Problem 64 - General Chemistry: Principles and Modern Applications

Question

A class of 84 students had a final grade distribution of 18\(\%\) A's, 25\(\%\) B's, 32\(\%\) C's, 13\(\%\) D's, 12\(\%\) F's. How many students received each grade?

Step-by-Step Solution

Answer

In the class of 84 students: 15 students received A's, 21 students received B's, 27 students received C's, 11 students received D's, and 10 students received F's.

Step 1 Compute number of students received A's

18\(\%\) of 84 is determined by multiplying \(0.18\) (18\(\%\) in decimal form) by 84. This yields \(0.18 \times 84 = 15.12\). Since the number of students cannot be a decimal, it rounds up to 15.

Step 2 Compute number of students received B's

25\(\%\) of 84 is determined by multiplying \(0.25\) (25\(\%\) in decimal form) by 84. This yields \(0.25 \times 84 = 21\).

Step 3 Compute number of students received C's

32\(\%\) of 84 is determined by multiplying \(0.32\) (32\(\%\) in decimal form) by 84. This yields \(0.32 \times 84 = 26.88\). Since the number of students cannot be a decimal, it rounds up to 27.

Step 4 Compute number of students received D's

13\(\%\) of 84 is determined by multiplying \(0.13\) (13\(\%\) in decimal form) by 84. This yields \(0.13 \times 84 = 10.92\). Since the number of students cannot be a decimal, it rounds up to 11.

Step 5 Compute number of students received F's

12\(\%\) of 84 is determined by multiplying \(0.12\) (12\(\%\) in decimal form) by 84. This yields \(0.12 \times 84 = 10.08\). Since the number of students cannot be a decimal, it rounds up to 10.

Key Concepts

Grade Distribution

Understanding grade distribution is crucial when analyzing how students have performed in a class. In this context, distribution refers to how grades are spread across different categories, such as A's, B's, C's, etc. Each percentage given in the distribution represents a part of the class that's achieved a specific grade.

To calculate the number of students that fall into each grade category, you multiply the total number of students by the percentage in decimal form for that category. For example, to find out how many students received A's, you would calculate 18% of 84, which is done by converting the percentage to a decimal (0.18) and multiplying it by 84. This calculation helps schools and educators understand the overall performance of a class and make decisions based on the data.

Accurate grade distribution insights can guide improvements in teaching methods and curriculum adjustments to ensure better student outcomes in the future.

Rounded Numbers

Rounding numbers is a fundamental concept in mathematics that you will encounter across various contexts, including calculating grades. In situations where calculations might result in decimals, and you need a whole number (since you can't have a fraction of a student), rounding becomes necessary.

In this exercise, after calculating the number of students for each grade where decimals are involved, you need to round them. The common rule for rounding is: if the decimal part is 0.5 or higher, round up to the next whole number; if it's less than 0.5, round down. For example, 15.12 students for A's is rounded to 15 because the decimal is less than 0.5.

Rounding helps present data in a more understandable and practical format, especially in situations where precision isn’t critical for small ranged numbers like school grades.

Student Grades

Student grades are numerical or letter symbols representing a student's academic performance. Knowing how to calculate the number of students that fall into each grade category, as seen in this exercise, helps track and understand student achievement levels.

Grades can directly impact a student's future opportunities, including college admissions and job prospects. Therefore, accurately distributing and rounding numbers when calculating grades can have significant implications.

For educators, detailed knowledge about student grades across different levels can assist in customizing teaching strategies and focus areas to enhance learning experiences. Meaningful analysis of grades and distribution can guide schools in policy making and curriculum design, ultimately improving educational outcomes.