Question

Use the data set $$ \\{2,11,8,10,6,11,7,14,20,9,1\\} . $$ What is the mode of this data set? A. 7 B. 8 C. 9 D. 11

Short answer

D. 11

Step-by-step solution

- Understand the Mode

The mode of a data set is the value that appears most frequently. To solve this problem, identify the number that occurs most often in the given data set.

- Count the Frequency

List each number in the data set and count how many times it appears: 2: 1 time11: 2 times8: 1 time10: 1 time6: 1 time7: 1 time14: 1 time20: 1 time9: 1 time1: 1 time

- Find the Maximum Frequency

Compare the frequencies of all the numbers in the data set. The number with the highest frequency is the mode. From the frequency list, the number 11 appears 2 times, which is more frequent than any other number in the data set.

- Select the Correct Answer

From the options given (A. 7, B. 8, C. 9, D. 11), match the mode found in Step 3. Since the mode is 11, the correct answer is D. 11.

Key concepts

Mode of a Data Set

The mode is an essential concept in statistical analysis. In simple terms, the mode is the value that appears most frequently in a data set. To identify the mode, you can count the frequency of each unique value. The value with the highest frequency is the mode. For example, consider the data set \( \{2,11,8,10,6,11,7,14,20,9,1\} \). By counting frequencies, we find that the number 11 appears twice, which is more frequent than any other number. Therefore, the mode is 11.

Frequency Distribution

Frequency distribution is a way to visualize how often each value in a data set occurs. This can be particularly handy when searching for patterns or trends within the data. In the given data set \( \{2,11,8,10,6,11,7,14,20,9,1\} \), creating a frequency distribution involves listing each unique value and counting its occurrences:

• 2: 1 time
• 11: 2 times
• 8: 1 time
• 10: 1 time
• 6: 1 time
• 7: 1 time
• 14: 1 time
• 20: 1 time
• 9: 1 time
• 1: 1 time

As noted, the number 11 appears the most frequently with a count of 2.

GED Test Preparation

Preparing for the GED test involves understanding various mathematical concepts, including statistical analysis. Knowing how to determine the mode and create frequency distributions can be crucial for the test.
For instance, you may encounter questions where you need to find the mode of a data set quickly and accurately. Practicing these steps:

• Identifying the mode by counting frequencies
• Understanding the importance of each value's frequency

will make you proficient in handling such questions. Remember, consistent practice and thorough understanding are key to excelling in your GED test.