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 mode of Elena’s math grades? A. 85 B. 86 C. 87 D. There is no mode

Short answer

D. There is no mode

Step-by-step solution

- List all the grades

First, list all of Elena's math grades from the table: 78, 83, 81, 85, 89, 94, 96.

- Define the mode

The mode is the number that appears most frequently in a set of data.

- Count the occurrences

Count how many times each grade appears: 78 (1 time), 83 (1 time), 81 (1 time), 85 (1 time), 89 (1 time), 94 (1 time), 96 (1 time).

- Determine if any grade repeats

Notice that each grade appears exactly once. Therefore, no grade repeats.

- Conclude the mode

Since no grade appears more frequently than the others, there is no mode in this set of data.

Key concepts

Mode Calculation

Understanding the mode is crucial in statistics. Mode is the value that appears most frequently in a data set. To find it, list all data points and count the frequency of each one. For example, for the grades: 78, 83, 81, 85, 89, 94, 96, each grade occurs only once. Since no grade repeats, this dataset has no mode.
To summarize:

• List all data points.
• Count the frequency of each value.
• Identify the most frequent value for the mode.
• If no value repeats, state there's no mode.

Easy to compute but remember, not all datasets will have a mode.

Data Frequency

Data frequency indicates how often each value appears in a dataset. For accurate mode calculation, knowing how to determine data frequency is key. Let's break down the steps:
Say we have a dataset: 78, 83, 81, 85, 89, 94, 96. You count each occurrence:

• 78 (appears 1 time)
• 83 (appears 1 time)
• 81 (appears 1 time)
• 85 (appears 1 time)
• 89 (appears 1 time)
• 94 (appears 1 time)
• 96 (appears 1 time)

None of these grades appears more than once. Thus, each has a frequency of 1. Remember, understanding data frequency helps identify trends and patterns in your dataset.

GED Math

The GED math test covers various topics, including statistics, where you might need to calculate the mode. Having a solid foundation in basic statistics is instrumental for success.
In our exercise, we learned how to find the mode by understanding data frequency. Here’s how these skills apply:

• Mode calculation helps identify the most common value in a set.
• Data frequency analysis highlights how often each value appears.

By mastering these processes, you enhance your analytical skills, reflecting on other topics within GED math. Strong basic skills make complex problems more manageable, thus improving your overall score.