Learn about the bell-shaped distribution, its characteristics, and why it represents a normal distribution in data analysis. Understand its significance for statistical modeling.
Question
What is it called when a graph of data has a single peak at the center?
A. Skewed distribution
B. Multimodal distribution
C. Bi-modal distribution
D. Bell-shaped distribution
Answer
D. Bell-shaped distribution
Explanation
A bell-shaped distribution refers to the graphical representation of a normal distribution, which is symmetric and unimodal, with a single peak at the center. This shape is characteristic of data that follows a normal probability distribution, where most values cluster around the mean, and frequencies gradually decrease as you move away from the center toward the tails.
Key Characteristics of a Bell-Shaped Distribution
- Symmetry: The left and right sides of the graph are mirror images.
- Single Peak (Unimodal): The highest point occurs at the mean, which is also equal to the median and mode.
- Tapering Tails: The frequencies decrease symmetrically as they move away from the mean.
- Defined by Mean and Standard Deviation: The spread and height of the curve depend on these two parameters.
This type of distribution is central to many statistical analyses because it reflects natural phenomena and adheres to the empirical rule (68-95-99.7 rule), where approximately 68% of data lies within one standard deviation of the mean, 95% within two, and 99.7% within three.
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