III. The table below shows the scores attained by high school graduates in an entrance exam for college Class interval f 65-69 70-74 75-79 80-84 85-89 90-94 95-99 2 8 10 9 2 2 n= X fx Σfx= d SIU fd Σfd= 21: quote rose to nsem eri bnit:notonic eotteitste ni stueen feet ort rebieno levisini eest 8 2 Ə ON 8 ▬▬▬▬ A3-34 ra 88-sa 27-28 $8-81 28
III. The table below shows the scores attained by high school graduates in an entrance exam for college Class interval f 65-69 70-74 75-79 80-84 85-89 90-94 95-99 2 8 10 9 2 2 n= X fx Σfx= d SIU fd Σfd= 21: quote rose to nsem eri bnit:notonic eotteitste ni stueen feet ort rebieno levisini eest 8 2 Ə ON 8 ▬▬▬▬ A3-34 ra 88-sa 27-28 $8-81 28
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Scores Attained by High School Graduates in an Entrance Exam for College
The table below presents the scores attained by high school graduates in a college entrance exam. The data is organized into class intervals, with corresponding frequencies and columns designated for various statistical calculations.
| Class Interval | Frequency (f) | Midpoint (x) | fx | Deviation (d) | fd |
|----------------|---------------|--------------|----|---------------|----|
| 65 - 69 | 2 | | | | |
| 70 - 74 | 8 | | | | |
| 75 - 79 | 10 | | | | |
| 80 - 84 | 9 | | | | |
| 85 - 89 | 7 | | | | |
| 90 - 94 | 2 | | | | |
| 95 - 99 | 2 | | | | |
Total: n =
\[
\sum fx =
\]
\[
\sum fd =
\]
### Explanation of Terms:
- **Class Interval**: The range of scores grouped together.
- **Frequency (f)**: The number of students who scored within the given class interval.
- **Midpoint (x)**: The midpoint of each class interval. It is calculated as the average of the lower and upper bounds of each interval.
- **fx**: The product of the frequency and the midpoint of each class interval.
- **Deviation (d)**: The difference between each midpoint and a reference value.
- **fd**: The product of the frequency and the deviation of each class interval.
### Steps to Complete the Table:
1. **Determine the Midpoint (x) for Each Class Interval**:
- For the interval 65-69, the midpoint is (65+69)/2 = 67.
- Repeat this calculation for each interval.
2. **Calculate fx**:
- Multiply the frequency (f) by the midpoint (x) for each interval.
3. **Calculate d**:
- Choose a reference value (often the median class midpoint or mean midpoint) and subtract each interval’s midpoint from this reference.
4. **Calculate fd**:
- Multiply the frequency (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbfefd57-6cd5-45bf-b890-c343c2fceb41%2Fce67b819-aac3-4260-9e83-98f4c69cf278%2F3w4fer_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Scores Attained by High School Graduates in an Entrance Exam for College
The table below presents the scores attained by high school graduates in a college entrance exam. The data is organized into class intervals, with corresponding frequencies and columns designated for various statistical calculations.
| Class Interval | Frequency (f) | Midpoint (x) | fx | Deviation (d) | fd |
|----------------|---------------|--------------|----|---------------|----|
| 65 - 69 | 2 | | | | |
| 70 - 74 | 8 | | | | |
| 75 - 79 | 10 | | | | |
| 80 - 84 | 9 | | | | |
| 85 - 89 | 7 | | | | |
| 90 - 94 | 2 | | | | |
| 95 - 99 | 2 | | | | |
Total: n =
\[
\sum fx =
\]
\[
\sum fd =
\]
### Explanation of Terms:
- **Class Interval**: The range of scores grouped together.
- **Frequency (f)**: The number of students who scored within the given class interval.
- **Midpoint (x)**: The midpoint of each class interval. It is calculated as the average of the lower and upper bounds of each interval.
- **fx**: The product of the frequency and the midpoint of each class interval.
- **Deviation (d)**: The difference between each midpoint and a reference value.
- **fd**: The product of the frequency and the deviation of each class interval.
### Steps to Complete the Table:
1. **Determine the Midpoint (x) for Each Class Interval**:
- For the interval 65-69, the midpoint is (65+69)/2 = 67.
- Repeat this calculation for each interval.
2. **Calculate fx**:
- Multiply the frequency (f) by the midpoint (x) for each interval.
3. **Calculate d**:
- Choose a reference value (often the median class midpoint or mean midpoint) and subtract each interval’s midpoint from this reference.
4. **Calculate fd**:
- Multiply the frequency (
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