To determine whether the provided statement is true or false, let's analyze the statistical aspects of mean and median in relation to datasets with outliers or skewed data.
The original statement is:
"If one or more data items are much greater than the other items, the mean, rather than the median, is more representative of the data."
To understand if the mean or median is more representative in the presence of outliers, we need to recap the definitions and properties of the mean and median:
1. Mean: The mean (average) is the sum of all data points divided by the number of data points. It can be significantly affected by outliers, because it takes every value into account, including extreme values.
2. Median: The median is the middle value of a data set when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers. The median is less affected by outliers and skewed data, because it depends only on the order and position of values, not their magnitude.
Given these properties:
- If a dataset contains one or more extremely high values (outliers), the mean will increase significantly, making it less representative of the central tendency of the majority of the data.
- The median, however, will likely remain closer to the majority of the data points, as it is not skewed by extreme values.
Therefore, the original statement is indeed false. The more accurate interpretation would be:
"If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data."
The correct option is:
C. The statement is false. It should be changed to if one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.
