Answer:
The mean, median, and mode are all equal in a perfectly symmetrical distribution. This is a fundamental property of symmetrical distributions.
Given that the median is 30, the mean must also be 30.
Therefore, the correct answer is:
A. 30
Step-by-step explanation:
let me explain, Let's delve into why the mean of a perfectly symmetrical distribution is equal to its median.
Symmetrical Distribution
A distribution is symmetrical if it is mirrored around a central point. This means that the left side of the distribution is a mirror image of the right side. Common examples of symmetrical distributions include the normal distribution (bell curve) and the uniform distribution when graphed properly.
Mean, Median, and Mode in a Symmetrical Distribution
- Mean: The average of all data points.
- Median: The middle value when the data points are arranged in order.
- Mode: The most frequently occurring value(s) in the data set.
In a perfectly symmetrical distribution:
- The mean is at the center of the distribution.
- The median is also at the center of the distribution.
- The mode is also at the center if the distribution is unimodal (one peak).
Since the distribution is symmetrical, the data is evenly distributed around the center. Thus, the mean, median, and mode coincide at the center.
Given Information and Conclusion
You are given that the median of the distribution is 30. Because the distribution is perfectly symmetrical, the mean must be the same as the median. Thus, if the median is 30, the mean is also 30.
Hence, the value of the mean is:
A. 30
For a perfectly symmetrical distribution with a median of 30, the value of the mean is (A) 30.
Consider that in a symmetric distribution, such as a normal distribution, the shape is mirrored on both sides of the central value.
This symmetry ensures that the measures of central tendency (mean, median, and mode) all coincide at the same point. Therefore, if the median is 30, the mean must also be 30.