What 2 aspects of data determine which measure of central tendency to use ?
When determining which measure of central tendency to use, there are two key aspects of the data that you need to consider:
1. The type of data: The first aspect to consider is the nature or type of data you are working with. Different measures of central tendency are suitable for different types of data. The three main types of data are:
a. Numerical (Quantitative) Data: If you have numerical data, such as heights or test scores, you can use measures like the mean, median, or mode to describe the central tendency. The mean is often preferred as it takes into account all the data points.
b. Categorical (Qualitative) Data: For categorical data, like eye color or clothing sizes, the mode is the most appropriate measure of central tendency. It represents the category or value that appears most frequently in the dataset.
c. Ordinal Data: If the data can be ordered but the exact differences between values are not meaningful, such as rankings or survey responses with Likert scales, the median tends to be a better measure of central tendency. It represents the middle value when the data is sorted in ascending or descending order.
2. Skewness of the data: The second aspect to consider is the skewness of the data distribution. Skewness refers to the asymmetry of the data. It can be either positively skewed (tail on the right) or negatively skewed (tail on the left).
a. Symmetrical Data: For symmetrical data, which has a roughly equal balance on both sides of the central value, any measure of central tendency (mean, median, or mode) can be used. They will all provide similar results.
b. Skewed Data: If the data is skewed, the choice of measure depends on the direction of skewness and the presence of outliers.
- Positively Skewed Data: If the data is positively skewed (tail on the right), the median is typically preferred as it is less influenced by extreme values. However, if there are no extreme outliers, the mean can still provide a reasonable estimate.
- Negatively Skewed Data: For negatively skewed data (tail on the left), the median is also generally preferred as it is less affected by extreme values. Again, unless extreme outliers are present, the mean can be considered.
In summary, to determine which measure of central tendency to use, consider the type of data (numerical, categorical, ordinal) and the skewness of the data distribution (symmetrical, positively skewed, or negatively skewed).