In Standard normal distribution, the value of median is ___________a)1...
In a standard normal distribution the value of mean is o and in normal distribution mean, median and mode coincide.
View all questions of this testIn Standard normal distribution, the value of median is ___________a)1...
The correct answer is option 'B' (0).
Standard normal distribution, also known as the Z-distribution or the Gaussian distribution, is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. It is symmetrical and bell-shaped.
In a standard normal distribution, the median is always equal to the mean, which is 0. This means that exactly half of the values in the distribution are below the median, and the other half are above it. The median is the value that separates the distribution into two equal parts.
Explanation:
1. Standard Normal Distribution:
- The standard normal distribution is a continuous probability distribution with a mean of 0 and a standard deviation of 1.
- It is often used in statistics and probability theory to analyze and describe various phenomena.
2. Median in a Distribution:
- The median is a measure of central tendency in a distribution.
- It represents the middle value when the data is arranged in ascending or descending order.
- In a symmetric distribution, the median is equal to the mean.
3. Symmetry of Standard Normal Distribution:
- The standard normal distribution is symmetric around its mean, which is 0.
- This means that the left and right tails of the distribution are mirror images of each other.
- The area under the curve to the left of the mean is equal to the area under the curve to the right of the mean.
4. Median and Mean in a Standard Normal Distribution:
- In a standard normal distribution, the mean is 0.
- Since the distribution is symmetric, the median is also 0.
- This implies that exactly half of the values in the distribution are below 0 and half are above 0.
In conclusion, the median value in a standard normal distribution is always 0 because of the symmetry of the distribution around its mean.