Question
What is the mode for them following data set? \[ 2,14,5,16,8,17,11,9,10,8,14 \]
Ask by Ward Murphy. in Australia
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The data set has two modes: 8 and 14.
Solution
1. List the data set:
\[2,\; 14,\; 5,\; 16,\; 8,\; 17,\; 11,\; 9,\; 10,\; 8,\; 14\]
2. Count the frequency of each number:
- \(2\) appears once.
- \(14\) appears twice.
- \(5\) appears once.
- \(16\) appears once.
- \(8\) appears twice.
- \(17\) appears once.
- \(11\) appears once.
- \(9\) appears once.
- \(10\) appears once.
3. Identify the most frequently occurring numbers:
Both \(14\) and \(8\) appear twice, which is more than any other numbers.
4. Therefore, the data set is bimodal and the modes are:
\(\boxed{8 \text{ and } 14}\).
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Simplify this solution The Deep Dive
The mode of a data set is the number that appears most frequently. In your data set: 2, 14, 5, 16, 8, 17, 11, 9, 10, 8, 14, the number 14 appears twice, and so does the number 8. Therefore, the modes of this data set are 8 and 14 since they both occur with the highest frequency. When determining the mode, it’s important to check for outliers or single occurrences that might mislead you. If two or more numbers appear with the same highest frequency, it means your data set is bimodal or multimodal! Remember, always double-check your counts to avoid missing any repeating numbers.
