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Chapter 1: Problem 56

Find the average of four test grades of \(86,92,80,\) and 78 .

Short Answer

Expert verified
The average grade is 84.

Step by step solution

01

- Sum the Grades

Add up all the given test grades: \[86 + 92 + 80 + 78 \]
02

- Calculate the Total

Perform the addition: \[86 + 92 = 178 \]\[178 + 80 = 258 \]\[258 + 78 = 336 \]
03

- Count the Number of Grades

There are four test grades to be averaged.
04

- Divide the Total by the Number of Grades

Divide the sum by the number of test grades: \[\frac{336}{4} = 84 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

summing grades
When dealing with multiple grades, one of the first and fundamental steps is summing the grades. This means adding all individual grades together to get a total sum. For example, in the given problem, the grades 86, 92, 80, and 78 are added to find the sum. This is important because the sum represents the cumulative score of all tests combined.
Here's the addition for our given grades:
- 86 + 92 = 178
- 178 + 80 = 258
- 258 + 78 = 336
So, the total sum is 336.
division for average
Once you have the total sum of all the grades, the next step is to find the average. This is done by division. You divide the total sum by the number of grades. This process is known as calculating the mean. For example, our total sum of 336 will be divided by the number of grades, which is 4.
The division looks like this: \[ \frac{336}{4} = 84 \]
Thus, the average grade is 84. Dividing helps in finding an equal representation of all grades combined into one number.
basic arithmetic operations
To solve math problems like finding the average grade, knowing basic arithmetic operations is crucial. The main operations include addition, subtraction, multiplication, and division. In our example, we mainly used addition to find the total sum and division to find the average.
Being comfortable with these operations allows you to solve a wide range of math problems easily and effectively.
Review these basic arithmetic operations frequently to keep your skills sharp. Combine this knowledge with practice on various problems to solidify your understanding.
step-by-step math problem
Breaking down a math problem into clear, manageable steps makes it easier to understand and solve. This approach ensures that you don鈥檛 miss any crucial part of the process.
For the given problem, the steps were as follows:
1. Sum the grades: Find the total sum of all the provided grades.
2. Calculate the total: Perform the addition carefully and correctly.
3. Count the number of grades: Identify how many grades you have.
4. Divide for the average: Divide the total sum by the number of grades.
Following these steps methodically helps in arriving at the correct solution. Always approach math problems with a clear step-by-step strategy to build your confidence and proficiency.

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