Symmetrical Distribution

Symmetrical distribution refers to a probability distribution in which the values are evenly distributed around the mean, resulting in a balanced and bell-shaped curve. It is also known as a normal distribution or Gaussian distribution. The correct answer to the given question is option 'B', which states that the shape of symmetrical distribution is bell-shaped.

Characteristics of Symmetrical Distribution

Symmetrical distributions have several key characteristics:

1. Bell-shaped Curve: Symmetrical distributions have a bell-shaped curve, with the highest frequency of values located at the mean and tapering off symmetrically on both sides.

2. Mean, Median, and Mode: In a symmetrical distribution, the mean, median, and mode are all equal and located at the center of the distribution.

3. Equal Tails: The left and right tails of the distribution are equal in length and shape, mirroring each other.

4. Skewness: Symmetrical distributions have a skewness of zero, indicating that the data is evenly distributed around the mean without any skewness to the left or right.

5. Standard Deviation: The spread of data in symmetrical distributions can be characterized by the standard deviation. The standard deviation determines the width of the bell curve and represents the average distance between data points and the mean.

Examples of Symmetrical Distributions

Several real-world phenomena follow a symmetrical distribution:

1. Height: Heights of individuals in a population tend to follow a symmetrical distribution, with most people clustered around the average height.

2. IQ Scores: IQ scores are often distributed symmetrically, with the majority of scores concentrated around the average intelligence level.

3. Measurement Errors: Errors in measurement, such as errors in reading a thermometer or weight scale, often follow a symmetrical distribution.

4. Random Variables: Many random variables, such as the sum of two dice or the average of a large number of random samples, tend to have a symmetrical distribution.

Conclusion

In conclusion, the shape of a symmetrical distribution is bell-shaped. It is characterized by a balanced curve with the highest frequency of values at the mean and equal tails on both sides. Symmetrical distributions have several characteristics, including equal mean, median, and mode, as well as zero skewness. Real-world examples of symmetrical distributions include height, IQ scores, measurement errors, and various random variables.