Select the statement that correctly describes a normal distribution.
A. It is a negatively skewed distribution, as the extreme values are less than the median.
B. It is a symmetric distribution, as the mean and the median are the same.
C. It is a positively skewed distribution, as the extreme values are greater than the median.
D. It is a uniform distribution, as all of the values have equal frequency.
The Correct Answer and Explanation is :
The correct answer is:
B. It is a symmetric distribution, as the mean and the median are the same.
Explanation:
A normal distribution, also known as a Gaussian distribution, is a probability distribution that is widely used in statistics and data analysis. It has the following key characteristics:
- Symmetry:
The normal distribution is symmetric about its mean. This means that the left and right halves of the distribution are mirror images of each other. The majority of the data is concentrated around the central peak, and the frequencies of values decrease as you move further away from the mean. - Mean, Median, and Mode:
In a perfectly normal distribution, the mean (average), median (middle value), and mode (most frequent value) are all equal and located at the center of the distribution. This characteristic distinguishes it from skewed distributions where these measures differ. - Bell Shape:
The normal distribution has a characteristic “bell-shaped” curve. It is unimodal, meaning there is a single peak, and the tails of the distribution extend infinitely in both directions without touching the horizontal axis. - Negatively or Positively Skewed Distributions:
The given options A and C describe skewed distributions. In a negatively skewed distribution, the tail extends to the left (toward smaller values), while in a positively skewed distribution, the tail extends to the right (toward larger values). These descriptions do not apply to a normal distribution. - Uniform Distribution:
Option D describes a uniform distribution, where all values have equal probability or frequency. This is distinctly different from the bell shape of a normal distribution.
The symmetry of the normal distribution is why it is a cornerstone of many statistical methods, as it simplifies mathematical analysis and reflects numerous real-world phenomena, such as heights, test scores, and measurement errors.