ASSIGNMENT 2: The intelligence quotients of 100 freshmen students admitted at the College of Engineering of a certain university were taken and shown below. 91 94 111 105 108 108 115 110 119 98 93 112 111 110 115 107 96 107 109 89 107 100 103 100 94 108 105 101 120 90 85 116 106 101 100 112 107 102 90 105 87 118 94 117 108 91 88 120 106 107 106 107 106 100 98 103 106 106 106 110 107 94 106 100 114 99 96 106 103 110 95 99 83 107 119 95 99 97 114 96 107 68 109 101 92 100 113 101 106 108 112 97 106 105 107 100 97 97 107 106 112 Using the data above, construct a frequency distribution with 10 classes. For each class interval of the frequency distribution, determine the class midpoint, the lower and upper class boundaries. Use 83 as the lowest lower limit.
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Answer:
Thank you for providing more information! Based on your message, it seems that you're asking for help with constructing a frequency distribution with 10 classes using the data provided. Here's how you can do it:
1. Find the range of the data by subtracting the smallest value from the largest value: Range = Largest Value - Smallest Value = 120 - 68 = 52
2. Determine the width of each class interval by dividing the range by the number of classes (10): Class Width = Range / Number of Classes = 52 / 10 = 5.2
3. Round up the class width to the nearest whole number to get a convenient class width: Rounded Class Width = Round Up(Class Width) = Round Up(5.2) = 6
4. Determine the lower limit of the first class interval by subtracting one rounded class width from the smallest value: Lower Limit of First Class Interval = Smallest Value - Rounded Class Width = 68 - 6 = 62
5. Construct a table with ten rows (one for each class interval) and four columns (Class Interval, Frequency, Midpoint, Lower and Upper Boundaries).
6. Fill in the first row of the table with the following values:
- Class Interval: 62-67
- Frequency: Count how many values in your data set fall into this interval
- Midpoint: (Lower Bound + Upper Bound) / 2
- Lower Boundary: The lowest value that falls into this interval
- Upper Boundary: The highest value that falls into this interval
7. Repeat step 6 for each row of the table, incrementing the lower and upper boundaries by one rounded class width each time.
Here's an example of what your table might look like:
| Class Interval | Frequency | Midpoint | Lower Boundary | Upper Boundary |
|----------------|-----------|----------|----------------|----------------|
| 62-67 | | | | |
| 68-73 | | | | |
| 74-79 | | | | |
| 80-85 | | | | |
| 86-91 | | | | |
| 92-97 | | | | |
| 98-103 | | | | |
| 104-109 | | | | |
| 110-115 | | | | |
| 116-121 | | | |
I hope this helps!