If a dataset has both its mean and median equal to 10, this suggests the dataset has a specific characteristic in terms of its distribution. Here’s a detailed explanation:
1. Definition of Mean: The mean of a dataset is the sum of all the data points divided by the number of data points. It gives us an average value.
2. Definition of Median: The median is the middle value of a dataset when it is ordered in ascending or descending order. If there is an even number of data points, the median is the average of the two middle numbers.
3. Relationship: When the mean and median of a dataset are equal, it indicates that the data is symmetrically distributed. This means that the data points are equally distributed around the center value.
4. Symmetry in Distributions:
- In a perfectly symmetric distribution, the left side of the distribution mirrors the right side.
- Commonly, this property is observed in normal distributions, where the curve is bell-shaped, but other symmetric shapes are possible.
Thus, given that both the mean and the median are 10, the dataset is said to be symmetric.
This symmetry implies that the data points are evenly spread out around the central value, which results in equal mean and median values.
