Final answer:
To approximate the mean, examine the shape of the data. If symmetric, use mean. If skewed or has outliers, use median. Mean absolute deviation is the average of absolute differences between each value and mean. Median is the middle value. Mode is the most frequent value.
Step-by-step explanation:
The mean for a data set can be calculated by adding up all the values in the set and dividing by the total number of values. To approximate the mean, we need to examine the shape of the data. If the data is symmetric, then the mean is a more appropriate measure of center. If the data is skewed or contains outliers, then the median would be a better choice.
To find the mean absolute deviation, we need to calculate the absolute difference between each value in the data set and the mean, then find the average of these differences.
The median is the middle value when the data set is arranged in ascending or descending order. If there is an even number of data points, the median is the average of the two middle values.
The mode is the value that occurs most frequently in the data set. If there are multiple values with the same highest frequency, the data set is considered bimodal or multimodal.