Are the answers correct? ### Frequency Distribution AnalysisThe frequency distribution in the following table lists the results of a quiz given in Professor Gilbert's statistics class. The objective is to find the mean, median, and mode of the scores.#### Quiz Grades| **Score** | **Number of Students** ||-----------|------------------------|| 10 | 4 || 9 | 11 || 8 | 10 || 7 | 9 || 6 | 11 || 5 | 3 |#### Calculations- **Mean**: The mean is calculated by finding the sum of all the scores divided by the number of students.- **Median**: The median is the middle value of the sorted list of scores.- **Mode**: The mode is the score that appears most frequently. In this case, if more than one mode exists, they should be separated with commas.**Results:**- **Mean**: 7.6- **Median**: 8- **Mode**: 9, 6The data is summarized and calculated as follows:1. **Mean Calculation**: - Total number of students = 4 + 11 + 10 + 9 + 11 + 3 = 48 - Sum of all scores: (10×4) + (9×11) + (8×10) + (7×9) + (6×11) + (5×3) - Sum = 40 + 99 + 80 + 63 + 66 + 15 = 363 - Mean = 363 / 48 ≈ 7.62. **Median Calculation**: - Sort the data in ascending order and find the middle value(s). - For 48 students, the middle values will be the 24th and 25th scores. When sorted, both fall within the score of 8. - Median = 83. **Mode Calculation**: - Determine the score(s) with the highest frequency. - Both scores 9 and 6 have the highest frequency (11 occurrences each). - Mode = 9, 6

given data score (x) number of student (f) cumulative 5 3 3 6 11 14 7 9 23 8 10 33 9 11…

The frequency distribution in the following table lists the results of a quiz given in Professor Gilbert's statistics class. Find the mean, median, and mode of the scores. (Round the mean to one decimal place. If more than one mode exists, separate your answers with commas. If an answer does not exist, enter DNE.) Quiz grades Number of Score Students 10 4. 6. 11 10 7 9. 6. 11 3. Mean: 7.6 Median: 8 Mode: 9,6

The frequency distribution in the following table lists the results of a quiz given in Professor Gilbert's statistics class. Find the mean, median, and mode of the scores. (Round the mean to one decimal place. If more than one mode exists, separate your answers with commas. If an answer does not exist, enter DNE.) Quiz grades Number of Score Students 10 4. 6. 11 10 7 9. 6. 11 3. Mean: 7.6 Median: 8 Mode: 9,6

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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Concept explainers

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.

Question

Are the answers correct?

### Frequency Distribution Analysis

The frequency distribution in the following table lists the results of a quiz given in Professor Gilbert's statistics class. The objective is to find the mean, median, and mode of the scores.

#### Quiz Grades

| **Score** | **Number of Students** |
|-----------|------------------------|
| 10 | 4 |
| 9 | 11 |
| 8 | 10 |
| 7 | 9 |
| 6 | 11 |
| 5 | 3 |

#### Calculations

- **Mean**: The mean is calculated by finding the sum of all the scores divided by the number of students.

- **Median**: The median is the middle value of the sorted list of scores.

- **Mode**: The mode is the score that appears most frequently. In this case, if more than one mode exists, they should be separated with commas.

**Results:**

- **Mean**: 7.6
- **Median**: 8
- **Mode**: 9, 6

The data is summarized and calculated as follows:
1. **Mean Calculation**:
- Total number of students = 4 + 11 + 10 + 9 + 11 + 3 = 48
- Sum of all scores: (10×4) + (9×11) + (8×10) + (7×9) + (6×11) + (5×3)
- Sum = 40 + 99 + 80 + 63 + 66 + 15 = 363
- Mean = 363 / 48 ≈ 7.6

2. **Median Calculation**:
- Sort the data in ascending order and find the middle value(s).
- For 48 students, the middle values will be the 24th and 25th scores. When sorted, both fall within the score of 8.
- Median = 8

3. **Mode Calculation**:
- Determine the score(s) with the highest frequency.
- Both scores 9 and 6 have the highest frequency (11 occurrences each).
- Mode = 9, 6

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