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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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### 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
Transcribed Image Text:### 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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