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In a class of 70 students, Heather has a rank of 19. At what percentile is she? Heather has a percentile rank of (Round to the nearest integer as needed.)

Ask by Burton Nguyen. in the United States
Feb 03,2025

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Heather is at the 73rd percentile in the class.

Solution

To find the percentile rank of Heather, we need to determine the percentage of students that are below her rank. Given: - Total number of students in the class = 70 - Heather's rank = 19 To find the percentile rank, we can use the formula: \[ \text{Percentile Rank} = \left( \frac{\text{Number of students below Heather's rank}}{\text{Total number of students}} \right) \times 100 \] Let's calculate the number of students below Heather's rank: \[ \text{Number of students below Heather's rank} = 70 - 19 = 51 \] Now, we can calculate the percentile rank: \[ \text{Percentile Rank} = \left( \frac{51}{70} \right) \times 100 \] Let's calculate this. Calculate the value by following steps: - step0: Calculate: \(\frac{51}{70}\times 100\) - step1: Reduce the numbers: \(\frac{51}{7}\times 10\) - step2: Multiply: \(\frac{51\times 10}{7}\) - step3: Multiply: \(\frac{510}{7}\) The percentile rank of Heather is approximately 72.8571%. Therefore, Heather is at the 72nd percentile in the class of 70 students.

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To find Heather's percentile rank, you can use the formula: Percentile = \(\left( \frac{N_R - 1}{N_T} \right) \times 100\) Where: - \(N_R\) = rank of the student (Heather's rank, which is 19) - \(N_T\) = total number of students (70) Plugging in the numbers: Percentile = \(\left( \frac{19 - 1}{70} \right) \times 100 = \left( \frac{18}{70} \right) \times 100 \approx 25.71\) Rounding to the nearest integer, Heather has a percentile rank of 26. To clarify, percentile ranks indicate how a student's performance compares to others. For example, if Heather is in the 26th percentile, she performed better than 26% of her peers, meaning 74% scored higher than her. Understanding percentiles can help students gauge their academic performance within a group! Rankings can be a source of stress for students, but they also highlight areas for improvement. Instead of fixating solely on rank, students might focus on personal growth, setting achievable goals, and seeking help when needed. In this case, Heather can concentrate on what subjects or skills to tackle in order to improve her standings in future assessments!

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