Question

Use the following for questions 31–38. $$ \begin{aligned} &\text { Elena's math scores }\\\ &\begin{array}{|l|l|} \hline \text { Test 1 } & 78 \\ \hline \text { Test 2 } & 83 \\ \hline \text { Test 3 } & 81 \\ \hline \text { Midterm exam } & 85 \\ \hline \text { Test 4 } & 89 \\ \hline \text { Test 5 } & 94 \\ \hline \text { Final Exam } & 96 \\ \hline \end{array} \end{aligned} $$ What is the average of Elena's math grades? A. 85 B. 86 C. 87 D. 88

Short answer

The average of Elena's math grades is C. 87.

Step-by-step solution

Identify All the Scores

List out all the scores given in the problem: 78, 83, 81, 85, 89, 94, and 96.

Add All the Scores

Sum the scores: \( 78 + 83 + 81 + 85 + 89 + 94 + 96 = 606 \)

Count the Number of Scores

There are 7 tests given, so the number of scores is 7.

Divide the Total by the Number of Scores

Calculate the average by dividing the total sum by the number of scores: \( \frac{606}{7} = 86.57 \)

Round to the Nearest Whole Number

Round the result from Step 4 to the nearest whole number. 86.57 rounded to the nearest whole number is 87.

Select the Correct Answer

Based on the rounded average score of 87, the correct answer is: C. 87.

Key concepts

Mean Calculation

Calculating the mean (or average) is a common task in math and statistics. It helps to find the central value of a set of numbers. The mean gives us a single value that represents the entire dataset.

To calculate the mean, follow these simple steps:

1. **Identifying the Scores**: First, make sure you have all the numbers in the dataset. For example, Elena's math scores are 78, 83, 81, 85, 89, 94, and 96.
2. **Sum the Scores**: Add all the numbers together. In our case, it would be: \( 78 + 83 + 81 + 85 + 89 + 94 + 96 = 606 \)
3. **Count the Scores**: Determine how many numbers are in your dataset. Elena has taken 7 tests, so we have 7 scores.
4. **Divide the Sum by the Count**: To find the mean, divide the total sum by the number of scores: \( \frac{606}{7} = 86.57 \).

This process helps to find the average score that best summarizes the dataset.

Rounding Numbers

Rounding numbers makes them simpler to use while still keeping their value close to the original. It's particularly useful when dealing with decimals.

In our example, after calculating the mean, we got 86.57. To round this to the nearest whole number:

1. **Identify the Tenths Place**: Look at the number in the tenths place (the first digit after the decimal point). In 86.57, the tenths place is 5.
2. **Determine Action**: If the tenths place is 5 or higher, round up. If it's 4 or lower, round down.
3. **Apply Rounding**: Since the tenths place in 86.57 is 5, we round up to 87.

So, 86.57 rounded to the nearest whole number is 87. Rounding helps to simplify the number, making it easier to interpret.

Basic Arithmetic

Basic arithmetic involves simple mathematical operations like addition, subtraction, multiplication, and division. These operations are the foundation of most math problems.

For calculating the average of Elena's grades, we used the following operations:

1. **Addition**: We added all the scores together to get the sum. For example, 78 + 83 + 81 + 85 + 89 + 94 + 96 = 606.
2. **Division**: We divided the sum by the number of scores. In this case, we divided 606 by 7 to get 86.57.

Understanding and practicing these basic operations is key to solving many math problems accurately. These skills are essential for high school math and beyond.