Which of the following is the best description for the data set below?
1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9
A.
Uniform
B.
Right-skewed
C.
Bimodal
D.
Left-skewed
The Correct answer and Explanation is:
The correct answer is C. Bimodal.
To understand why the data set is best described as bimodal, let’s first analyze the distribution of the data points:
The data set provided is: 1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9.
Frequency Distribution
We can tally the occurrences of each number:
- 1 occurs 2 times
- 2 occurs 4 times
- 3 occurs 2 times
- 7 occurs 2 times
- 8 occurs 4 times
- 9 occurs 2 times
Modes in the Data
A mode is a value that appears most frequently in a data set. In this case, both 2 and 8 appear four times, making them the most frequent values. The presence of two modes (2 and 8) indicates that the data set is bimodal, as it has two peaks in the frequency distribution.
Skewness and Uniformity
- Uniform: A uniform distribution would mean all values occur with the same frequency, which is not the case here.
- Right-skewed: A right-skewed distribution has a longer tail on the right side, typically indicating that most data points cluster towards the lower end, with a few larger values extending the tail. While the data does have larger values, the concentration of modes does not support this description.
- Left-skewed: A left-skewed distribution would have a longer tail on the left side, indicating that most data points cluster towards the higher end. Again, this is not supported by the data.
Conclusion
Given that the data set has two distinct peaks (2 and 8) with significant frequency, it clearly falls under the category of bimodal distributions. This characteristic is crucial in statistics, as it influences how we interpret the data, understand its variability, and apply appropriate statistical methods. Thus, the best description for the data set is indeed C. Bimodal.