Question

$$ \begin{aligned} &\text { Elena's math scores }\\\ &\begin{array}{|l|l|} \hline \text { Test 1 } & 78 \\ \hline \text { Test 2 } & 83 \\ \hline \text { Test 3 } & 81 \\ \hline \text { Midterm exam } & 85 \\ \hline \text { Test 4 } & 89 \\ \hline \text { Test 5 } & 94 \\ \hline \text { Final Exam } & 96 \\ \hline \end{array} \end{aligned} $$ If Elena's teacher drops each student's lowest grade, what would Elena's new average be? A. 86 B. 87 C. 88 D. 89

Short answer

The new average is 88.

Step-by-step solution

Identify the Scores

List all of Elena's scores. They are 78, 83, 81, 85, 89, 94, and 96.

Drop the Lowest Score

Identify and remove the lowest score from the list. The lowest score is 78. The remaining scores are 83, 81, 85, 89, 94, and 96.

Calculate the Sum of the Remaining Scores

Add up the remaining scores: 83 + 81 + 85 + 89 + 94 + 96.

Perform the Addition

Calculate the sum: 83 + 81 = 164, 164 + 85 = 249, 249 + 89 = 338, 338 + 94 = 432, 432 + 96 = 528.

Divide by the Number of Scores

Since there are 6 scores left after dropping the lowest one, divide the sum by 6: \ \[528 \div 6 = 88 \]

Select the Correct Answer

The new average is 88, so the correct answer is C. 88.

Key concepts

average calculation

To understand average calculation, let's start with the basic formula. An average is simply the sum of all values divided by the number of values. This gives a single value that represents the center of the data set. For example, if you add together Elena's scores (83 + 81 + 85 + 89 + 94 + 96), you get 528. Next, you divide this sum by the number of scores (6) to get the average: \ \[ \frac{528}{6} = 88 \ \]. This means Elena's new average score is 88.
This method is very useful in understanding the overall performance across multiple assessments. Remember, always check for accuracy in your addition and division to ensure the correct average.

dropping the lowest score

Sometimes, teachers drop the lowest score to give students a fair chance, especially if one test did not reflect their true understanding. Let's look at how this works. First, list all your scores and find the lowest one. For Elena, her scores are 78, 83, 81, 85, 89, 94, and 96, and the lowest of these is 78.
Remove this lowest score to leave the remaining scores: 83, 81, 85, 89, 94, and 96. By eliminating the lowest score, Elena's performance appears more favorable. Dropping the lowest score can sometimes significantly increase a student's average, leading to a better reflection of their skills and effort.

test scores

Test scores are a numerical representation of your performance on any given test. They help teachers and students identify strengths and weaknesses. In Elena's case, her different test scores ranging from 78 to 96 showed varied performance.
Calculating and understanding these scores can help in setting targets for improvement. Each test contributes differently to the overall average. Knowing how each test score affects your final grade can motivate better preparation for future exams.
Keeping track of your scores also allows you to identify patterns or subjects that might need more attention.