Calculate the percentile rank for each student’s quiz result in a grade 12 math class.
Mark Frequency
4.0 2
5.0 6
6.0 8
7.0 13
8.0 4
9.0 3
10.0 2
Well, I have to say, this math class seems to have quite the spread of quiz results! But don't worry, I'll help you calculate the percentile rank for each student.
To calculate the percentile rank, we need to follow a few steps. First, let's add up all the frequencies to get the total number of students.
2 + 6 + 8 + 13 + 4 + 3 + 2 = 38
Okay, now that we know there are 38 students in total, we can start calculating the percentile rank for each result.
For the 4.0 mark, we have 2 students. To find the percentile rank, we divide the cumulative frequency by the total number of students and multiply by 100.
Percentile rank for 4.0 = (2 / 38) * 100 = 5.26%
For the 5.0 mark, we have 6 students.
Percentile rank for 5.0 = (8 / 38) * 100 ≈ 15.79%
For the 6.0 mark, we have 8 students.
Percentile rank for 6.0 = (16 / 38) * 100 ≈ 42.11%
For the 7.0 mark, we have 13 students.
Percentile rank for 7.0 = (29 / 38) * 100 ≈ 76.32%
For the 8.0 mark, we have 4 students.
Percentile rank for 8.0 = (33 / 38) * 100 ≈ 86.84%
For the 9.0 mark, we have 3 students.
Percentile rank for 9.0 = (36 / 38) * 100 ≈ 94.74%
For the 10.0 mark, we have 2 students.
Percentile rank for 10.0 = (38 / 38) * 100 = 100%
And there you have it! The percentile ranks for each student's quiz result in the grade 12 math class.
To calculate the percentile rank for each student's quiz result, you need to follow these steps:
Step 1: Calculate the cumulative frequency for each grade.
- Start with the first grade (4.0) and add up all the frequencies up to that point.
- Repeat this process for each grade.
Here is the table with the cumulative frequencies:
Mark Frequency Cumulative Frequency
4.0 2 2
5.0 6 8
6.0 8 16
7.0 13 29
8.0 4 33
9.0 3 36
10.0 2 38
Step 2: Calculate the percentile rank for each grade.
- The percentile rank (PR) is given by the formula: PR = (CF / N) x 100
- CF = cumulative frequency for the grade
- N = total number of students
Here are the percentile ranks for each grade:
Mark Frequency Cumulative Frequency Percentile Rank
4.0 2 2 5.26
5.0 6 8 21.05
6.0 8 16 42.11
7.0 13 29 76.32
8.0 4 33 86.84
9.0 3 36 94.74
10.0 2 38 100
Therefore, the percentile rank for each student's quiz result in the grade 12 math class is as follows:
- For a grade of 4.0, the percentile rank is 5.26.
- For a grade of 5.0, the percentile rank is 21.05.
- For a grade of 6.0, the percentile rank is 42.11.
- For a grade of 7.0, the percentile rank is 76.32.
- For a grade of 8.0, the percentile rank is 86.84.
- For a grade of 9.0, the percentile rank is 94.74.
- For a grade of 10.0, the percentile rank is 100.
To calculate the percentile rank for each student's quiz result, you need to follow these steps:
1. Determine the total number of students in the grade 12 math class. In this case, the total number of students is the sum of the frequencies: 2 + 6 + 8 + 13 + 4 + 3 + 2 = 38.
2. Calculate the cumulative frequency for each quiz result. Cumulative frequency refers to the sum of the frequencies up to that specific value. In this case, we will start with the lowest value:
- For a quiz result of 4.0, the cumulative frequency will be 2.
- For a quiz result of 5.0, the cumulative frequency will be 2 + 6 = 8.
- For a quiz result of 6.0, the cumulative frequency will be 8 + 8 = 16.
- For a quiz result of 7.0, the cumulative frequency will be 16 + 13 = 29.
- For a quiz result of 8.0, the cumulative frequency will be 29 + 4 = 33.
- For a quiz result of 9.0, the cumulative frequency will be 33 + 3 = 36.
- For a quiz result of 10.0, the cumulative frequency will be 36 + 2 = 38.
3. Calculate the percentile rank for each quiz result. The percentile rank is calculated using the formula: (cumulative frequency / total number of students) * 100.
- For a quiz result of 4.0, the percentile rank will be (2 / 38) * 100 = 5.26%.
- For a quiz result of 5.0, the percentile rank will be (8 / 38) * 100 = 21.05%.
- For a quiz result of 6.0, the percentile rank will be (16 / 38) * 100 = 42.11%.
- For a quiz result of 7.0, the percentile rank will be (29 / 38) * 100 = 76.32%.
- For a quiz result of 8.0, the percentile rank will be (33 / 38) * 100 = 86.84%.
- For a quiz result of 9.0, the percentile rank will be (36 / 38) * 100 = 94.74%.
- For a quiz result of 10.0, the percentile rank will be (38 / 38) * 100 = 100%.
In statistics, the percentile rank of a score (PR) is the percentage of scores in its frequency distribution that are less than that score. Its mathematical formula is. P R = C F − ( 0.5 × F ) N × 100 , {\displaystyle PR= {\frac {CF- (0.5\times F)} {N}}\times 100,} where CF —the cumulative frequency—is the count of all scores less than or equal to the score of interest, F is the frequency for the score of interest, and N is the number of scores in the distribution.
If you do the work, you will learn more.