steps:
1. Determine the range of values covered by each bin. In this case, the bin width is 6, so the first bin will cover the range from 94 to 99, the second bin from 88 to 93, and so on.
2. Sort the exam scores in ascending order: 65 66 66 70 71 73 76 76 78 78 80 82 83 84 90 90 91 91 94 96.
3. Create a table with the following columns: Bin Range, Frequency, Relative Frequency, and Cumulative Frequency.
4. Start with the first bin range (94 to 99) and count how many scores fall within this range. In our case, there are no scores that fall within this range, so the frequency is 0.
5. Repeat this process for each bin range, counting the number of scores within each range. The frequencies for each bin can be calculated as follows:
- 94 to 99: 0
- 88 to 93: 0
- 82 to 87: 1
- 76 to 81: 4
- 70 to 75: 3
- 64 to 69: 2
6. Calculate the relative frequency for each bin. The relative frequency is the frequency divided by the total number of scores (20 in this case). For example, for the first bin (94 to 99), the relative frequency is 0/20 = 0.
7. Calculate the cumulative frequency for each bin. The cumulative frequency is the sum of the frequencies up to that point. For example, for the first bin, the cumulative frequency is 0.
8. Fill in the table with the values obtained in steps 4-7.
| Bin Range | Frequency | Relative Frequency | Cumulative Frequency |
|------------|-----------|--------------------|----------------------|
| 94 to 99 | 0 | 0.00 | 0 |
| 88 to 93 | 0 | 0.00 | 0 |
| 82 to 87 | 1 | 0.05 | 1 |
| 76 to 81 | 4 | 0.20 | 5 |
| 70 to 75 | 3 | 0.15 | 8 |
| 64 to 69 | 2 | 0.10 | 10 |
This table represents the frequency, relative frequency, and cumulative frequency for each bin of the exam scores provided.