Question

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

Short answer

The median of Elena's math grades is 85.

Step-by-step solution

- Understand the definition of median

The median is the middle number in a sorted list of numbers. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.

- List Elena’s grades

Write down all the grades: 78, 83, 81, 85, 89, 94, 96.

- Sort the grades in ascending order

Sort the list of grades from the lowest to the highest: 78, 81, 83, 85, 89, 94, 96.

- Identify the middle number

Count the number of grades. Since there are 7 grades (an odd number), the median is the middle number in the sorted list. The middle number is the fourth grade: 85.

- Confirm the median

Verify that 85 is indeed the middle number in the sorted list of grades: 78, 81, 83, 85, 89, 94, 96.

Key concepts

Math Grades

Math grades are an important part of a student's academic performance. They are often used to measure understanding and proficiency in mathematics.
In this example, we are looking at Elena's math grades, which include scores from several tests and exams.
These scores can tell us a lot about her performance throughout the term.
To analyze these grades, it's often useful to calculate statistical measures such as the median.
The median is particularly valuable because it gives us a central value that can represent Elena’s performance more accurately than just an average. Let's dive into how we find this 'middle number' in a list of grades.

Sorted List

A sorted list arranges data in a specific order, which makes it easier to find key values like the median.
For Elena’s grades, we first list them without any specific order.
The initial list is: 78, 83, 81, 85, 89, 94, 96.
Next, we sort these grades in ascending order to make it easy to find the middle number:
78, 81, 83, 85, 89, 94, 96.
This sorted list allows us to quickly determine that there are 7 grades, which is an odd number. Hence, the median will be the grade positioned at the center of this sorted list.

Middle Number

The middle number, or median, in a sorted list of numbers is simply the value located at the mid-point.
If the count of numbers is odd, the median is the exact middle number. For Elena's seven grades, the middle number of the sorted list is the fourth grade.

• 78
• 81
• 83
• 85
• 89
• 94
• 96

Here, 85 is the fourth number, making it the median of her grades.
This means that half of her scores are below 85 and the other half are above 85, giving a good central value of her performance.