Final answer:
The arithmetic mean, median, and mode are measures of the center of a data set used to describe its distribution. The mean considers all data points, the median is less affected by outliers, and the mode indicates the most frequent value. Based on the distribution of these measures, we can assess the data's skewness, indicating whether the distribution is symmetric, or has a positive or negative bias.
Step-by-step explanation:
To calculate the arithmetic mean, we find the midpoint of each class by adding the lower and upper boundaries and dividing by two. We then multiply each midpoint by the frequency and sum these products. Finally, we divide by the total number of data values.
The median is the value that separates the higher half of a data sample from the lower half. Since we have a frequency distribution, we locate the median class by adding the frequencies cumulatively until we reach the middle of the dataset, which is the 50th value given that the full frequency is 100.
The mode is the value that appears most often. In a frequency distribution, the mode is the class with the highest frequency.
Once these calculations are done, we can describe the distribution's bias. If the mean is less than the median, which is less than the mode, the distribution is skewed left (negative bias). If the mean is greater than the median, which is greater than the mode, the distribution is skewed right (positive bias). If all three measures are similar, the distribution is symmetrical.